,transcrib]'s ,note ,9 :at foll[s1 italic text is d5ot$ by und]scores :ile bold text is d5ot$ by equal signs4 ,small capitals 9 ! orig9al text h be5 transcrib$ z ,,all ,,capitals4 ,sup]script$ text is prefix$ by ! #8' symbol4 ,braces #8' may enclose ! text :5 necess>y to avoid ambiguity4 ,subscript$ text is always enclos$ 9 braces #8' b w n be prec$$ by a #8'4 ---------- ,see ! end ( ?is docum5t = details ( corrections & o!r *anges4 ---------------------------------- ,/>t ( ,book ---------------------------------- ,illu/ration3 ,a ,,*ri/mas ,,lecture ,,at ,,! ,,royal ,,in/itution3 8,,waves ,,& ,,ripples ,,9 ,,! ,,air40 ,,fig4 #df 7see p4 #aji74 ,drawn by ,f4 ,c4 ,dick9son4 ,f ! 8,graphic40 ,,waves ,,& ,,ripples ,,9 ,,wat]1 ,,air1 ,,& ,,!r ,,be+ ,a ,,c\rse ,,( ,,*ri/mas ,,lectures ,,deliv]$ ,,at ,,! ,,royal ,,in/itution ,,( ,,great ,,brita9 ,,by ,j4 ,a4 ,,flem+1 ,m4,a41 ,d4,sc41 ,f4,r4,s4 ,m4 ,,in/4 ,e4,e41 ,m4,r4,i41 ,,etc41 ,,etc4 ,,pr(essor ,,( ,,electrical ,,eng9e]+ ,,9 ,,univ]sity ,,college1 ,,london ,,second ,,issue1 ,,revis$ ,,london ,,society ,,= ,,promot+ ,,*ri/ian ,,k ,,nor?umb]l& ,,av5ue1 ,w4,c4 #dc1 ,,que5 ,,victoria ,,/reet1 ,e4,c4 ,,brighton3 #abi1 ,,nor? ,,/reet ,,new ,,york3 ,e4 ,s4 ,,gorham #aiab ,,publi%$ ,,"u ,,! ,,direction ,,( ,,! ,,g5]al ,,lit]ature ,,committee ,,pr9t$ ,,by ,,william ,,cl[es ,,& ,,sons1 ,,limit$1 ,,london ,,& ,,beccles4 ,,preface4 ,! ,*ri/mas ,lectures at ! ,royal ,in/itution are1 by a "t-hon\r$ cu/om1 inv>iably address$ to a 8juv5ile audi5ce40 ,?is t]m1 h[ev]1 has always be5 held to be an ela/ic "o1 & to include ^? :o are "y 9 _s z well z ^? :o are "y 9 ye>s4 ,! conditions1 !re=e1 necess>ily impose on ! ,lectur] ! duty ( treat+ "s subject 9 su* a mann] t1 :il/ n beyond ! rea* ( y\?ful m9ds1 x may yet possess "s elem5ts ( int]e/ = ^? ( matur] ye>s4 ,a subject :i* admits ( abundant exp]im5tal illu/rations is accord+ly1 on ^! occasions1 a popul> "o1 p>ticul>ly if x has a be>+ ^u topics !n attract+ public att5tion4 ,! progress ( practical inv5tion or discov]y (t5 removes at "o /roke "s fact or pr9ciple out ( ! region ( purely sci5tific inve/igation1 & places x )9 ! purview ( ! popul> m9d4 ,a dem& !n arises = explanations :i* %all dovetail x on to ! ord9>y exp]i5ces ( life4 ,! practical use ( !r waves 9 wireless telegraphy has ?us made ! subject ( waves 9 g5]al an int]e/+ "o4 ,h5ce1 :5 p]mitt$ ! privilege1 = a second "t1 ( address+ ,*ri/mas audi5ces 9 ! ,royal ,in/itution1 ! au?or v5tur$ to indulge ! hope t an exp]im5tal treatm5t ( ! subject ( ,waves & ,ripples 9 v>i\s m$ia w\ld n be want+ 9 int]e/4 ,al?\gh su* lectures1 :5 reproduc$ 9 pr9t1 are de/itute ( ! attractions furni%$ by successful exp]im5ts1 yet1 9 response to ! wi% ( _m correspond5ts1 !y h be5 committ$ to writ+1 9 ! hope t ! explanations giv5 may /ill be useful to a circle ( read]s4 ,! au?or tru/s t ! attempt to make ! op]ations ( visible waves a key to a compreh5sion ( "s ( ! effects produc$ by waves ( an invisible k9d may n be altoge!r )\t success1 & t ^? :o f9d "s ( ! imp]fect expositions 9 ?is little book 9 any degree helpful may !reby be impell$ to /udy ! facts m closely f t 8op5 page ( ,nature0 :i* lies ev] unfold$ = ! in/ruction ( ^? :o h ! pati5ce & p[] to read x aright4 ,j4 ,a4 ,f4 ,,univ]sity ,,college1 ,,london1 #aijb4 ,,cont5ts4 ---- ,,*apt] ,i4 ,,wat] ,,waves ,,& ,,wat] ,,ripples4 ,,page ,a visit to ! seaside--,:at is a wave8--,wave-motion on wat]--,def9ition ( a wave--,sea waves--,v>i\s =ms ( wave-motion--,wave l5g?1 velocity1 & frequ5cy--,atlantic waves--,rules = spe$ ( sea waves--,illu/rations ( wave-motion--,a /one fall+ on wat]--,production ( a wave-tra9--,wave-en]gy--,conditions = ! production ( wave-motion--,di/9ction betwe5 wave-velocity & wave-tra9 velocity--,:y a wave breaks--,waves 9 canals--,rule = spe$ ( a canal wave--,fall+ bodies--,a 8bore0--,tidal waves--,ripples--,di/9ction betwe5 waves & ripples--,surface t5sion on liquids--,a ne$le float+ on wat]--,exp]im5tal production ( ripples--,reflection & refraction ( ripples & waves--,int]f]5ce ( waves & ripples--,photography ( waves & ripples #a ,,*apt] ,,ii4 ,,waves ,,& ,,ripples ,,made ,,by ,,%ips4 ,%ip-waves--,! viscosity ( liquids--,h[ x is demon/rat$--,rotational & irrotational motion 9 fluids--,eddies & :irls--,smoke r+s--,vortex motion--,pr(essor ,hele-,%aw's exp]im5ts--,irrotational or /ream-l9e motion 9 wat]--,! motion ( wat] r\nd a %ip--,! motion ( wat] along a pipe--,fl[ 9 uni=m pipes & non-uni=m pipes--,relation betwe5 fluid velocity & pressure--,sk9 resi/ance & wave-mak+ resi/ance--,! movem5t ( a fi%--,motion ?r\gh a p]fect fluid--,! waves made by mov+ objects--,waves made by ducks & swans--,e*elon waves--,%ip b[ waves--,! =m ( %ip-waves--,mr4 ,fr\de's exp]im5ts--,%ip-models & exp]im5tal tanks--,h[ a %ip is design$--,fr\de's laws--,te/+ %ip-models--,! design ( a rac+-ya*t--,comp>ison ( ,briti% & ,am]ican ya*ts--,! ,cup race--,scott ,russell's exp]im5ts on canal-boats #eg ,,*apt] ,,iii4 ,,waves ,,& ,,ripples ,,9 ,,! ,,air4 ,air necess>y = ! production ( s\nd--,a s\nd+ body is 9 vibration--,h>monic motion--,! diff]5ce betwe5 noise & music--,! nature ( an air wave--,! physical qualities ( air--,longitud9al or compressional waves--,wave-models to illu/rate ! nature ( s\nd waves--,quality ( a s\nd--,velocity ( an air wave--,an illu/ration on a gigantic scale--,! voice ( a volcano he>d r\nd ! _w--,! effect ( temp]ature on air-wave velocity--,comp>ison ( !ory & exp]im5t--,circum/ances affect+ di/ance at :i* s\nds c be he>d--,fun]al guns--,fog-signals & sir5s--,effect ( w9d & d5sity--,s5sitive flames z s\nd-detectors--,inaudible s\nds--,! reflection & refraction ( s\nd waves--,a s\nd-l5s & s\nd-prism--,! int]f]5ce ( s\nds--,two s\nds produc+ sil5ce--,! phonograph--,a soap-bubble film set 9 vibration by air waves #ajc ,,*apt] ,,iv4 ,,s\nd ,,& ,,music4 ,! diff]5ce betwe5 s\nds & musical tones--,! natural p]iod ( vibration ( an ela/ic body--,! effect ( accumulat$ impulses--,free & =c$ vibrations--,break+ d[n a bridge ) a pea-%oot]--,! vibration ( a /ret*$ /r+--,/ation>y waves--,a /r+ vibrat+ 9 segm5ts--,ac\/ic resonance--,nodes & anti-nodes--,! musical scale or gamut--,musical int]vals--,! natural gamuts & ! scale ( equal temp]am5t--,concords & discords--,musical beats--,helmholtz's !ory ( discords--,musical in/rum5ts--,pipes--,/r+s & plates--,a pan-pipe--,an organ-pipe--,op5 & clos$ organ-pipes--,! di/ribution ( air pressure & velocity 9 a s\nd+ organ-pipe--,s++ flames--,/r+$ in/rum5ts--,! viol9--,! ,/roh viol9--,! /ructure ( ! e>--,! e> a wond]ful air-wave detector & analyz] #adg ,,*apt] ,v4 ,,electric ,,oscillations ,,& ,,electric ,,waves4 ,! conception ( an !r--,! ph5om5a ( light require ! assumption ( an !r--,! velocity ( light--,int]f]5ce ( light--,two rays ( light c produce d>kness--,an electric curr5t--,! ph5om5a ( electricity require ! assumption ( an electro-magnetic m$ium--,prop]ties & p[]s ( an electric curr5t--,alt]nat+ & cont9u\s electric curr5ts--,electromotive =ce & electric /ra9--,a ,leyd5 j>--,! oscillatory dis*>ge ( a cond5s]--,oscillatory sp>ks--,trans=mation ( electric oscillations--,h]tz oscillator--,production ( a wave ( electric displacem5t--,detection ( electric waves--,metallic fil+s detectors--,! coh]]--,inductance & capacity ( circuits--,electro-/atic & electro-magnetic en]gy--,an induction coil--,electric oscillations give rise to electric waves--,! electron !ory ( electricity #ahe ,,*apt] ,,vi4 ,,waves ,,& ,,ripples ,,9 ,,! ,,!r4 ,! exp]im5ts ( ,he9ri* ,h]tz--,electric radiation--,lecture app>atus = produc+ & detect+ electric radiation--,electric transp>5cy & opacity--,:y ?is diff]5ce--,! reflection ( electric radiation--,! refraction ( electric rays--,an electric prism & an electric l5s--,! electric refractive index--,int]f]5ce ( electric rays--,! velocity ( electric radiations id5tical ) t ( light--,d>k heat rays--,act9ic or photographic rays--,! cause ( col\r--,! frequ5cy ( light waves--,! classification ( electric or !r waves--,! gamut ( !r waves--,! eye an !r-wave detector ( limit$ p[]--,! electro-magnetic !ory ( light--,artificial production ( light--,use ( ,h]tz waves 9 wireless telegraphy--,m>coni's me?ods--,m>coni's a]ial & wave-detector--,! ,morse alphabet--,h[ a wireless message is s5t--,! tun+ ( wireless /ations--,communication betwe5 %ips & %ore--,! velocity ( wireless waves--,conclusion #bcb ,,app5dix #bhg ,,index #bic ,,useful ,,memor&a4 ,"o /atute mile is #ebhj feet4 ,"o nautical mile is #fjhf feet #a /atute mile4 ,a knot is a spe$ ( #a nautical mile p] h\r4 ,h5ce ! foll[+ rules3-- ,to conv]t ,knots to miles p] h\r--multiply by #a4 ,miles p] h\r to knots--multiply by 4 ,feet p] second to miles p] h\r--multiply by 4 ,feet p] second to knots--multiply by 4 ,knots to feet p] m9ute--multiply by #ajj4 ,,waves ,,& ,,ripples ,,9 ,,wat]1 ,,air1 ,,& ,,!r4 ---- ,,*apt] ,i4 ,,wat] ,,waves ,,& ,,wat] ,,ripples4 ,we h all /ood _m times by ! sea%ore1 wat*+ ! waves1 cre/$ ) :ite foam1 roll 9 & break ^u ! rocks or bea*4 ,e "o has m ?an once ca/ a /one ^u /ill wat] 9 a lake or pond1 & notic$ ! exp&+ r+s ( ripples2 & "s h voyag$ ov] /ormy seas1 :]eon great %ips are toss$ by mighty bill[s ) no m seem+ ef=t ?an ! rock+ ( a cradle4 ,9 all ^! ?+s we h be5 spectators ( a wave-motion1 z x is call$1 tak+ place ^u a wat] surface4 ,p]haps x did n occur to u at ! "t t ! s\nd ( ! spla% or ?und] ( ^! break+ waves 0 convey$ to our e>s z a wave-motion ( ano!r sort 9 ! air we brea!1 nay1 ev5 t ! light by :i* we see ^! beautiful objects is also a wave-motion ( a m recondite description1 produc$ 9 a m$ium call$ ! !r1 :i* fills all space4 ,a progressive /udy ( ,nature has %[n u t we are surr\nd$ on all sides by wave-motions ( v>i\s descriptions--waves 9 wat]1 waves 9 air1 & waves 9 !r--& t our mo/ preci\s s5ses1 our eyes & e>s1 are really wave-detectors ( a v special =m4 ,! exam9ation ( ^! waves & _! prop]ties & p[]s has l$ u to see t waves 9 wat]1 air1 & !r1 ?\gh diff]+ greatly 9 detail1 h mu* 9 common2 & _m ?+s ab\t !m t are difficult to und]/& become m intelligible :5 we comp>e ^! v>i\s wave-motions toge!r4 ,9 ^! lectures1 !re=e1 ,i %all make use ( y\r famili> exp]i5ces conc]n+ sea & wat] waves to assi/ y to und]/& "s ( ! prop]ties ( air waves to :i* we owe our s5sations ( s\nd & music2 &1 z f> z possible1 attempt an explanation ( ! nature ( !r waves1 creat$ 9 ! all-p]vad+ !r1 to :i* are due n only light & sight1 b also _m electrical effects1 includ+ su* mod]n wond]s z wireless telegraphy4 ,9 all dep>tm5ts ( natural sci5ce we f9d ourselves confront$ by ! ph5om5a ( wave-motion4 ,9 ! /udy ( e>?quakes & tides1 telegraphs & telephones1 z well z t]re/rial temp]ature1 no less ?an 9 ! exam9ation ( wat] waves & ripples1 s\nd1 music1 or light & heat1 we are b\nd to consid] waves ( "s p>ticul> k9d4 ,fa/5+ our att5tion = ! mom5t on surface wat] waves1 ! fir/ "q we %all ask ourselves is--,:at is a wave8 ,if we take our /ation on a high cliff look+ d[n on ! sea1 on "s cle> day1 :5 ! w9d is fre%1 we see ! waves on its surface l gre5 r\nd$ ridges rac+ =w>d1 & x appe>s at fir/ sight z if ^! elevations 7 !mselves mov+ masses ( wat]4 ,if1 h[ev]1 we look in/ead at "s pat* ( seawe$1 or float+ cork1 or seagull1 z ea* wave passes ov] x1 we %all notice t ?is object is m]ely lift$ up & let d[n aga91 or1 at mo/1 has a small movem5t to & fro4 ,we are l$1 !re=e1 to inf] t1 ev5 :5 agitat$ by waves1 ea* p>ticle ( wat] nev] moves f> f its position :5 at re/1 & t ! real movem5t ( ! wat] is some?+ v diff]5t f its app>5t motion4 ,if we place on ! surface ( wat] a numb] ( corks or pieces ( pap]1 & !n wat* !m z a wave passes ov] !m1 we %all notice t ! corks or bits ( pap] rise & fall successively1 t is1 "o aft] ! o!r1 & n all toge!r4 ,a little m c>eful scrut9y w %[ u t1 9 ! case ( sea waves 9 deep wat]1 ! motion ( ! float+ object z ! wave passes ov] x is a circul> "o1 t is to say1 x is fir/ lift$ up1 !n pu%$ =w>d1 next let d[n1 &1 la/ly1 pull$ back2 & s x repeats a r\nd-&-r\nd motion1 ) ! plane ( ! circle 9 ! direction 9 :i* ! wave is progress+4 ,?is may be illu/rat$ by ! diagram 9 ,fig4 #a1 :]e ! circul> dott$ l9es repres5t ! pa?s describ$ by corks float+ on ! sea-surface :5 waves are travell+ ov] x4 ,illu/ration3 ,,fig4 #a4 ,accord+ly1 we conclude t we h to di/+ui% cle>ly betwe5 ! actual individual motion ( ea* wat] p>ticle & t g5]al motion call$ ! wave-motion4 ,we may def9e ! latt] by say+ t to produce a wave-motion1 ea* sep>ate p>ticle ( a m$ium1 be x wat]1 or air1 or any o!r fluid1 mu/ execute a movem5t :i* is repeat$ aga9 & aga91 & ! sev]al p>ticles along any l9e mu/ p]=m ?is same motion "o aft] ! o!r1 t is1 lagg+ beh9d ea* o!r1 & n simultane\sly4 ,we might illu/rate ?is p]=mance by suppos+ a r[ ( fifty boys to /& 9 a l9e 9 a play-gr\nd1 & ea* boy 9 turn to lift up 8 arm & let x d[n aga91 & to cont9ue to p]=m ?is action4 ,if all ! boys lift$ up _! arms toge!r1 t w\ld n produce a wave-motion2 b if ea* boy did x "o aft] ! o!r 9 ord]1 along ! rank1 x w\ld con/itute a wave-motion travell+ along ! l9e ( boys4 ,9 m le>n$ language1 we may def9e a wave-motion by say+ t a wave-motion exi/s 9 any m$ium :5 ! sep>ate portions ( x along any l9e execute 9 ord] any k9d ( cyclical or repeat$ motion1 ! p>ticles along ?is l9e p]=m+ ! movem5t "o aft] ! o!r1 & ) a c]ta9 assign$ delay betwe5 ea* adjac5t p>ticle z reg>ds _! /age 9 ! movem5t4 ,x w be evid5t1 !re=e1 t !re c be _m diff]5t k9ds ( waves1 dep5d+ ^u ! sort ( repeat$ motion ! sev]al p>ts p]=m4 ,"s ( ! num]\s =ms ( wave-motion c be illu/rat$ by me*anical models z foll[s3-- ,a bo>d has fa/5$ to x a s]ies ( wood5 :eels1 & on ! edge ( ea* :eel is fix$ a :ite knob4 ,! :eels are connect$ toge!r by endless b&s1 s t on turn+ "o :eel r\nd !y all revolve 9 ! same direction4 ,if ! knobs are s arrang$ to beg9 )1 t ea* "o is a little 9 advance ( its neighb\r on ! way r\nd ! :eel1 !n :5 ! :eels are /&+ /ill ! knobs w be arrang$ along a wavy l9e 7see ,fig4 #b74 ,on turn+ r\nd ! fir/ :eel1 ea* knob w move 9 a circle1 b e knob w be lagg+ a little beh9d its neighb\r on "o side1 & a little 9 advance ( its neighb\r on ! o!r side4 ,! result w be to produce a wave-motion1 &1 look+ at ! g5]al effect ( ! mov+ knobs1 we %all see t x resembles a hump mov+ along1 j z 9 ! case ( a wat] wave4 ,illu/ration3 ,,fig4 #b4 ,illu/ration3 ,,fig4 #c4 ,! motion ( ! p>ticles ( ! wat] 9 a deep-sea wave resembles t ( ! :ite knobs 9 ! model describ$4 ,^? :o swim w recall to m9d _! s5sations z a sea wave surges ov] !m4 ,! wave lifts up ! swimm]1 !n pu%es him a little =w>d1 !n lets him d[n1 &1 la/ly1 drags him back4 ,x is ?is dragg+-back action :i* is s dang]\s to p]sons :o _c swim1 :5 !y are ba?+ on a /eep coa/ :]e /rong waves are roll+ 9 t[>ds ! %ore4 ,two o!r k9ds ( wave-motion may be illu/rat$ by ! model %[n 9 ,fig4 #c4 ,9 ?is appliance !re are a numb] ( ecc5tric :eels fix$ to a %aft4 ,ea* :eel is embrac$ by a b& c>ry+ a long rod :i* ends 9 a :ite ball4 ,! :eels are s plac$ on ! %aft t1 :5 at re/1 ! balls are arrang$ 9 a wavy l9e4 ,!n1 on turn+ r\nd ! %aft1 ea* ball rises & falls 9 a v]tical l9e1 & executes a p]iodic motion1 lagg+ beh9d t ( its neighb\r on "o side4 ,! result is to produce a wave-motion along ! l9e ( balls4 ,by slightly alt]+ ! model1 ea* ball c be made to describe a circle 9 a direction at "r angles to ! l9e ( ! balls1 & !n we h a sort ( corkscrew wave-motion propagat$ along ! l9e ( balls4 ,illu/ration3 ,,fig4 #d4 ,aga91 ano!r =m ( wave-motion may be illu/rat$ by ! model %[n 9 ,fig4 #d4 ,9 ?is case a numb] ( golf-balls are hung up by /r+s1 & spiral brass spr+s are int]pos$ betwe5 ea* ball4 ,on giv+ a slight tap to ! end ball1 we notice t its to-&-fro motion is h&$ on f ball to ball1 & we h a wave-motion 9 :i* ! individual movem5t ( ! balls is 9 ! direction ( ! wave-movem5t1 & n across x4 ,! k9d ( wave illu/rat$ by ! model 9 ,fig4 #c is call$ a transv]se wave1 & t %[n 9 ,fig4 #d is call$ a longitud9al wave4 ,at ?is /age x may be well to def9e ! mean+ ( "s o!r expressions :i* w be mu* us$ 9 ^! lectures4 ,we h se5 t 9 a wave-motion ea* "p ( ! m$ium makes "s k9d ( movem5t ov] & ov] aga92 & ( its neighb\rs on ei!r side1 "o is a little ahead ( x 9 its p]=mance1 & ! o!r a little 9 arre>4 ,if we look along ! l9e1 we %all see t we c select portions ( x :i* are exactly 9 ! same /age ( movem5t--t is1 are mov+ 9 ! same way at ! same "t4 ,! di/ance betwe5 ^! portions is call$ "o wave-l5g?4 ,?us1 9 ! case ( sea waves1 ! di/ance betwe5 two adjac5t cre/s1 or humps1 is "o wave-l5g?4 ,:5 we use ! expression1 a long wave1 we d n mean a wave :i* is ( great l5g? 9 ! direction ( ! ridge1 b waves 9 :i* ! cre/s1 or humps1 are sep>at$ f> ap>t1 measur+ f cre/ to cre/ across ! ridges4 ,/rictly speak+1 ! wave-l5g? may be def9$ z ! %orte/ di/ance f cre/ to cre/1 or holl[ to holl[1 or f "o p>ticle to ! next "o :i* is 9 ! same /age ( its movem5t at ! same "t4 ,ano!r way ( illu/rat+ ! same ?+ w\ld be to pleat or puck] a %eet ( pap] into p>allel ridges4 ,if we make ^! pleats v n>r[1 !y w\ld repres5t :at we call %ort waves2 b if we make ^! pleats v f> ap>t1 !y w\ld repres5t long waves4 ,ano!r phrase mu* us$ is ! t]m wave-velocity4 ,suppose t a seagull 7 to fly along ov] a set ( sea waves s z to keep always above "o p>ticul> hump1 or wave-cre/2 ! spe$ ( ! gull1 reckon$ 9 miles p] h\r or feet p] m9ute1 w\ld be call$ ! spe$ ( ! waves4 ,?is is some?+ v diff]5t f ! actual spe$ ( ea* p>ticle ( wat]4 ,a ?ird & con/antly us$ expression is ! t]m wave-frequ5cy4 ,if we wat* a cork float+ on a wave-toss$ sea1 we obs]ve t x bobs up & d[n s _m times 9 a m9ute4 ,! numb] ( times p] second or p] m9ute t ea* p>ticle ( ! m$ium p]=ms its cycle ( motion is call$ ! wave-frequ5cy1 or simply ! frequ5cy4 ,aga91 we employ ! t]m amplitude to d5ote ! extreme di/ance t ea* individual p>ticle ( ! m$ium moves f its mean position1 or position ( re/4 ,9 speak+ ( sea waves1 we g5]ally call ! v]tical di/ance betwe5 ! cre/ & ! holl[ ! height ( ! wave1 & ?is is twice ! amplitude4 ,) reg>d to ! height ( sea waves1 !re is g5]ally mu* exagg]ation4 ,voyag]s are 9 ! habit ( speak+ ( 8waves runn+ m\nta9s high10 yet a sea wave :i* exce$s #dj feet 9 height is a r>e sight4 ,waves h be5 measur$ on ! ,s\!rn ,indian ,ocean1 betwe5 ! ,cape ( ,good ,hope & ! ,isl& ( ,/4 ,paul1 & ( ?irty waves obs]v$ ! av]age height 0 f\nd to be j "u #cj feet4 ,! highe/ 0 only #cg feet 9 height4 ,on ! o!r h&1 waves ( #af to #bj feet are n uncommon4 ,travell]s :o h cross$ ! ,atlantic ,ocean 9 /ormy wea!r w (t5 rec\nt exp]i5ces ( waves said to be #ajj feet high2 b ^! are exce$+ly r>e1 if ev5 ev] met )1 & unless wave-heights are obta9$ by "s accurate me?od ( measurem5t1 ! eye ( ! inexp]i5c$ voyag] is apt to be deceiv$4 ,9 all cases ( wave-motion !re is a v close connection betwe5 ! wave-velocity1 or spe$1 ! wave-l5g?1 & ! wave-frequ5cy4 ,?is connection is express$ by ! num]ical law t ! velocity is equal to ! product ( ! l5g? & ! frequ5cy4 ,?us1 suppos+ we consid] ! case ( ,atlantic waves #cjj feet f cre/ to cre/1 :i* are travell+ at ! rate ( #bg miles an h\r1 x is requir$ to calculate ! frequ5cy or numb] ( times p] m9ute or p] second t any float+ object1 say a boat1 w be lift$ up z ^! waves pass ov] x4 ,we mu/ fir/ trans=m a spe$ ( #bg miles p] h\r into its equival5t 9 feet p] second4 ,s9ce "o mile is #ebhj feet1 #bg miles p] h\r is equal to #bcgf feet p] m9ute4 ,accord+ly1 x is easy to see t ! wave-frequ5cy mu/ be #gib1 or ne>ly #h1 because #gib times #cjj is #bcgf4 ,! answ] to ! "q is1 !n1 t ! float+ object w rise & fall eight times a m9ute4 ,?is rule may be embodi$ 9 a compact =m1 :i* x is desirable to hold firmly 9 ! memory1 viz4-- ,wave-velocity wave-l5g? wave-frequ5cy4 ,?is relation1 :i* we %all h frequ5t occasion to recall1 may be /at$ 9 ano!r mann]4 ,we call ! p]iod ( a wave ! "t tak5 to make "o complete movem5t4 ,! p]iodic "t is !re=e inv]sely proportional to ! frequ5cy4 ,h5ce we c say t ! wave-l5g?1 divid$ by ! p]iodic "t1 gives u ! wave-velocity4 ,9 ! case ( wat] waves & ripples1 ! wave-velocity is det]m9$ by ! wave-l5g?4 ,?is is n ! case1 z we %all see1 ) waves 9 air or waves 9 !r4 ,9 ^! latt] cases1 z f> z we "k1 waves ( all wave-l5g?s travel at ! same rate4 ,long sea waves1 h[ev]1 on deep wat] travel fa/] ?an %ort ones4 ,a =mal & exact pro( ( ! law connect+ spe$ & wave-l5g? = deep-sea waves requires ma!matical reason+ ( an advanc$ "*2 b its results may be express$ 9 a v simple /atem5t1 by say+ t1 9 ! case ( waves on deep wat]1 ! spe$ ) :i* ! waves travel1 reckon$ 9 miles p] h\r1 is equal to ! squ>e root ( #b times ! wave-l5g? measur$ 9 feet4 ,?us1 = in/ance1 if we notice waves on a deep sea :i* are #ajj feet f cre/ to cre/1 !n ! spe$ ) :i* ^? waves are travell+1 reckon$ 9 miles p] h\r1 is a numb] obta9$ by tak+ ! squ>e root ( #b times #ajj1 viz4 #bbe4 ,s9ce #ae is ! squ>e root ( #bbe 7because #ae times #ae is #bbe71 ! spe$ ( ^! waves is !re=e #ae miles an h\r4 ,9 ! same way x c be f\nd t ,atlantic waves #cjj feet long w\ld travel at ! rate ( #bf miles an h\r1 or z fa/ z a sl[ railway tra91 & mu* fa/] ?an any ord9>y %ip4#a ,! above rule = ! spe$ ( deep-sea waves1 viz4 wave-velocity squ>e root ( #b times ! wave-l5g?1 comb9$ ) ! g5]al rule1 wave-velocity wave-l5g? multipli$ by frequ5cy1 provides u ) a useful practical me?od ( f9d+ ! spe$ ( deep-sea waves :i* are pass+ any fix$ po9t4 ,suppose t a good way out at sea !re is a fix$ buoy or rock1 & we notice waves rac+ pa/ x1 & desire to "k _! spe$1 we may d x z foll[s3 ,c\nt ! numb] ( waves :i* pass ! fix$ po9t p] m9ute1 & divide ! numb] into #aih2 ! quoti5t is ! spe$ ( ! waves 9 miles p] h\r4 ,?us1 if t5 waves p] m9ute race pa/ a fix$ buoy1 _! velocity is v ne>ly #bj miles an h\r4#b ,waves h be5 obs]v$ by ! ,*all5g] #dbj to #dhj feet long1 ) a p]iod ( #i seconds4 ,^! waves 7 #ah to #bb feet high4 ,_! spe$ 0 !re=e #ej feet p] second1 or ne>ly #cj knots4 ,atlantic /orm waves are v (t5 #ejj to #fjj feet long1 & h a p]iod ( #aj to #aa seconds4 ,waves h be5 obs]v$ by (fic]s 9 ! ,fr5* ,navy half a mile 9 l5g?1 & ) a p]iod ( #bc seconds4 ,x has already be5 expla9$ t 9 ! case ( deep-sea waves ! individual p>ticles ( wat] move 9 circul> pa?s4 ,x c be %[n t ! diamet] ( ^! circul> pa?s decreases v rapidly ) ! dep? ( ! p>ticle bel[ ! surface1 s t at a di/ance bel[ ! surface equal only to "o wave-l5g?1 ! diamet] ( ! circle :i* is describ$ by ea* wat]-p>ticle is only ( t at ! surface4#c ,h5ce /orm waves on ! sea are a purely surface effect4 ,at a few hundr$ feet d[n--a di/ance small comp>$ ) ! dep? ( ! ocean--! wat] is q /ill1 ev5 :5 ! surface is toss$ by fe>ful /orms1 except 9 s f> z !re may be a /eady movem5t due to ocean curr5ts4 ,by a m elaborate exam9ation ( ! propagation ( wave-motion on a fluid1 ,sir ,george ,/okes %[$1 _m ye>s ago1 t 9 addition to ! circul> motion ( ! wat]-p>ticles con/itut+ ! wave1 !re is also a transf] ( wat] 9 ! direction 9 :i* ! wave is mov+1 ! spe$ ( ?is transf] dep5d+ on ! dep?1 & decreas+ rapidly z ! dep? increases4 ,?is effect1 :i* is kn[n to sailors z ! 8heave ( ! sea10 c cle>ly be se5 on wat*+ waves on n v deep wat]4 ,= ! cre/ ( ! wave w be se5 to advance m rapidly ?an ! holl[ until ! wave falls ov] & breaks2 & !n a fre% wave is =m$ beh9d x1 & ! process is repeat$4 ,h5ce waves break if ! dep? ( wat] "u !m dim9i%es2 & we "k by ! pres5ce ( break]s at any place t "s %all[ or s&bank is locat$ !re4 ,x is necess>y1 9 ! next place1 to po9t out ! diff]5ce betwe5 a m]e wave-motion & a true wave4 ,x has be5 expla9$ t 9 a wave-motion ea* "o ( a s]ies ( contigu\s objects executes "s id5tical movem5t 9 turn4 ,we h all se5 ! w9d bl[+ on a breezy day across a cornfield1 & produc+ a sort ( d>k %ad[ :i* sweeps along ! field4 ,?is is cle>ly caus$ by ! w9d b5d+ d[n1 9 turn1 ea* r[ ( corn/alks1 & z r[ aft] r[ b[s itself & spr+s up aga91 we are pres5t$ ) ! appe>ance ( a wave-motion 9 ! =m ( a rift ru%+ across ! field4 ,illu/ration3 ,,fig4 #e4 ,illu/ration3 ,,fig4 #f4 ,illu/ration3 ,,fig4 #g4 ,a v simil> effect c be produc$1 & ano!r illu/ration giv5 ( a wave-motion1 z foll[s3 ,coil a piece ( brass wire into an op5 spiral l a corkscrew1 & affix to x a small fragm5t ( seal+-wax 7see ,fig4 #e74 ,hold ?is 9 ! sun1 & let ! %ad[ ( x fall ^u pap]4 ,!n turn x r\nd l a screw4 ,we %all see t ! %ad[ ( ! spiral is a wavy l9e1 & t1 z x is turn$ r\nd1 ! humps appe> to move along j z d ! cre/s ( sea waves1 b t ! %ad[ ( ! little bit ( seal+-wax simply moves up & d[n4 ,ano!r wave-motion model may be made z foll[s3 ,procure a pa9t]'s comb4 ,?is is a ?9 /eel plate1 cut into long n>r[ tee?4 ,provide also a slip ( glass ab\t #c in*es wide & #ab in*es long4 ,pa9t "o side ( ?is glass ) black enamel v>ni%1 & :5 x is q dry scrat* a wavy l9e ^u x 7see ,fig4 #f74 ,place ! glass slip close 9 front ( ! comb be=e ! light1 &1 hold+ ! comb /ill1 move ! glass slip to & fro1 l5g?ways4 ,! obs]v] w see a r[ ( dots ( light ly+ 9 a wavy l9e1 & ^!1 z ! glass moves1 w rise & fall4 ,if ! movem5t is rapid en\gh1 ! appe>ance ( a wave mov+ along w be se54#d ,9 all ^! exhibitions ( wave-motion ! movem5t ( ! p>ticles is due to a common cause1 b ! mov+ p>ticles d n control ea* o!r's motion4 ,!re is no connection or tie betwe5 !m4 ,suppose1 h[ev]1 t we susp5d a s]ies ( heavy balls l p5dulums1 & int]connect !m by ela/ic ?reads 7see ,fig4 #g71 !n we h an arrangem5t along :i* we c propagate a true wave4 ,draw ! end ball to "o side1 & notice :at takes place :5 x is releas$4 ,! fir/ ball1 be+ displac$1 pulls ! second "o ?r\gh a less di/ance1 & t ! ?ird "o1 & ! ?ird ! f\r?1 & s on4 ,?is happ5s because ! balls are ti$ toge!r by ela/ic ?reads1 :i* resi/ /ret*+4 ,:5 ! fir/ ball is releas$1 x is pull$ back by ! t5sion ( ! ?read connect+ x to its neighb\rs1 & x beg9s to return to its old position4 ,! ball possesses1 h[ev]1 a quality call$ in]tia1 & accord+ly1 :5 once set 9 motion1 its motion p]si/s until an oppos+ =ce br+s x to re/4 ,h5ce ! return+ ball ov]%oots ! m>k1 & passes to ! opposite side ( its orig9al position ( re/4 ,!n1 aga91 ?is displacem5t /ret*es ! ela/ic ?reads connect+ x to its fell[s1 & a controll+ or ret>d+ =ce is ?us creat$1 :i* br+s x to re/1 & =ces x aga9 to return on its /eps4 ,we see1 !re=e1 t ea* ball mu/ oscillate1 or sw+ to & fro1 & t its movem5t is gradually communicat$ to its neighb\rs4 ,a wave-motion is ?us />t$1 & a true wave is propagat$ along ! l9e ( balls1 9 consequ5ce ( ! pres5ce ( ela/icity & in]tia4 ,! necess>y conditions = ! production ( a true wave 9 a m$ium ( any k9d are !re=e3 7#a7 t ! m$ium mu/ ela/ically resi/ "s sort ( de=mation2 & 7#b7 :5 x is de=m$ at any place1 & returns to its orig9al /ate1 x mu/ ov]%oot ! m>k or p]si/ 9 movem5t1 9 consequ5ce ( in]tia1 or some?+ equival5t to x4 ,briefly speak+1 any mat]ial or m$ium 9 or on :i* a true self-propagat+ wave-motion c be made mu/ resi/ & p]si/4 ,x mu/ h an ela/ic resi/ance to "s *ange or de=mation1 & x mu/ h an in]tia :i* causes x to p]si/ 9 movem5t :5 once set 9 motion4 ,^! two qualities1 or o!rs equival5t to !m1 mu/ inv>iably be pres5t if we are to h a true wave produc$ 9 a m$ium4 ,^! ?+s may be be/ und]/ood by consid]+1 = example1 ! production ( surface waves on wat]4 ,let u ask ourselves1 9 ! fir/ place1 :at alt]ation or *ange x is t a wat]-surface resi/s4 ,! answ] is1 t1 = "o ?+1 x resi/s be+ made unlevel4 ,a /ill wat] surface is ev]y:]e a level surface4 ,if we attempt to make x unlevel by p\r+ wat] on to x at "o po9t1 or by heap+ x up1 ! wat] surface w\ld resi/ ?is process4 ,we c dig a hole 9 s&1 or heap up s& to =m a hillock1 b we "k full well we _c d ! same ?+ ) wat]4 ,if1 = in/ance1 "s wat] is plac$ 9 a glass tube %ap$ l ! lett] 1 !n x /&s at ! same level 9 bo? limbs4 ,aga91 if wat] is set 9 motion1 be+ a heavy sub/ance1 x _c be br\ght to re/ in/antly4 ,l e o!r body1 x possesses in]tia4 ,accord+ly1 if we d succe$ by any means 9 mak+ a depression 9 a wat]-surface = an in/ant1 ! wat] w\ld imm$iately press 9 to fill up ! hole2 b m1 x w\ld1 s to speak1 ov]%oot ! m>k1 &1 9 consequ5ce ( its in]tia1 x w\ld create a mom5t>y hump1 or elevation1 9 ! place on ! surface :]e an in/ant ago !re 0 a depression4 ,?is elevation w\ld aga9 subside into a holl[1 & ! process w\ld be cont9u$ until ! wat]-motion 0 br\ght to re/ by friction1 or by ! gradual disp]sion ( ! orig9al en]gy4 ,! process by :i* a wave is />t$ on ! surface ( wat]1 z a consequ5ce ( ^! two qualities ( resi/ance to be+ made unlevel & p]si/5ce 9 motion1 is beautifully %[n by ! /udy ( waves made by ?r[+ /ones into a pond4 ,! ev5ts :i* give rise to ! exp&+ wave are1 h[ev]1 ov] s quickly t !y c only be /udi$ by ! aid ( in/antane\s photography4 ,! mo/ int]e/+ "w on ?is subject is t ( ,pr(essor ,a4 ,m4 ,wor?+ton1 :o has photograph$1 by ! exce$+ly brief light ( an electric sp>k1 ! v>i\s /ages ( ! ev5ts :i* happ5 :5 a drop ( wat] or a /one falls into wat]4#e ,^! photographs %[ u all t happ5s :5 ! fall+ object t\*es ! wat]1 & ! mann] 9 :i* x gives rise to ! wave or ripple :i* results4 ,"s ( ,pr(essor ,wor?+ton's results = a drop ( wat] fall+ into milk are reproduc$ 9 ! app5d$ diagrams4 ,9 ! fir/ place 7,fig4 #h7 ! drop is se5 j ent]+ ! wat]4 ,z x plunges d[n1 x leaves beh9d x a cavity1 or1 z x may be call$1 a hole 9 ! wat] 7see ,fig4 #i74 ,illu/ration3 ,"t aft] contact #jbfb sec4 ,,fig4 #h4 ,?is hole1 at a c]ta9 /age1 beg9s to fill up4 ,! wat] ru%es 9 on all sides1 & ! impetus c>ries up ! inru%+ wat] s t x builds up a tall pill> ( wat] 9 ! place :]e an in/ant ago !re 0 a hole 7see ,fig4 #aj74 ,no "o c\ld anticipate su* an extraord9>y effect2 b ! in/antane\s photographs1 tak5 by ! light ( an electric sp>k1 :i* reveal x1 _c b be tru?ful4 ,! next /age is t ?is pill> ( wat] breaks up1 & falls back aga9 on ! surface4 ,h5ce ! wat]1 at ! place :]e ! drop plunges into x1 is subject$ to two viol5t impulses--a d[nw>d1 succe$$ by an up-lift+1 =ce4 ,! effect ( ?is is exactly analog\s to t ( giv+ a bl[ to ! int]connect$ /r+ ( balls 9 ! model %[n 9 ,fig4 #g--;x propagates a wave4 ,9 ,fig4 #aj is illu/rat$ ! next /age1 9 :i* ?is outw>d-mov+ initial wave-cre/ is %[n4 ,illu/ration3 ,"t aft] contact #jcia sec4 ,,fig4 #i4 ,illu/ration3 ,"t aft] contact #aja sec4 ,,fig4 #aj4 ,s mu* = ! ev5ts reveal$ by ! fla%-light ( an electric sp>k2 b succe$+ ^! !re is a long tra9 ( int]e/+ wave-mak+ p]=mance :i* c be wat*$ ) ! eye1 or ! /ages photograph$ ) a h& cam]a4 ,?is wave production is be/ se5 :5 a l>ge /one is ?r[n into calm wat] 9 a lake or pond4 ,a /ory is record$ ( ! great arti/ ,turn]1 t he once sp5t a morn+ ?r[+ /ones into a pond4 ,a fri5d reprov$ him = 8 idl5ess4 8,no10 said ! pa9t]1 8,i h n be5 idle2 ,i h le>nt h[ to pa9t a ripple40 ,if ! arti/'s eye has to be c>efully tra9$ to notice all t !re is to see :5 a /one is hurl$ into a pond1 x is n /range t a c>eless obs]v] _c grasp at once :at really happ5s to ! wat] 9 ?is ord9>y occurr5ce4 ,illu/ration3 ,,fig4 #aa4--,ripples on a lake 7,si]re71 produc$ by ?r[+ 9 a /one4 ,! photograph 9 ,fig4 #aa w1 h[ev]1 %[ "o /age 9 ! ev5t4 ,z soon z ! fir/ wave-cre/1 ! orig9 ( :i* we h already expla9$1 is =m$1 x beg9s to move outw>ds 9 a circul> =m1 & z x moves x gives rise to a wave-tra91 t is1 x multiplies itself into a s]ies ( conc5tric ripples1 or waves1 :i* move outw>ds1 multiply+ 9 numb]1 b gett+ small] z !y move4 ,?us if a l>ge /one is ?r[n f> out into a deep1 /ill lake1 aft] ! fir/ spla% we %all see a circul> wave spread+ out f ! place :]e ! commotion 0 made 9 ! wat]4 ,z we look at ?is wave we %all see x gr[+ 9 size & multiply+ itself4 ,at fir/ !re is b a s+le wave1 !n two1 f\r1 sev51 t51 or m conc5tric ripples are se51 ea* circul> wave exp&+ & gett+ feebl]1 b seem+ to give bir? to o!rs z x moves4 ,moreov]1 a v c>eful exam9ation w %[ u t ! :ole gr\p ( waves1 or ! wave-tra91 has an outw>d motion ) a less spe$ ?an any individual wave4 ,?is obs]vation w s]ve to initiate ! conceptions ( a wave-tra9 & ( a wave-gr\p velocity4 ,at fir/ x is difficult to und]/& t a gr\p ( waves may move m sl[ly ?an ! individual waves :i* compose x4 ,if1 h[ev]1 we ca/ a /one into a pond1 & look v c>efully at :at takes place1 we %all see t ! circul> exp&+ b& ( ripples has an ill-def9$ b visible inn] & out] edge1 & t wavelets or ripples :i* compose x are be+ cont9ually br\ght into exi/5ce on its inn] edge1 & dy+ away on its out] edge4 ,waves1 s to speak1 pass ?r\gh ! ripple b& ) a great] spe$ ?an t at :i* ! :ole b& ( waves moves =w>d4 ,?is r difficult1 b important1 idea ( ! di/9ction betwe5 ! velocity ( a gr\p ( waves & t ( an individual wave 0 fir/ sugge/$ by ,sir ,george ,/okes1 :o set a "q 9 a ,cambridge ,exam9ation on ! subject 9 #ahgf1 & subsequ5tly x 0 elucidat$ by ,pr(essor ,osborne ,reynolds#f & ,"l ,rayleigh4 ,x c be fur!r expla9$ z foll[s3 ,let u consid] a wave-motion model su* z t repres5t$ 9 ,fig4 #g1 9 :i* a numb] ( susp5d$ heavy balls are connect$ to "o ano!r by ela/ic ?reads4 ,let "o ball 9 ! c5tre be drawn on "o side & !n releas$4 ,x w sw+ to & fro1 & w />t a wave outw>ds 9 bo? directions4 ,if ! r[ ( balls is suffici5tly long1 x w be se5 t ! ball by :i* ! wave 0 />t$ soon comes to re/1 & t ! wave-motion is conf9$ to a c]ta9 gr\p ( balls on ei!r side4 ,z "t goes on1 ! wave-motion 9 ea* gr\p dies away on ! side ne>e/ ! orig91 & ext5ds on ! side fur!/ away4 ,h5ce ! p>ticul> gr\p ( balls :i* are ! seat ( ! visible wave-motion is cont9ually be+ %ift$ along4 ,! rate at :i* ! c5tre ( ?is active gr\p ( vibrat+ balls is displac$ may be call$ ! velocity ( ! wave-tra94 ,! velocity ( ! wave is1 h[ev]1 some?+ great]1 s9ce ! waves are all ! "t mov+ ?r\gh ! gr\p4 ,?is wave-velocity is num]ically e/imat$ by tak+ ! product ( ! wave-l5g? & frequ5cy ( ! motion4 ,at ?is /age x is necess>y to expla9 t waves are n m]ely a mode ( motion2 !y are a means ( convey+ en]gy4 ,x is difficult to give 9 a compact =m any simple def9ition ( :at is meant 9 mod]n sci5tific writ+s by ! ^w ,en]gy4 ,briefly speak+1 we may say t !re are two fundam5tal ag5cies or ?+s 9 ,nature ) :i* we are 9 contact1 manife/+ !mselves 9 _m diff]5t =ms1 b ( :i* ! total quantity is un*angeable by human op]ations4 ,"o ( ^! is call$ ,matt]4 ,?is t]m is ! collective "n giv5 to all ! sub/ance or /uff we c see or t\*1 & :i* c be weigh$ or has weight4 ,all kn[n solids1 liquids1 or gases1 su* ?+s z ice1 wat]1 /eam1 iron1 oil1 or air1 are call$ mat]ial sub/ances1 & !y h 9 common ! two qualities ( occupy+ space or tak+ up room1 & ( hav+ weight4 ,exp]im5t has %[n t !re are "s eighty diff]5t k9ds ( simple matt] :i* _c be trans=m$ into ea* o!r1 & ^! =ms are call$ ! ,elem5ts4 ,any o!r mat]ial sub/ance is made up ( mixtures or comb9ations ( ^! elem5ts4 ,! elem5t>y sub/ances are !re=e l ! lett]s ( ! alphabet1 :i*1 tak5 9 gr\ps1 make up words1 ^! la/ correspond+ to comp\nd *emical bodies4 ,exact rese>* has %[n t no *emical *anges tak+ place 9 a clos$ space c alt] ! total weight or am\nt ( gravitat+ matt] 9 x4 ,if a *emi/ & num]\s *emicals 7 enclos$ 9 a great glass ball1 & ! ball balanc$ on a gigantic b v s5sitive pair ( scales1 no op]ations :i* ! *emi/ c\ld conduct 9 ! int]ior ( 8 cry/al laboratory w\ld alt]1 by ! t5-?\s&? "p ( a gra91 ! total weight ( x all4 ,he might analyze or comb9e 8 *emicals1 burn or mix !m z he pleas$1 b z long z no?+ ent]$ or escap$ f ! ball1 ! total gravitat+ mass w\ld rema9 precisely ! same4 ,?is great fact is call$ ! ,law ( ,cons]vation ( ,matt]1 & x tea*es u t al?\gh a scuttle ( coal may seem to disappe> :5 burnt1 yet ! weight ( ! a%es & ( all ! gase\s products ( combu/ion are toge!r equal to ! weight ( ! orig9al coal & ! air requir$ to burn x4 ,9 addition to v>i\s mat]ial sub/ances we f9d t we h to recognize diff]5t =ms ( some?+ call$ ,en]gy1 associat$ ) ,matt]4 ,?us an iron ball may be m or less hot1 m or less electrifi$ or magnetiz$1 or mov+ ) m or less spe$4 ,! production ( ^! /ates ( heat1 electrification1 magnetization1 or movem5t1 involves ! transf] to ! iron ( ,en]gy1 & !y are !mselves =ms ( ,en]gy4 ,?is ,en]gy 9 all its v>i\s =ms c be evaluat$ or measur$ 9 t]ms ( ,en]gy ( movem5t4 ,?us ! ,en]gy requir$ to heat a ball ( iron weigh+ "o imp]ial p\nd f a temp]ature ( ! melt+ po9t ( ice to t ( boil+ wat]1 is ne>ly equal to ! ,en]gy requir$ to imp>t to x a spe$ ( #ajjj feet a second4 ,9 ! same way1 e def9ite /ate ( electrification or magnetization c be express$ 9 its me*anical equival5t1 z x is call$4 ,moreov]1 x is f\nd t we c nev] create any am\nt ( heat or me*anical motion or o!r =m ( en]gy )\t putt+ out ( exi/5ce an equival5t ( en]gy 9 "s o!r =m4 ,we are !re=e compell$ to consid] t ,en]gy /&s on ! same foot+ z ,matt] 9 reg>d to our inability to create or de/roy x1 & its con/ancy 9 total am\nt1 z f> z we c asc]ta91 gives x ! same "* ( p]man5ce4 ,! diff]5ce1 h[ev]1 is t we _c1 s to speak1 e>-m>k any giv5 quantity ( en]gy & foll[ x ?r\gh all its trans=mations 9 ! same mann] 9 :i* we c m>k & id5tify a c]ta9 portion ( ,matt]4 ,! mom5t1 h[ev]1 t we pass beyond ^! m]ely quantitative ideas & proce$ to ask fur!r que/ions ab\t ! nature ( ,en]gy & ,matt]1 we f9d ourselves 9 ! pres5ce ( inscrutable my/]ies4 ,we are n able z yet to analyze into any?+ simpl] ?is 8some?+0 we call ,en]gy :i* pres5ts itself 9 ! guise ( heat or light1 electricity or magnetism1 movem5t or *emical action4 ,x is protean 9 =m1 intangible1 yet measurable 9 magnitude1 & all its *anges are by def9ite equival5t am\nt & value4 ,!re is a mo/ rigid sy/em ( book-keep+ 9 ! transactions ( ! physical univ]se4 ,y may h any?+ y l 9 ! way ( ,en]gy s]v$ out to y1 b ! am\nt ( x is debit$ to y\r acc\nt imm$iately1 & ! bill has to be dis*>g$ by pay+ an equival5t 9 "s o!r =m ( ,en]gy be=e y c remove ! goods f ! c\nt]4 ,matt] 9 its v>i\s =ms s]ves z ! vehicle ( ,en]gy4 ,we h no exp]i5ce ( ,en]gy ap>t f ,matt] ( "s k9d1 nor ( ,matt] altoge!r devoid ( ,en]gy4 ,we d n ev5 "k :e!r ^! two ?+s c exi/ sep>ately1 & we c give no def9ition ( ! "o :i* does n 9 "s way presuppose ! exi/5ce ( ! o!r4 ,return+1 !n1 to ! subject ( waves1 we may say t a true wave c only exi/ :5 ,en]gy is capable ( be+ associat$ ) a m$ium 9 two =ms1 & ! wave is a means by :i* t ,en]gy is transf]r$ f place to place4 ,x has already be5 expla9$ t a true wave c only be creat$ 9 a m$ium :i* ela/ically resi/s "s k9d ( de=mation1 & p]si/s 9 motion 9 virtue ( in]tia4 ,:5 any mat]ial possesses su* a quality ( resi/ance to "s k9d ( /ra9 or de=mation ( su* a "* t ! de=mation disappe>s :5 ! =ce creat+ x is )drawn1 x is call$ an ela/ic mat]ial4 ,?is ela/icity may arise f v>i\s causes4 ,?us air resi/s be+ compress$1 & if ! compress+ =ce is remov$ ! air exp&s aga94 ,x possesses s-call$ ela/icity ( bulk4 ,9 ! case ( wat] hav+ a free surface !re is1 z we h se51 a resi/ance to any *ange ( level 9 ! surface4 ,?is may be call$ an ela/icity ( surface =m4 ,:5ev] an ela/ic mat]ial is /ra9$ or de=m$1 en]gy has to be exp5d$ on x to create ! de=mation4 ,?us to w9d up a wat*-spr+1 /ret* a piece ( indi>ubb]1 compress "s air1 or b5d a b[1 requires an en]gy exp5diture4 ,z long z ! mat]ial is kept /ra9$1 x is said to h pot5tial en]gy associat$ ) x4 ,?is t]m is n a v expressive "o1 & x w\ld be bett] to call x ,en]gy ( /ra91 or de=mation4 ,if1 h[ev]1 we relax ! b5t b[ or release ! compress$ air1 ! ,en]gy ( ,/ra9 disappe>s1 & we h x replac$ by ,en]gy ( ,motion4 ,! arr[ :i* flies f a b[ c>ries ) x1 z en]gy ( motion1 "s "p ( ! en]gy ( /ra9 associat$ ) ! b5t b[4 ,a little exam9ation ( wave-motion %[s u1 !re=e1 t we always h at any in/ant associat$ ) ! mat]ial 9 :i* ! wave is be+ propagat$1 bo? ,en]gy ( ,/ra9 & ,en]gy ( ,motion4 ,x c be %[n t 9 a true wave ( p]man5t type1 ! :ole en]gy at any "o mom5t is half en]gy ( /ra9 & half en]gy ( motion1 or1 z x is call$1 half pot5tial & half k9etic4 ,?us if we consid] a wave be+ propagat$ along a l9e ( balls ela/ically connect$1 at any "o mom5t "s ( ! balls are mov+ ) _! greate/ velocity1 & "s are at ! extremity ( _! sw+4 ,! =m] h en]gy ( motion1 & ! latt] en]gy ( /ra94 ,or1 look at a tra9 ( sea waves4 ,"s p>ts ( ! wat] are at any mom5t lift$ high above ! av]age level ( ! sea1 or are mu* bel[ x1 b are o!rwise ne>ly at re/4 ,^! portions possess :at is call$ pot5tial en]gy1 or en]gy ( position4 ,o!r p>ts ( ! wat] are at ! av]age level ( ! sea1 b are mov+ ) consid]able velocity1 & ^! portions possess en]gy ( motion4 ,e o!r "p ( ! wave has 9 "s degree bo? en]gy ( motion & en]gy ( position1 & x c be %[n t ! en]gy ( ! :ole wave is half ( "o k9d & half ( ! o!r4 ,z a wave progresses ov] ! surface1 wave-en]gy is cont9ually be+ imp>t$ to portions ( ! wat] 9 front1 & x is transf]r$ away f o!rs 9 ! re>4 ,9 ! v act ( sett+ a fre% p>ticle ( wat] 9 oscillation1 ! portions already vibrat+ mu/ dim9i% _! own motion4 ,!y may h& on ! :ole ( _! en]gy or only a "p ( x to _! neighb\rs4 ,?is di/9ction is a v important "o1 & x det]m9es :e!r a s+le act ( di/urbance %all create a solit>y wave or wave-tra9 9 a m$ium4 ,illu/ration3 ,,fig4 #ab4 ,! diff]5ce may be illu/rat$ z foll[s3 ,consid] a r[ ( glass or /eel balls susp5d$ by ?reads s hung z to be q close to ea* o!r 7see ,fig4 #ab74 ,)draw ! fir/ ball1 & let x fall aga9/ ! second "o4 ,! result is t ! la/ ball ( ! r[ flies (f ) a j]k4 ,9 ?is case ! :ole en]gy imp>t$ to ! fir/ ball is transmitt$ along ! r[ ( balls4 ,! fir/ ball1 on fall+ aga9/ ! second "o1 ex]ts on x a pressure :i* slightly squeezes bo? out ( %ape4 ,?is pressure is j suffici5t to br+ ! fir/ ball to re/4 ,! second ball1 9 turn1 exp&s aft] ! bl[ & squeezes ! ?ird1 & s on4 ,h5ce1 9 virtue ( ,newton's ,?ird ,law ( ,motion1 t 8action & reaction are equal & opposite10 x foll[s t ! pressure produc$ by ! bl[ ( ! fir/ ball is h&$ on f ball to ball1 & f9ally causes ! la/ ball to fly (f4 ,9 ?is case1 ow+ to ! rigid connection betwe5 ! ela/ic balls1 ea* "o h&s on to its neighb\r ! :ole ( ! en]gy x receives4 ,suppos+1 h[ev]1 t we sep>ate ! balls slightly1 & give ! fir/ ball a transv]se1 or side-to-side sw+4 ,!n1 ow+ to ! fact t !re is no connection betwe5 ! balls1 ! en]gy imp>t$ to ! fir/ ball w\ld n be h&$ on at all1 & no wave w\ld be propagat$4 ,betwe5 ^! two extremes ( ! :ole en]gy transf]r$ & a solit>y wave produc$1 & no en]gy transf]r$ & no wave produc$1 we h a condition 9 :i* an initial di/urbance ( "o ball gives rise to a wave-tra9 & "p ( ! en]gy is transf]r$4 ,= if we int]connect ! balls by loose ela/ic ?reads1 & !n give1 z be=e1 a transv]se or sideways impulse to ! fir/ ball1 ?is w pull ! second "o & set x sw++1 b x w be pull$ back itself1 & w be to "s ext5t depriv$ ( its motion4 ,! same %>+ or division ( en]gy w take place betwe5 ! second & ?ird1 & ?ird & f\r? balls1 & s on4 ,h5ce ! initial solit>y vibration ( ! fir/ ball draws out into a wave-tra91 & ! orig9ally imp>t$ en]gy is spread out ov] a numb] ( balls1 & n conc5trat$ 9 "o ( !m4 ,accord+ly1 z "t goes on1 ! wave-tra9 is ev] ext5d+ 9 l5g? & ! oscillatory motion ( ea* ball is dy+ away1 & ! orig9al en]gy gets spread ov] a wid] & wid] area or numb] ( balls1 b is propagat$ ) less spe$ ?an ! wave-velocity = t m$ium4 ,!re ne$ be no difficulty 9 di/+ui%+ betwe5 ! notion ( a wave-velocity & a wave-tra9 velocity1 if we rememb] t ! wave travels a di/ance equal to a wave-l5g? 9 ! "t tak5 by "o oscillation4 ,h5ce ! wave-velocity is measur$ by tak+ ! quoti5t ( ! wave-l5g? by ! "t ( "o complete vibration4 ,if1 = example1 ! wave-l5g? ( a wat] wave is #d in*es1 & we obs]ve t twelve waves pass any giv5 po9t 9 #c seconds1 we c at once inf] t ! wave-velocity is #af in*es p] second4 ,! transf]5ce ( en]gy may1 h[ev]1 take place s t ! :ole gr\p ( waves moves =w>d mu* m sl[ly4 ,!y move =w>d because ! waves are dy+ out 9 ! re> ( ! gr\p & be+ creat$ 9 ! front1 & ! rate ( movem5t ( ! gr\p is1 9 ! case ( deep-wat] waves1 equal to half t ( ! s+le-wave velocity4 ,a v r\gh illu/ration ( ?is diff]5ce betwe5 a gr\p velocity & an individual velocity may be giv5 by suppos+ a b>ge to be sl[ly t[$ along a riv]4 ,let a gr\p ( boys run along ! b>ge1 dive ov] ! b[s1 & reappe> at ! /]n & climb 9 aga94 ,!n ! velocity ( ! gr\p ( boys on ! b>ge is ! same z ! spe$ ( ! b>ge1 b ! spe$ ( ea* individual boy 9 space is equal to ! spe$ ( ! b>ge add$ to ! spe$ ( ea* boy relatively to ! b>ge4 ,if ! b>ge is be+ t[$ at #c miles an h\r1 & ! boys run along ! boat also at #c miles an h\r1 !n ! velocity ( ! gr\p ( boys is only half t ( ! individual boy1 because ! =m] is #c miles an h\r & ! latt] is #f miles an h\r4 ,be=e leav+ ! subject ( sea waves !re are two or ?ree int]e/+ matt]s :i* mu/ be consid]$4 ,9 ! fir/ place1 ! break+ ( a wave on ! %ore or on %all[ wat] calls = an explanation4 ,if we wat* a sea wave roll+ 9 t[>ds ! bea*1 we %all notice t1 z x ne>s ! %ore1 x gets /eep] on ! %ore side1 & gradually curls ov] until x falls & breaks into spray4 ,! reason is because1 z ! wave gets into ! %all[ wat]1 ! top "p ( ! wave advances m rapidly ?an ! bottom portion4 ,x has already be5 expla9$ t ! pa? ( ! wat]-p>ticle is a circle1 ) its plane v]tical & p]p5dicul> to ! wave-front or l9e4 ,accord+ly1 if ! wave is mov+ 9 %all[ wat]1 ! friction ( ! wat] aga9/ ! bottom ret>ds ! backw>d movem5t at ! l[e/ position ( ! wat]1 b no su* ob/acle exi/s to ! =w>d movem5t ( ! wat] at its highe/ position4 ,an additional reason = ! de=mation ( ! wave on a g5tly slop+ %ore may be f\nd 9 ! fact t ! front "p ( ! wave is !n 9 %all[] wat]1 & h5ce moves m sl[ly ?an ! re>w>d portion 9 deep] wat]4 ,f bo? causes1 h[ev]1 ! wave cont9ually gets /eep] & /eep] on its l&w>d side until x curls ov] & tumbles d[n l a h\se :i* leans too mu* on "o side4 ,! act ( curl+ ov] 9 a break+ wave is a beautiful ?+ to wat*1 & "o :i* attracts ! eye ( e arti/ :o pa9ts seascapes & /orm waves1 or ( any lov] ( ,nature :o l+]s by ! %ore4 ,ano!r matt] ( int]e/ is ! orig9 ( sea waves4 ,und\bt$ly !y are due orig9ally to ! action ( ! w9d ^u ! wat]4 ,:5ev] two lay]s ( fluid lie 9 contact ) ea* o!r1 & "o moves fa/] ?an ! o!r1 ! fa/]-mov+ lay] w ?r[ ! o!r into waves4 ,?is is se51 n only 9 ! action ( mov+ air or w9d ^u wat]1 b ev5 9 ! action ( air ^u air or wat] ^u wat]4 ,f ! tops ( high m\nta9s we may sometimes look d[n ^u a flat surface ( cl\d b5ea?4 ,on "o occasion ! au?or enjoy$ a curi\s spectacle f ! summit ( an ,alp9e peak4 ,! climb up _h be5 ?r\gh damp & mi/y air1 b on rea*+ ! summit ! cl\ds 7 left beh9d1 & a canopy ( blue sky & glori\s sun%9e 7 f\nd ov]head4 ,b5ea? ! cl\ds lay closely pack$ l a sea ( :ite vap\r1 & ?r\gh ?is ocean ( cl\d ! peaks ( _m high m\nta9s project$ & /ood up l isl&s4 ,! surface ( ?is sea ( :ite cl\d1 brilliantly illum9at$ by ! sun%9e1 0 n1 h[ev]1 p]fectly smoo?4 ,x 0 toss$ into cl\d waves & bill[s by ! action ( curr5ts ( air bl[+ ov] its upp] surface1 & x _h a /rik+ resemblance to ! surface ( a r\gh sea4 ,:5 su* a cl\d lay] is n too ?ick1 ! ruffl+ ( its upp] or "u surface into cl\d waves may ?9 x away into regul> cl\d rolls1 & ^! cl\d roll]s may !n be cut up aga9 by cross air-curr5ts into pat*es1 & we h ! appe>ance kn[n z a 8mack]el sky40 ,ano!r famili> ph5om5on is t kn[n z ! 8ripple-m>k0 on wet s&4 ,z ! tide ebbs out ov] a smoo? bank ( sea-s&1 x leaves ! surface pl\gh$ into regul> r\nd$ ridges & furr[s1 :i* are /ation>y waves on ! s&4 ,?is is call$ ! ripple-m>k4 ,x is due to ! fact t ! s&1 :5 cov]$ by ! wat]1 =ms a surface :i* 9 a c]ta9 s5se is fluid1 be+ saturat$ & fill$ ) wat]1 b ! movem5t ( ?is bottom s&-logg$ wat] is h9d]$ by ! s&1 & h5ce ! lay] ( ov]ly+ wat] moves ov] x at a diff]5t spe$ 9 ebb+ out1 & c>ves x into :at are virtually s& waves4 ,ev5 a dry s& or sn[ surface may 9 ?is mann] be m\ld$ into a wave-=m by ! w9d1 & v curi\s effects ( ?is k9d h be5 notic$ & describ$ by ,dr4 ,vaughan ,corni%1 :o has made a great /udy ( ! sci5ce ( waves4#g ,! production ( waves on wat] by means ( a curr5t ( air bl[+ ov] x is easily exhibit$ on a small scale by bl[+ ?r\gh an indi>ubb] pipe1 ! end ( :i* is held ne> ! surface ( ! wat] 9 a tub or tank4 ,! exact mann] 9 :i* ! mov+ air gets a grip ( ! wat] is n q pla91 b x is cle> t1 if once an inequality ( level is set up1 ! mov+ air has !n an oblique surface aga9/ :i* x c press1 & s increase ! inequality by heap+ up ! wat] 9 "s places1 & holl[+ x out 9 o!rs4 ,h5ce oscillations ( ! wat]-surface are set up1 :i* g on accumulat+4 ,^! waves !n travel away ) a spe$ dep5d+ ^u _! wave-l5g?1 & we may h great di/urbances ( ! sea-surface at places :]e !re is no actual /orm-w9d4 ,^! 8e*oes ( a f>-(f /orm0 are kn[n z a 8gr\nd swell40 ,9 "s localities ! inhabitants are able to apprise !mselves ( ! com+ ( a /orm by notic+ movem5ts ( ! sea :i* indicate ! arrival ( waves :i* h travell$ m quickly ?an ! /orm-c5tre itself4 ,e visitor to ! seaside w h notic$ occasions on :i* ! sea is viol5tly di/urb$ by waves1 & yet ! air 9 ! locality is tol]ably calm4 ,9 ?is case ! waves h be5 propagat$ f "s po9t ( di/urbance at a di/ance4 ,a /udy ( break+ waves %[s u t ! cause ( _! great p[] to effect damage to coa/ /ructures1 su* z pi]s1 h>b\r works1 & %ipp+ 9 h>b\rs1 is really due to ! =w>d motion ( ! wat] z ! wave is break+4 ,e cubic foot ( wat] weighs #fc lbs41 s t a cubic y>d ( wat] weighs ab\t ?ree-qu>t]s ( a ton4 ,if ?is wat] is mov+ ) a spe$ ( _m feet p] second 9 a =w>d direction1 ! en]gy ( motion /or$ up 9 x is trem5d\s1 & fully suffici5t to acc\nt = ! de/ructive p[] ( /orm waves on a coa/4 ,! total volume ( wat] :i* is compris$ 9 ! space occupi$ by ev5 "o sea-/orm wave ( mod]ate dim5sions may h a mass ( _m hundr$s ( tons1 & its en]gy ( motion may easily am\nt to t ( an express tra9 9 motion4 ,h5ce :51 9 ! la/ /age ( its c>e]1 ?is mass ( wat] is hurl$ =w>d on ! %ore1 its de/ructive effects are n a matt] = surprise4 ,we mu/ n[ leave ! subject ( waves 9 ! op5 sea on a l>ge level surface1 & consid] t ( waves 9 n>r[ *annels1 su* z canals or riv]s4 ,! laws :i* gov]n wat]-wave production 9 a canal c be/ be /udi$ by plac+ "s wat] 9 a long tank ) glass sides4 ,if at "o end we ins]t a flat piece ( wood & give x a pu% =w>d1 we %all />t :at is call$ a long wave 9 ! tank4 ,! *>act]i/ic ( ?is k9d ( wave is t ! oscillatory motion is *iefly to-&-fro1 & n up-&-d[n4 ,?is may be v easily se5 by plac+ "s bran 9 ! wat]1 or float+ 9 x "s glass balls :i* h be5 adju/$ s z to j float any:]e 9 ! wat]4 ,:5 ?is is done1 & a wave />t$ 9 ! tank1 x runs up & d[n1 be+ reflect$ at ea* end 7see ,fig4 #ac74 ,illu/ration3 ,,fig4 #ac4--,wat]-wave produc$ 9 a tank4 ,f ! motion ( ! bran we c see t ! wat] sw+s backw>ds & =w>ds 9 a horizontal l9e ) a p5dulum-l motion1 b its up-&-d[n or v]tical motion is mu* m re/rict$4 ,a wave ( ?is k9d travels along a canal ) a spe$ :i* dep5ds ^u ! dep? ( ! canal4 ,if waves ( ?is k9d are />t$ 9 a v long tr\gh1 ! wave-l5g? be+ l>ge comp>$ ) ! dep? ( ! tr\gh1#h x c be %[n t ! spe$ ( ! wave is equal to ! velocity :i* w\ld be ga9$ by a /one or o!r heavy body 9 fall+ ?r\gh half ! dep? ( ! canal4 ,h5ce1 ! deep] ! wat]1 ! quick] ! wave travels4 ,?is c be %[n z an exp]im5tal fact z foll[s3 ,let two galvaniz$ iron tanks be provid$1 ea* ab\t #f feet long & #a foot wide & deep4 ,at "o end ( ea* tank a holl[ cyl9d]1 su* z a c(fee-cani/] or ball made wat]-tight1 is float$1 & x may be prev5t$ f mov+ f its place by be+ atta*$ to a h+$ rod l ! ball-cock ( a ci/]n4 ,! two tanks are plac$ side by side1 & "o is fill$ to a dep? ( #f in*es1 & ! o!r to a dep? ( #c in*es1 ) wat]4 ,two pieces ( wood are !n provid$ & jo9$ toge!r z 9 ,fig4 #ad1 s z to =m a d\ble paddle4 ,by pu%+ ?is ?r\gh ! wat] simultane\sly 9 bo? tanks at ! end opposite to t at :i* ! float+ cyl9d]s are plac$1 x is possible to />t two solit>y waves1 "o 9 ea* tank1 at ! same in/ant4 ,^! waves ru% up to ! o!r end & cause ! floats to bob up4 ,x w easily be se5 t ! float on ! deep] wat] bobs up fir/1 ?us %[+ t ! wave on ! deep] wat] has travell$ along ! tank m quickly ?an ! wave on ! %all[] wat]4 ,illu/ration3 ,,fig4 #ad4 ,9 ord] to calculate ! spe$ ( ! waves1 we mu/ call to m9d ! law gov]n+ ! spe$ ( fall+ bodies4 ,if a /one falls f a height its spe$ increases z x falls4 ,x c be %[n t ! spe$ 9 feet p] second aft] fall+ f any height is obta9$ by multiply+ toge!r ! numb] #h & a numb] :i* is ! squ>e root ( ! height 9 feet4 ,?us1 = in/ance1 if we desire to "k ! spe$ atta9$ by fall+ f a height ( #be feet above ! e>?'s surface1 we multiply #h by #e1 ?is la/ numb] be+ ! squ>e root ( #be4 ,accord+ly1 we f9d ! velocity to be #dj feet p] second1 or ab\t #bf miles an h\r4 ,! =ce ( ! bl[ :i* a body adm9i/]s & suff]s on /rik+ ! gr\nd dep5ds on ! en]gy ( motion x has acquir$ dur+ ! fall1 & z ?is v>ies z ! squ>e ( ! spe$1 x v>ies also z ! height fall5 ?r\gh4 ,let u apply ^! rules to calculate ! spe$ ( a long wave 9 a canal hav+ wat] #h feet deep 9 x4 ,! half-dep? ( ! canal is !re=e #d feet4 ,! squ>e root ( #d is #b2 h5ce ! spe$ ( ! wave is t ( a body :i* has fall5 f a height ( #d feet1 & is !re=e #af feet p] second1 or ne>ly #aa miles an h\r4 ,:5 we come to consid] ! "q ( waves made by %ips1 9 ! next *apt]1 a /ory w be relat$ ( a sci5tific discov]y made by a horse employ$ 9 dragg+ canal-boats1 :i* dep5d$ on ! fact t ! spe$ ( long waves 9 ?is canal 0 ne>ly ! same z ! trott+ spe$ ( ! horse4 ,illu/ration3 ,,fig4 #ae4 ,x may be well1 z a little digression1 to po9t out h[ ! law connect+ height fall5 ?r\gh & velocity acquir$ by ! fall+ body may be exp]im5tally illu/rat$ = tea*+ purposes4 ,! app>atus is %[n 9 ,fig4 #ae4 ,x consi/s ( a long bo>d plac$ 9 a horizontal position & held ) ! face v]tical4 ,?is bo>d is ab\t #af feet long4 ,atta*$ to ?is bo>d is a groov$ railway1 "p ( :i* is on a slope & "p is horizontal4 ,a smoo? iron ball1 ,a1 ab\t #b in*es 9 diamet]1 c run d[n ?is railway1 & is /opp$ by a movable buff] or bell1 ,b1 :i* c be clamp$ at v>i\s positions on ! horizontal rail4 ,at ! bottom ( ! incl9$ plane is a light lev]1 ,t1 :i* is t\*$ by ! ball on rea*+ ! bottom ( ! hill4 ,! trigg] releases a p5dulum1 ,p1 :i* is held engag$ on "o side1 &1 :5 releas$1 x takes "o sw+ & /rikes a bell1 ,g4 ,! p5dulum occupies half a second 9 mak+ its sw+4 ,an exp]im5t is !n p]=m$ 9 ! foll[+ mann]3 ,! iron ball is plac$ at a di/ance1 say1 ( #a foot up ! hill & releas$4 ,x rolls d[n1 deta*es ! p5dulum at ! mom5t x arrives at ! bottom ( ! hill1 & !n exp5ds its mom5tum 9 runn+ along ! flat "p ( ! railway4 ,! buff] mu/ be s plac$ by trial t ! iron ball hits x at ! in/ant :5 ! p5dulum /rikes ! bell4 ,! di/ance :i* ! buff] has to be plac$ f ! bottom ( ! hill is a measure ( ! velocity acquir$ by ! iron ball 9 fall+ d[n ! set di/ance along ! hill4 ,! exp]im5t is !n repeat$ ) ! iron ball plac$ respectively f\r times & n9e times high] up ! hill1 & x w be f\nd t ! di/ances :i* ! ball runs along ! flat "p 9 "o half-second are 9 ! ratio ( #a1 #b1 & #c1 :5 ! heights fall5 ?r\gh d[n ! hill are 9 ! ratio ( #a1 #d1 & #i4 ,! inf]5ce we make f ?is exp]im5t is t ! velocity acquir$ by a body 9 fall+ ?r\gh any di/ance is proportional to ! squ>e root ( ! height4 ,! same law holds good1 no matt] h[ /eep ! hill1 & !re=e x holds good :5 ! body1 su* z a /one or ball1 falls freely ?r\gh ! air4 ,! exp]im5t ) ! ball roll+ d[n a slope is an in/ructive "o to make1 because x br+s cle>ly be=e ! m9d :at is meant by say+1 9 sci5tific language1 t "o ?+ 8v>ies z ! squ>e root0 ( ano!r4 ,we meet ) s _m in/ances ( ?is mode ( v>iation 9 ! /udy ( physics1 t ! read]1 especially ! "y read]1 %\ld n be cont5t until ! idea convey$ by ^! words has become q cle> to him or h]4 ,?us1 = in/ance1 ! "t ( vibration ( a simple clock p5dulum 8v>ies z ! squ>e root ( ! l5g?20 ! velocity ( a canal wave 8v>ies z ! squ>e root ( ! dep? ( ! canal20 & ! velocity or spe$ acquir$ by a fall+ ball 8v>ies z ! squ>e root ( ! di/ance fall5 ?r\gh40 ,^! phrases mean t if we h p5dulums ^: l5g?s are 9 ! ratio ( #a to #d to #i1 !n ! respective times ( _! vibration are 9 ! ratio ( #a to #b to #c4 ,also a simil> relation connects ! canal-dep? & wave-velocity1 or ! ball-velocity & height ( fall4 ,return+ aga9 to canal waves1 x %\ld be po9t$ out t ! real pa? ( a p>ticle ( wat] 9 ! canal1 :5 long waves are pass+ along x1 is a v flat oval curve call$ an ellipse4 ,9 ! extreme cases1 :5 ! canal is v wide & deep1 ?is ellipse w become ne>ly a circle2 &1 on ! o!r h&1 :5 n>r[ & %all[1 x w be ne>ly a /raight l9e4 ,h5ce1 if long waves are creat$ 9 a canal :i* is %all[ comp>$ ) ! l5g? ( ! wave1 ! wat]-p>ticles simply oscillate to & fro 9 a horizontal l9e4 ,!re is1 h[ev]1 "o important fact connect$ ) wave-propagation 9 a canal1 :i* has a great be>+ on ! mode ( =mation ( :at is call$ a 8bore40 ,z a wave travels along a canal1 x c be %[n1 bo? exp]im5tally & !oretically1 t ! cre/ ( ! wave travels fa/] ?an ! holl[1 & z a consequ5ce ! wave t5ds to become /eep] on its front side1 & its %ape !n resembles a saw-too?4 ,a v well kn[n & /rik+ natural ph5om5on is ! s-call$ 8bore0 9 c]ta9 tidal riv]s or e/u>ies4 ,x is well se5 on ! ,sev]n 9 c]ta9 /ates ( ! tide & w9d4 ,! tidal wave return+ along ! ,sev]n *annel1 :i* n>r[s rapidly z x leaves ! coa/1 becomes conv]t$ into a 8canal wave10 & travels ) great rapidity up ! *annel4 ,! front side ( ?is great wave takes an almo/ v]tical position1 resembl+ an advanc+ wall ( wat]1 & works great havoc ) boats & %ipp+ :i* h _h ! mis=tune to be left 9 its pa?4 ,to und]/& m completely h[ a 8bore0 is =m$1 ! read] mu/ be rem9d$ ( ! cause ( all tidal ph5om5a4 ,any "o :o lives by ! sea or an e/u>y kn[s well t ! sea-level rises & falls twice e #bd h\rs1 & t ! av]age int]val ( "t betwe5 high wat] & high wat] is ne>ly #ab h\rs4 ,! cause ( ?is *ange ( level 9 ! wat]-surface is ! attraction ex]t$ by ! sun & moon ^u ! ocean4 ,! e>? is1 s to speak1 clo!d ) a flexible g>m5t ( wat]1 & ?is g>m5t is pull$ out ( %ape by ! attractive =ce ( our lum9>ies2 v r\ghly speak+1 we may say t ! ocean-surface is di/ort$ into a %ape call$ an ellipsoid1 & t !re are !re=e two elevations ( wat] :i* m>* across ! sea-cov]$ regions ( ! e>? z x revolves on its axis4 ,^! elevations are call$ ! tidal waves4 ,! effects1 h[ev]1 are mu* complicat$ by ! fact t ! ocean does n cov] all p>ts ( ! e>?4 ,!re is no difficulty 9 %[+ t1 z ! tidal wave progresses r\nd ! e>? across ea* great ocean1 x produces an elevation ( ! sea-surface :i* is n simultane\s at all places4 ,! "t :5 ! cre/ ( ! tidal wave rea*es any place is call$ ! 8"t ( high tide40 ,?us if we consid] an e/u>y1 su* z t ( ! ,?ames1 !re is a m>k$ diff]5ce betwe5 ! "t ( high tide z we asc5d ! e/u>y4 ,tak+ ?ree places1 ,m>gate1 ,graves5d1 & ,london ,bridge1 we f9d t if ! "t ( high tide at ,m>gate is at noon on any day1 !n x is high tide at ,graves5d at #b4ae p4m41 & at ,london ,bridge a little be=e ?ree o'clock4 ,?is diff]5ce is due to ! "t requir$ = ! tidal wave to travel up ! e/u>y ( ! ,?ames4 ,:5 an e/u>y contracts consid]ably z x proce$s1 z is ! case ) ! ,bri/ol ,*annel1 !n ! range ( ! tide or ! height ( ! tidal wave becomes greatly increas$ z x travels up ! gradually n>r[+ *annel1 because ! wave is squeez$ into a small] space4 ,= example1 ! range ( spr+ tides at ! entrance ( ! ,bri/ol ,*annel is ab\t #ah feet1 b at ,*ep/[ x is ab\t #ej feet4#i ,at oceanic ports 9 op5 sea ! range ( ! tide is g5]ally only #b or #c feet4 ,if we look at ! map ( ,engl&1 we %all see h[ rapidly ! ,bri/ol ,*annel contracts1 & h5ce1 z ! tidal wave advances f ! ,atlantic ,ocean1 x gets jamb$ up 9 ?is rapidly contract+ *annel1 & z ! dep? ( ! *annel 9 :i* x moves rapidly %all[s1 ! re> portion ( ?is tidal wave1 be+ 9 deep] wat]1 travels fa/] ?an ! front "p & ov]takes x1 produc+ ?us a flat or /raight-front$ wave :i* goes =w>d ) trem5d\s spe$4#aj ,we mu/1 9 ! next place1 turn our att5tion to ! /udy ( wat] ripples4 ,! t]m 8ripple0 is g5]ally us$ to signify a v small & %ort wave1 & 9 ord9>y language x is n di/+ui%$ f :at might be call$ a wavelet1 or little wave4 ,!re is1 h[ev]1 a sci5tific di/9ction betwe5 a wave & a ripple1 ( a v fundam5tal "*4 ,x has already be5 /at$ t a wave c only exi/1 or be creat$1 9 or on a m$ium :i* resi/s 9 an ela/ic mann] "s displacem5t4 ,! ord9>y wat]-surface wave is t]m$ a gravitation wave1 & x exi/s because ! wat]-surface resi/s be+ made unlevel4 ,!re is1 h[ev]1 ano!r ?+ :i* a wat]-surface resi/s4 ,x (f]s an opposition to small /ret*+1 9 virtue ( :at is call$ its surface t5sion4 ,9 a popul> mann] ! matt] may ?us be /at$3 ,! surface ( e liquid is cov]$ ) a sort ( sk9 :i*1 l a %eet ( indi>ubb]1 resi/s /ret*+1 & 9 fact contracts "u exi/+ conditions s z to become z small z possible4 ,we c see an illu/ration ( ?is 9 ! case ( a soap-bubble4 ,if a bubble is bl[n on a r wide glass tube1 on remov+ ! m\? ! bubble rapidly %r9ks up1 & ! conta9$ air is squeez$ out ( ! tube ) suffici5t =ce to bl[ out a c&le held ne> ! end ( ! tube4 ,aga91 if a dry /eel sew+-ne$le is laid g5tly 9 a horizontal position on clean wat]1 x w float1 al?\gh ! metal itself is heavi] ?an wat]4 ,x floats because ! weight ( ! ne$le is n suffici5t to break ?r\gh ! surface film4 ,x is = ?is reason t v small & light insects c run freely ov] ! surface ( wat] 9 a pond4 ,?is surface t5sion is1 h[ev]1 de/roy$ or dim9i%$ by plac+ v>i\s sub/ances on ! wat]4 ,?us if a small disc ( writ+-pap] ! size ( a waf] is plac$ on ! surface ( clean wat] 9 a sauc]1 x w re/ 9 ! middle4 ,! surface film ( ! wat] on :i* x re/s is1 h[ev]1 /ra9$ or pull$ equally 9 diff]5t directions4 ,if a wire is dipp$ 9 /rong spirits ( w9e or :isky1 & "o side ( ! waf] t\*$ ) ! drop ( _s1 ! pap] %oots away ) great spe$ 9 ! opposite direction4 ,! surface t5sion on "o side has be5 dim9i%$ by ! _s1 & ! equality ( t5sion de/roy$4 ,^! exp]im5ts & _m o!rs %[ u t we mu/ reg>d ! surface ( a liquid z cov]$ ) an invisible film1 :i* is 9 a /ate ( /ret*1 or :i* resi/s /ret*+4 ,if we imag9e a jam-pot clos$ ) a cov] ( ?9 %eet indi>ubb] pull$ tightly ov] x1 x is cle> t any attempt to make puck]s1 pleats1 or wr9kles 9 x w\ld involve /ret*+ ! indi>ubb]4 ,x is exactly ! same ) wat]4 ,if v small wr9kles or pleats1 z waves1 are made on its surface1 ! resi/ance :i* is br\ght into play is t due to ! surface t5sion1 & n m]ely ! resi/ance ( ! surface to be+ made unlevel4 ,wavelets s made1 or due to ! above cause1 are call$ ripples4 ,x c be %[n by ma!matical reason+#aa t on ! free surface ( a liquid1 l wat]1 :at are call$ capill>y ripples c be made by agitations or movem5ts ( a c]ta9 k9d1 & ! *>act]i/ic ( ^! surface-t5sion waves or capill>y ripples1 z comp>$ ) gravitation waves1 is t ! velocity ( propagation ( ! capill>y ripple is less ! great] ! wave-l5g?1 :]eas ! velocity ( gravitation on ord9>y surface waves is great] ! great] ! wave-l5g?4 ,x foll[s f ?is t = any liquid1 su* z wat]1 !re is a c]ta9 l5g? ( wave :i* travels mo/ sl[ly4 ,?is sl[e/ wave is ! divid+ l9e betwe5 :at are prop]ly call$ ripples1 & ^? t are prop]ly call$ waves4 ,9 ! case ( wat] ?is sl[e/ wave has a wave-l5g? ( ab\t two-?irds ( an in* 7#jfh in*71 & a spe$ ( travel approximately ( #i in*es 7#jgh foot7 p] second4 ,m /rictly speak+1 ! matt] %\ld be expla9$ z foll[s3 ,sir ,george ,/okes %[$1 z f> back z #ahdh1 t ! surface t5sion ( a liquid %\ld be tak5 into acc\nt 9 f9d+ ! pressure at ! free surface ( a liquid4 ,x 0 n1 h[ev]1 until #ahga t ,"l ,kelv9 discuss$ ! be>+ ( ?is fact on ! =mation ( waves1 & gave a ma!matical expression = ! velocity ( a wave ( oscillatory type on a liquid surface1 9 :i* ! wave-l5g?1 surface t5sion1 d5sity1 & ! accel]ation ( gravity 7 tak5 into acc\nt4 ,! result 0 to %[ t :5 waves are v %ort1 viz4 a small fraction ( an in*1 !y are pr9cipally due to surface t5sion1 & :5 long are entirely due to gravity4 ,x c easily be se5 t ripples run fa/] ! small] _! wave-l5g?4 ,if we take a ?9 wire & hold x p]p5dicul>ly 9 wat]1 & !n move x quickly p>allel to itself1 we %all see a /ation>y patt]n ( ripples r\nd ! wire :i* moves ) x4 ,^! ripples are small] & clos] toge!r ! fa/] ! wire is mov$4 ,ripples on wat] are =m$ 9 circul> exp&+ r+s :5 ra9-drops fall ^u ! /ill surface ( a lake or pond1 or :5 drops ( wat] =m$ 9 any o!r way fall 9 ! same mann]4 ,on ! o!r h&1 a /one flung into quiet & deep wat] w1 9 g5]al1 create waves ( wave-l5g? great] ?an two-?irds ( an in*1 s t !y are no long] )9 ! limits entitl+ !m to be call$ ripples4 ,h5ce we h a p]fectly sci5tific di/9ction betwe5 a ripple & a wave1 & a simple measurem5t ( ! wave-l5g? w decide :e!r di/urbances ( oscillatory type on a liquid surface %\ld be call$ ripples or waves 9 ! prop] s5se ( ! words4 ,! production ( wat] ripples & _! prop]ties1 & a beautiful illu/ration ( wave prop]ties 9 g5]al1 c be made by all[+ a /eady /ream ( wat] f a v small jet to fall on ! surface ( /ill wat] 9 a tank4 ,9 ord] to see ! ripples s =m$1 x is necess>y to illum9ate !m 9 a p>ticul> mann]4 ,! foll[+ is a description ( an app>atus1 design$ by ! au?or = exhibit+ all ^! effects to a l>ge audi5ce3-- ,! in/rum5t consi/s ess5tially ( an electric lant]n4 ,a h&-regulat$ or self-regulat+ arc lamp is employ$ to produce a p[]ful beam ( light4 ,?is is collect$ by a suitable cond5s+-l5s1 & x !n falls ^u a mirror plac$ at an angle ( #de1 :i* ?r[s x v]tically upw>ds4 ,! light is !n conc5trat$ by a pla9 convex l5s plac$ horizontally1 & passes ?r\gh a tr\gh ( metal hav+ a plane glass bottom4 ,?is tr\gh is fill$ to a dep? ( half an in* ) wat]1 & x has an ov]fl[ pipe to remove wa/e wat]4 ,above ! tank1 at ! prop] di/ance1 is plac$ a focuss+-l5s1 & ano!r mirror at an angle ( #de to ?r[ an image ( ! wat]-surface ^u a scre54 ,! la/ l5s is s arrang$ t ripples on ! surface ( ! wat] appe> l d>k l9es flitt+ across ! bright disc ( light :i* appe>s ^u ! scre54 ,two small brass jets are also arrang$ to drop wat] into ! tank1 & ^! jets mu/ be suppli$ ) wat] f a ci/]n elevat$ ab\t #d feet above ! tr\gh4 ,! jets mu/ be controll$ by screw-taps :i* p]mit ( v accurate adju/m5t4 ,^! jets %\ld "w on swivels1 s t !y may be turn$ ab\t to drop ! wat] at any po9t 9 ! tank4 ,! capill>y ripples :i* are produc$ on ! wat]-surface by all[+ wat] to drop on x f a jet1 flit across ! surface s rapidly t !y _c be foll[$ by ! eye4 ,!y may1 h[ev]1 be r5d]$ visible z foll[s3 ,a z9c disc1 hav+ holes 9 x1 is arrang$ 9 front ( ! focuss+-l5s1 & turn$ by h& or by means ( a small electric motor4 ,?is disc is call$ a /roboscopic disc4 ,:5 turn$ r\nd x eclipses ! light at int]vals1 s t ! image on ! scre5 is int]mitt5t4 ,if1 n[1 "o ( ! wat]-jets is adju/$ s z to orig9ate at ! c5tre ( ! tank a set ( div]g+ circul> ripples1 !y c be project$ z %ad[s ^u ! scre54 ,^! ripples move at ! rate ( #a or #b feet p] second1 & _! %ad[s move s rapidly across ! field ( view t we _c well obs]ve _! behavi\r4 ,if1 h[ev]1 ! metal disc ) holes 9 x is made to revolve & to int]mitt5tly obscure ! view1 x is possible to adju/ its spe$ s t ! int]val ( "t betwe5 two eclipses is j equal to t requir$ by ! ripples to move =w>d ?r\gh "o wave-l5g?4 ,:5 ?is exact spe$ is obta9$1 ! image ( ! ripples on ! scre5 becomes /ation>y1 & we see a s]ies ( conc5tric d>k circles ) int]m$iate bright spaces 7see ,fig4 #af71 :i* are ! %ad[s ( ! ripples4 ,9 ?is mann] we c /udy _m ( _! effects4 ,if1 = in/ance1 ! jet ( wat] is made to fall1 n 9 ! c5tre ( ! tr\gh1 b ne>] "o side1 we %all notice t !re are two sets ( ripples :i* int]sect--"o ( ^! is ! direct or orig9al set1 & ! o!r is a set produc$ by ! reflection ( ! orig9al ripples f ! side ( ! tr\gh4 ,^! direct & reflect$ ripple-%ad[s int]sect & produce a cross-hat*$ patt]n4 ,if a slip ( metal or glass is ins]t$ into ! tr\gh1 x is v easy to %[ t :5 a circul> ripple meets a plane h>d surface x is reflect$1 & t ! reflect$ ripple is also a circul> "o :i* proce$s z if x came f a po9t1 ,q1 on ! opposite side ( ! b\nd>y1 j z f> beh9d t b\nd>y z ! real c5tre ( di/urbance or orig9 ( ! ripple ,p is 9 front ( x 7see ,fig4 #ag74 ,9 ! diagram ! dott$ curves repres5t ! reflect$ ripple-cre/s4 ,illu/ration3 ,,fig4 #af4 ,if we make two sets ( ripples f orig9s ,p & ,q 7see ,fig4 #ah71 at diff]5t di/ances f a flat reflect+ b\nd>y1 x is n difficult to trace out t ea* set ( ripples is reflect$ indep5d5tly1 & accord+ to ! above-m5tion$ rule4 ,we "h obta9 a glimpse ( a pr9ciple :i* w come be=e u aga9 9 speak+ ( !r waves1 & furni%es an explanation ( ! famili> optical fact t :5 we view our own reflection 9 a look+-glass1 ! image appe>s to be z f> beh9d ! glass z we are 9 front ( x4 ,illu/ration3 ,,fig4 #ag4--,reflection ( circul> ripples4 ,illu/ration3 ,,fig4 #ah4 ,a v pretty exp]im5t c be %[n by fitt+ into ! tr\gh an oval b& ( metal b5t into ! =m ( an ellipse4 ,if two p9s are /uck into a %eet ( c>d1 & a loop ( ?read fitt$ loosely r\nd !m1 & a p5cil employ$ to trace out a curve by us+ x to /ra9 ! loop ( ?read tight & mov+ x r\nd ! p91 we obta9 a clos$ curve call$ an ellipse 7see ,fig4 #ai74 ,! positions ( ! two p9s ,a & ,b are call$ ! foci4 ,x is a prop]ty ( ! ellipse t ! two l9es ,,ap & ,,bp1 call$ radii vectores1 drawn f ! foci to any po9t ,p on ! curve1 make equal angles ) a l9e ,,tt call$ a tang5t1 drawn to t\* ! select$ po9t on ! ellipse4 ,if we draw ! tang5t ,,tt to ! ellipse at ,p1 !n x ne$s only a small k ( geometry to see t ! l9e ,,pb is 9 ! same position & direction z if x 7 drawn ?r\gh ,p f a false focus ,a1 :i* is z f> beh9d ! tang5t ,,tt z ! real focus ,a is 9 front ( x4 ,accord+ly1 x foll[s t circul> ripples div]g+ f "o focus ,a ( an ellipse mu/1 aft] reflection at ! elliptical b\nd>y1 be conv]g$ to ! o!r focus ,b4 ,?is c be %[n by ! use ( ! above describ$ app>atus 9 a pretty mann]4 ,illu/ration3 ,,fig4 #ai4 ,a /rip ( ?9 metal is b5t into an elliptical b& & plac$ 9 ! lant]n tr\gh4 ,! b& is s wide t ! wat] 9 ! tr\gh is ab\t halfway up x4 ,at a po9t correspond+ to "o focus ( ! ellipse1 drops ( wat] are !n all[$ to fall on ! wat]-surface & />t a s]ies ( div]g5t ripples4 ,:5 ! /roboscopic disc is set 9 revolution & its spe$ prop]ly adju/$1 we see t ! div]g5t ripples proce$+ f "o focus ( ! ellipse are all conv]g$ or conc5trat$ to ! o!r focus4 ,9 fact1 ! ripples seem to set out f "o focus1 & to be1 z x 71 swall[$ up at ! o!r4 ,:51 9 a lat] *apt]1 we are discuss+ ! production & reflection ( s\nd waves 9 ! air1 y w be able to br+ ?is /atem5t to m9d1 & x w be cle> to y t if1 in/ead ( deal+ ) waves on wat]1 we 7 to create waves 9 air 9 ! int]ior ( a simil> elliptically %ap$ room1 ! waves be+ creat$ at "o focus1 !y w\ld all be collect$ at ! o!r focus1 & ! tick ( a wat* or a :isp] w\ld be he>d at ! po9t correspond+ to ! o!r focus1 ?\gh x might n be he>d else:]e 9 ! room4 ,) ! appliances "h describ$ _m beautiful effects c be %[n1 illu/rat+ ! indep5d5ce ( diff]5t wave-tra9s & _! int]f]5ce4 ,if we hurl two /ones into a lake a little way ap>t1 & ?us create two sets ( circul> ripples 7see ,fig4 #bj71 we %all notice t ^! two ripple-tra9s pass freely ?r\gh ea* o!r1 & ea* behave z if ! o!r did n exi/4 ,a c>eful exam9ation w1 h[ev]1 %[ t at "s places ! wat]-surface is n elevat$ or di/urb$ at all1 & at o!rs t ! di/urbance is increas$4 ,illu/ration3 ,,fig4 #bj4--;,int]sect+ ripples produc$ on a lake by ?r[+ 9 simultane\sly two /ones4 ,if two sets ( waves set out f diff]5t orig9s & arrive simultane\sly at ! same spot1 !n x is cle> t if ! cre/s or holl[s ( bo? waves rea* t po9t at ! same in/ant1 ! agitation ( ! wat] w be increas$4 ,if1 h[ev]1 ! cre/ ( a wave f "o s\rce rea*es x at ! same "t z ! holl[ ( ano!r equal wave f ! o!r orig91 !n x is n difficult to see t ! two waves w oblit]ate ea* o!r4 ,?is mutual de/ruction ( wave by wave is call$ int]f]5ce1 & x is a v important fact 9 connection ) wave-motion4 ,x is n too mu* to say t :5ev] we c prove ! exi/5ce ( int]f]5ce1 t alone is an almo/ crucial pro( t we are deal+ ) wave-motion4 ,! conditions "u :i* int]f]5ce c take place mu/ be exam9$ a little m closely4 ,let u suppose t two wave-tra9s1 hav+ equal velocity1 equal wave-l5g?1 & equal amplitude or wave-height1 are />t$ f two po9ts1 ,a & ,b 7see ,fig4 #ba74 ,consid] any po9t1 ,p4 ,:at is ! condition t ! waves f ! two s\rces %all de/roy ea* o!r at t po9t8 ,obvi\sly x is t ! diff]5ce ( ! di/ances ,,ap & ,,bp %all be an odd numb] ( half wave-l5g?s4 ,= if 9 ! l5g? ,,ap !re are #ajj waves1 & 9 ! di/ance ,,bp !re are #ajj waves1 or #aja or #ajc1 etc41 waves1 !n ! cre/ ( a wave f ,a w rea* ,p at ! same "t z ! holl[ ( a wave f ,b1 & !re w be no wave at all at ! po9t ,p4 ,?is is true = all su* positions ( ,p t ! diff]5ce ( its di/ances f ,a & ,b are con/ant4 ,illu/ration3 ,,fig4 #ba4 ,b aga91 we may *oose a po9t1 ,q1 su* t ! diff]5ce ( its di/ances f ,a & ,b is equal to an ev5 numb] ( half wave-l5g?s1 s t :il/ 9 ! l5g? ,,aq !re are1 say1 #ajj waves1 9 ! di/ance ,,bq !re are #aja1 #ajb1 #ajc1 etc41 waves4 ,:5 ?is is ! case1 ! wave-effects w conspire or assi/ ea* o!r at ,q1 & ! wave-height w be d\bl$4 ,if1 !n1 we h any two po9ts1 ,a & ,b1 :i* are orig9s ( equal waves1 we c m>k out curv$ l9es su* t ! diff]5ce ( ! di/ances ( all po9ts on ^! l9es f ^! orig9s is con/ant4 ,^! curves are call$ hyp]bolas 7see ,fig4 #bb74 ,illu/ration3 ,,fig4 #bb4 ,illu/ration3 ,,fig4 #bc4--;,int]f]+ ripples on a m]cury surface1 %[+ int]f]5ce along hyp]bolic l9es 7,v9c5t74 ,all along ea* hyp]bola ! di/urbance due to ! comb9$ effect ( ! waves is ei!r d\bl$ or annull$ :5 comp>$ ) t due to ea* wave-tra9 sep>ately4 ,) ! app>atus describ$1 we c arrange to create & adju/ two sets ( simil> wat] ripples f orig9s n f> ap>t1 & on look+ at ! complicat$ %ad[-patt]n due to ! int]f]5ce ( ! waves1 we %all be able to trace out c]ta9 :ite l9es along :i* ! waves are annull$1 ^! l9es be+ hyp]bolic curves 7see ,fig4 #bc74 ,) ! same appliances ano!r *>act]i/ic ( wave-motion1 :i* is equally important1 c be well %[n4 ,illu/ration3 ,,fig4 #bd4 ,we make "o half ( ! circul> tank 9 :i* ! ripples are g5]at$ mu* m %all[ ?an ! o!r half1 by plac+ 9 x a ?ick semicircul> plate ( glass4 ,x has already be5 expla9$ t ! spe$ ) :i* long waves travel 9 a canal increases ) ! dep? ( ! wat] 9 ! canal4 ,! same is true1 ) c]ta9 re/rictions1 ( ripples produc$ 9 a conf9$ space or tank1 "o "p ( :i* is mu* %all[] ?an ! re/4 ,if waves are made by dropp+ wat] on to ! wat]-surface 9 ! deep] "p ( ! tank1 !y w travel m quickly 9 ?is deep] "p ?an 9 ! %all[] portion4 ,we c !n adju/ ! wat]-dropp+ jet 9 su* a position t x creates circul> ripples :i* orig9ate 9 deep wat]1 b at c]ta9 places pass ov] a b\nd>y into a region ( %all[] wat] 7see ,fig4 #bd74 ,! left-h& side ( ! circul> tank repres5t$ 9 ! diagram is m %all[ ?an ! "r-h& side4 ,:5 ?is is done1 we notice two int]e/+ facts1 viz4 t ! wave-l9es are b5t1 or refract$1 :]e !y pass ov] ! b\nd>y1 & t ! waves are %ort] or ne>] toge!r 9 ! %all[] region4 ,?is b5d+1 or refraction1 ( a wave-front 9 pass+ ! b\nd>y l9e betwe5 two di/ricts 9 :i* ! wave has diff]5t velocities is an exce$+ly important *>act]i/ic ( wave-motion1 & we %all h br\ght be=e u ! analog\s facts 9 speak+ ( waves 9 air & waves 9 !r4 ,illu/ration3 ,,fig4 #be4 ,x is necess>y to expla9 a little m 9 detail h[ x comes to pass t ! wave-l9e is ?us b5t4 ,imag9e a r[ ( soldi]s1 ab1 m>*+ ov] smoo? grass1 b go+ t[>ds a v r\gh field1 ! l9e ( sep>ation ,,ss betwe5 ! smoo? & ! r\gh field be+ oblique to ! l9e ( ! soldi]s 7see ,fig4 #be74 ,fur!rmore1 suppose ! soldi]s c m>* #d miles an h\r ov] ! smoo? grass1 b only #c miles an h\r ov] ! r\gh field4 ,!n let ! man on ! extreme left ( ! l9e be ! fir/ to /ep ov] ! b\nd>y4 ,imm$iately he passes into a region :]e 8 spe$ ( m>*+ is dim9i%$1 b 8 comrade on ! extreme "r ( ! r[ is /ill go+ easily on smoo? grass4 ,x is accord+ly cle> t ! direction ( ! l9e ( soldi]s w be swung r\nd because1 :il/ ! soldi] on ! extreme left m>*es1 say1 #cjj feet1 ! "o on ! extreme "r w h gone #djj feet =w>d2 & h5ce by ! "t all ! m5 h /epp$ ov] ! b\nd>y1 ! r[ ( soldi]s w no long] be go+ 9 ! same direction z be=e--x w h become b5t1 or refract$4 ,?is same action takes place ) waves4 ,if a wave meets obliquely a b\nd>y sep>at+ two regions1 9 "o ( :i* x moves sl[] ?an 9 ! o!r1 !n1 = ! same reason t ! direction ( ! r[ ( soldi]s 9 ! above illu/ration is b5t by reason ( ! ret>dation ( velocity exp]i5c$ by ea* man 9 turn z he /eps ov] ! divid+ l9e1 s ! wave-l9e or wave-front is b5t by pass+ f a place :]e x moves quickly to a place :]e x moves m sl[ly4 ,! ratio ( ! velocities or spe$s ( ! wave 9 ! two regions is call$ ! index ( refraction4 ,we c1 by arrang+ suitably curv$ reflect+ surfaces or prop]ly %ap$ %all[ places 9 a tank ( wat]1 illu/rate all ! facts connect$ ) ! *ange 9 wave-fronts produc$ by reflection & refraction4 ,we c g5]ate circul> waves or ripples div]g+ f a po9t1 & conv]t !m1 by reflection f a p>abolic reflector1 into plane waves2 & aga91 by means ( refraction at a curv$ or l5s-%ap$ %all[1 conv]ge ^! waves to a focus4 ,int]e/+ exp]im5ts ( ?is k9d h be5 made by means ( capill>y ripples on a m]cury surface by ,mr4 ,j4 ,h4 ,v9c5t1 & he has photograph$ ! ripples s =m$1 & giv5 examples ( _! reflection & refraction1 :i* are well wor? /udy4#ab ,we d n ne$1 h[ev]1 elaborate app>atus to see ^! effects :5 we "k :at to look =4 ,a /one ?r[n into a lake w create a ripple or wave-tra91 :i* moves outw>ds at ! rate ( a few feet a second4 ,if x %\ld happ5 t ! pond or lake has an imm]s$ wall z "p ( its b\nd>y1 ?is may =m an effective reflect+ surface1 & z ea* circul> wave meets ! wall x w be turn$ back ^u itself z a reflect$ wave4 ,at ! edge ( an absolutely calm sea1 at l[ tide1 ! au?or once obs]v$ little p>allel plane waves advanc+ obliquely to ! coa/2 ! edge ( ! wat] 0 by *ance j aga9/ a r /eep l$ge ( h>d s&1 & ea* wavelet1 z x met ?is reflect+ surface1 0 turn$ back & reflect$ at an angle ( reflection equal to t ( incid5ce4 ,x is well to notice t a plane wave1 or "o 9 :i* ! wave front or l9e is a /raight l9e1 may be consid]$ z made up out ( a numb] ( circul> waves div]g+ f po9ts arrang$ closely toge!r along a /raight l9e4 ,?us1 if we suppose t a1 b1 c1 d1 etc4 7see ,fig4 #bf71 are s\rce-po9ts1 or orig9s1 ( indep5d5t sets ( circul> waves1 repres5t$ by ! firm semicircul> l9es1 if !y s5d out simultane\s waves equal 9 all directions1 ! effect w be ne>ly equival5t to a plane wave1 repres5t$ by ! /raight ?ick black l9e1 provid$ t ! s\rce-po9ts are v num]\s & close toge!r4 ,suppos+1 !n1 we h a b\nd>y aga9/ :i* ?is plane wave imp+es obliquely1 x w be reflect$ & its subsequ5t c\rse w be exactly z if x _h proce$$ f a s]ies ( closely adjac5t s\rce-po9ts1 a1 b1 c1 d1 etc41 ly+ beh9d ! b\nd>y1 ea* ( :i* is ! image ( ! correspond+ real s\rce-po9ts1 & lies z f> beh9d ! b\nd>y z ! real po9t lies 9 front ( x4 ,illu/ration3 ,,fig4 #bf4 ,an imm$iate consequ5ce ( ?is is t ! plane reflect$ wave-front makes ! same angle ) ! plane reflect+ surface z does ! incid5t or arriv+ wave1 & we ?us e/abli% ! law1 s famili> 9 optics1 t ! angle ( incid5ce is equal to ! angle ( reflection :5 a plane wave meets a plane reflect+ surface4 ,at ! seaside1 :5 ! tide is l[ & ! sea calm or ruffl$ only by wavelets due to a slight w9d1 "o may (t5 notice tra9s ( small waves1 :i* are reflect$ at %>p edges ( s&1 or refract$ on pass+ into sudd5 %all[s1 or int]f]+ aft] pass+ r\nd ! two sides ( a rock4 ,a c>eful obs]v] c 9 ?is s*ool ( ,nature in/ruct himself 9 all ! laws ( wave-motion1 & ga!r a fund ( k on ?is subject dur+ an h\r's dalliance at l[ tide on "s s&y coa/1 or 9 ! quiet /udy ( seaside pools1 ! surface ( :i* is corrugat$ ) tra9s ( ripples by ! breeze4 ,,*apt] ,,ii4 ,,waves ,,& ,,ripples ,,made ,,by ,,%ips4 ,x is impossible = ! mo/ c>eless spectator to look at a /eam-vessel mak+ h] way along a lake1 a boy's boat skimm+ across a pond1 or ev5 a duck paddl+ on a /ream1 )\t notic+ t ! mov+ body is accompani$ 9 all cases by a trail ( waves or ripples1 :i* div]ge f x & ext5d beh9d4 ,9 ! case ( a /eam] !re is an additional irregul> wave-motion ( ! wat] caus$ by ! paddle-:eels or screw1 :i* *urn x up1 & leave a l9e ( r\gh wat] 9 ! /eam]'s wake4 ,?is1 h[ev]1 is n includ$ 9 ! true %ip-wave effect n[ to be discuss$4 ,we c be/ obs]ve ! prop] %ip-wave di/urbance ( ! wat] 9 ! case ( a ya*t runn+ freely be=e ! w9d :5 ! sea is fairly smoo?4 ,! /udy ( ^! %ip-waves has l$ to mo/ important & practical improvem5ts 9 ! art ( %ip-design+ & %ipbuild+1 & no treatm5t ( ! subject ( waves & ripples on wat] w\ld be complete 9 :i* all m5tion ( %ip-waves 0 omitt$4 ,9 ord] t we may expla9 ! mann] 9 :i* ^! waves are =m$1 & _! effect ^u ! motion ( ! %ip1 & ! p[] requir$ to move x =w>d1 we mu/ beg9 by a little discussion ( "s fundam5tal facts conc]n+ liquids 9 motion4 ,e "o is aw>e t c]ta9 liquids are1 z we say /icky1 or1 to use ! sci5tific t]m1 visc\s4 ,a reque/ to m5tion /icky liquids w\ld call up ! names ( su* fluids z t>1 treacle1 gum-wat]1 glyc]9e1 & honey4 ,v few p w\ld ?9k ( includ+ pure wat]1 f> less spirits ( w9e1 9 a li/ ( /icky1 or visc\s liquids2 & yet x is q easy to %[ by exp]im5t t ev5 ^! fluids possess "s degree ( /ick9ess1 or viscosity4 ,an illu/ration may be af=d$ z foll[s3 ,we provide sev]al v l>ge glass tubes1 ne>ly fill$ respectively ) quicksilv]1 wat]1 alcohol1 glyc]9e1 & oil4 ,a small space is left 9 ea* tube conta9+ a little air1 & ! tubes are clos$ by corks4 ,if we sudd5ly turn all ! tubes upside d[n1 ^! bubbles ( air beg9 to climb up f ! bottom ( ! tube to ! top4 ,we notice t 9 ! quicksilv] tube x arrives at ! top 9 a second or two1 9 ! wat] tube x takes a little long]1 9 ! oil tube long] /ill1 & 9 ! tube fill$ ) glyc]9e x is q a m9ute or m be=e ! bubble ( air has complet$ its j\rney up ! tube4 ,?is exp]im5t1 prop]ly int]pret$1 %[s u t wat] possesses 9 "s degree ! quality ( viscosity4 ,x c1 h[ev]1 be m =cibly prov$ by ano!r exp]im5t4 ,to a :irl+-table is fix$ a glass vessel half full ( wat]4 ,on ?is wat] a r\nd disc ( wood1 to :i* is atta*$ a long wire c>ry+ a pap] flag1 is made to float4 ,if we set ! bas9 ( wat] sl[ly 9 rotation1 at fir/ ! pap] flag does n move4 ,! bas9 rotates )\t sett+ ! conta9$ wat] 9 rotation1 & s to speak slips r\nd x4 ,pres5tly1 h[ev]1 ! flag beg9s to turn sl[ly1 & ?is %[s u t ! wat] has be5 gradually set 9 rotation4 ,?is happ5s because ! wat] /icks slightly to ! inn] surface ( ! bas91 & ! lay]s ( wat] likewise /ick to "o ano!r4 ,h5ce1 z ! glass vessel slides r\nd ! wat] x gradually =ces ! out] lay] ( wat] to move ) x1 & ?is aga9 ! inn] lay]s ( wat] "o by "o1 until at la/ ! float+ block ( wood p>takes ( ! motion1 & ! bas9 & its cont5ts turn r\nd z "o mass4 ,?is effect c\ld n take place unless ! wat] possess$ "s degree ( viscosity1 & also unless s-call$ sk9 friction exi/$ betwe5 ! inside ( a glass vessel & ! wat] x conta9s4 ,we may say1 h[ev]1 at once t no real liquid ) :i* we are acqua9t$ is entirely de/itute ( /ick9ess1 or viscosity4 ,we c nev]!less imag9e a liquid absolutely free f any trace ( ?is prop]ty1 & ?is hypo!tical sub/ance is call$ a p]fect fluid4 ,x is cle> t ?is ideal p]fect liquid mu/ necess>ily diff] 9 sev]al important respects f any real fluid1 su* z wat]1 & "s ( ^! diff]5ces we proce$ to exam9e4 ,we mu/ po9t out t 9 any liquid !re may be two k9ds ( motion1 "o call$ irrotational motion1 & ! o!r call$ rotational or vortex motion4 ,consid] any mass ( wat]1 su* z a riv]1 9 motion 9 any way2 we may 9 imag9ation fix our att5tion ^u "s small portion ( x1 :i* at any in/ant we w consid] to be ( a sph]ical %ape4 ,if1 z ?is sph]e ( liquid moves along emb$d$ 9 ! re/ ( ! liquid1 x is turn+ r\nd an axis 9 any direction z well z be+ di/ort$ 9 %ape1 ! motion ( t "p ( ! fluid is call$ rotational4 ,if1 h[ev]1 our little sph]e ( liquid is m]ely be+ /ret*$ or pull$ into an ovoid or ellipsoidal %ape )\t any rotation or sp9n+ motion1 !n ! motion ( ! liquid is said to be irrotational4 ,we might comp>e ^! small portions ( ! liquid to a cr[d ( p mov+ along a /reet4 ,if ea* p]son moves 9 su* a way z always to keep 8 face 9 ! same direction1 t movem5t w\ld be an irrotational movem5t4 ,if1 h[ev]1 !y 7 to move l c\ples danc+ 9 a ball-room1 n only mov+ along b turn+ r\nd1 _! motion w\ld be call$ rotational4 ,examples ( rotational1 or vortex motion are se5 :5ev] we empty a wa%-bas9 by pull+ up ! plug4 ,we see ! wat] swirl r\nd1 or rotate1 =m+ :at is call$ an eddy1 or :irlpool4 ,also eddies are se5 ne> ! m>g9 ( a swiftly fl[+ riv]1 s9ce ! wat] is set 9 rotation by friction aga9/ objects on ! banks4 ,eddies are likewise creat$ :5 two /reams ( wat] fl[ ov] ea* o!r ) diff]5t spe$s4 ,a beautiful in/ance ( ?is may be view$ at an int]e/+ place a mile or two out ( ! city ( ,g5eva4 ,! ,rhone1 a rapid riv]1 em]ges z a cle> blue /ream f ! ,lake ( ,g5eva4 ,at a po9t call$ ,junction d'eaux x meets ! riv] ,arve1 a m sluggi% & turbid glaci] /ream1 & ! two !n run toge!r 9 ! same *annel4 ,! wat]s ( ! ,rhone & ,arve d n at once mix1 b ! l9e ( sep>ation is m>k$ by a s]ies ( :irlpools or eddies set up by ! fl[ ( ! rapid ,rhone wat] aga9/ ! sl[] ,arve wat] 9 contact ) x4 ,aga91 x is impossible to move a solid body ?r\gh a liquid )\t sett+ up eddy-motion4 ,! movem5t ( an o> ?r\gh ! wat]1 or ev5 ( a teaspoon ?r\gh tea1 is se5 to be accompani$ by little :irls :i* deta* !mselves f ! o> or spoon1 & are really ! ends ( vortices set up 9 ! liquid4 ,! two facts to notice p>ticul>ly are t ! production ( eddies 9 liquids always involves ! exp5diture ( en]gy1 or1 9 me*anical language1 x necessitates do+ "w4 ,to set 9 rotation a mass ( any liquid requires ! deliv]y to x ( en]gy1 j z is ! case :5 a heavy :eel is made to rotate or a heavy tra9 set 9 movem5t4 ,?is en]gy mu/ be suppli$ by or absorb$ f ! mov+ solid or liquid :i* creates ! eddies4 ,9 ! next place1 we mu/ note t eddies or vortices set up 9 an imp]fect fluid1 su* z wat]1 are ultimately de/roy$ by fluid friction4 ,_! en]gy is fritt]$ d[n into heat1 & a mass ( wat] 9 :i* eddies h be5 creat$ by mov+ ?r\gh x a paddle1 is w>m] aft] ! eddies h subsid$ ?an be=e4 ,x is obvi\s1 f :at has be5 said1 t if a really p]fect fluid did exi/1 x w\ld be impossible by me*anical means to make eddies 9 x2 b if !y 7 creat$1 !y w\ld cont9ue = ev]1 & h some?+ ( ! p]man5ce ( mat]ial sub/ances4 ,illu/ration3 ,,fig4 #bg4--,! production ( a vortex r+ 9 air4 ,a vortex motion 9 wat] may be ei!r a t]m9at$ vortex1 9 :i* case its ends are on ! surface1 & are se5 z eddies1 or :irls2 or x may be an endless vortex1 9 :i* case x is call$ a vortex r+4 ,su* a r+ is v easily made 9 ! air z foll[s3 ,a cubical wood5 box ab\t #ah in*es 9 ! side has a hole #f in*es 9 diamet] made 9 ! bottom 7see ,fig4 #bg74 ,! op5 top ( ! box is cov]$ tightly ) ela/ic clo?4 ,! box is !n fill$ ) ! :ite vap\r ( ammonium *loride1 by lead+ into x at ! same "t dry hydro*loric acid gas & dry ammonia gas4 ,:5 q full ( d5se :ite fumes1 we give ! clo? cov] ( ! box a %>p bl[ ) ! fi/1 & f ! r\nd hole a :ite smoke r+ leaps out & slides ?r\gh ! air4 ,! exp]im5t may be made on a small] scale by us+ a c>dbo>d box & fill+ x ) ! smoke ( br[n pap] or tobacco4#ac ,if we look closely at ! smoke r+ z x glides ?r\gh ! air1 we %all see t ! motion ( ! air or smoke p>ticles compos+ ! r+ is l t ( an indi>ubb] umbrella-r+ fitt$ tightly on a r\nd rul] & pu%$ along4 ,! r+ turns itself cont9ually ov] & ov]1 ! rotation be+ r\nd ! circul> r+ axis l9e4 ,?is rotatory motion is set up by ! friction ( ! smoky air aga9/ ! edge ( ! hole 9 ! box1 z ! puff ( air em]ges f x :5 ! back ( ! box is ?ump$4 ,a simple b /rik+ exp]im5t may be made )\t fill+ ! box ) smoke4 ,place a light$ c&le at a few feet away f ! op5+ ( ! above-describ$ box1 & /rike ! back4 ,an invisible vortex r+ ( air is =m$ & bl[s out ! c&le z x passes ov] x4 ,al?\gh x is q easy to make a rotational motion 9 an imp]fect fluid1 & 9 fact difficult n to d x1 yet ( late ye>s a v int]e/+ & valuable discov]y has be5 made by ,pr(essor ,hele-,%aw1 ( a me?od ( creat+ & r5d]+ visible a motion 9 an imp]fect liquid l wat]1 :i* is irrotational4 ,?is discov]y 0 t1 if wat] is made to fl[ 9 a ?9 %eet betwe5 two plates1 say ( flat glass1 n m ?an a fiftie? ( an in* or s ap>t1 ! motion ( ! wat] is exactly t ( a p]fect fluid1 & is irrotational4 ,no matt] :at objects may be plac$ 9 ! pa? ( ! wat]1 x !n fl[s r\nd !m j z if all fluid friction or viscosity 0 abs5t4 ,?is int]e/+ fact c be %[n by means ( an app>atus design$ by ,pr(essor ,hele-,%aw4#ad ,two glass plates are held 9 a frame1 & sep>at$ by a v small di/ance4 ,by means ( an inlet-pipe wat] is caus$ to fl[ betwe5 ! plates4 ,a metal block pi]c$ ) small holes is atta*$ to ! end ( "o plate1 & ?is s]ves to introduce sev]al small jets ( col\r$ wat] into ! ma9 %eet4 ,9 con/ruct+ ! app>atus great c>e has to be ex]cis$ to make ! holes 9 ! above-m5tion$ block v small 7n m ?an in* 9 diamet]7 & plac$ exactly at ! "r slope4 ,! ma9 wat] inlet-pipe is connect$ by a rubb] tube ) a ci/]n ( wat] plac$ ab\t #d feet above ! level ( ! app>atus4 ,! frame & glass plates are held v]tically 9 ! field ( an optical lant]n s z to project an image ( ! plates ^u ! scre54 ,! side inlet-pipe lead+ to ! pi]c$ metal block is connect$ to ano!r res]voir ( wat]1 col\r$ purple ) p]manganate ( pota% 7,condy's fluid71 & ! fl[ ( bo? /reams ( wat] controll$ by taps4 ,! cle> wat] is fir/ all[$ to fl[ d[n betwe5 ! plates1 s z to exclude all air-bubbles1 & create a ?9 film ( fl[+ wat] betwe5 two glass plates4 ,! jets ( col\r$ wat] are !n introduc$1 &1 aft] a little adju/m5t1 we %all see t ! col\r$ wat] fl[s d[n 9 n>r[1 p>allel /reams1 n mix+ ) ! cle> wat]1 & n %[+ any trace ( eddies4 ,! regul>ity ( ^! /reams ( col\r$ wat]1 & _! %>p def9ition1 %[s t ! liquid fl[ betwe5 ! plates is altoge!r irrotational4 ,! l9es m>k$ out by ! col\r$ wat] are call$ /ream-l9es1 & !y cut up ! :ole space into uni=m tubes ( fl[4 ,! *>act]i/ic ( ?is fl[ ( liquid is t ! cle> wat] 9 ! space betwe5 two col\r$ /reams ( wat] nev] passes ov] into an adjac5t tube4 ,h5ce we c divide up ! :ole %eet ( liquid into tubul> spaces call$ tubes ( fl[1 by l9es call$ /ream-l9es4 ,if n[ we dism\nt ! app>atus & place betwe5 ! glass a ?9 piece ( indi>ubb] %eet--cut1 say1 into ! %ape ( a %ip1 & ( su* ?ickness t x fills up ! space betwe5 ! glass plates--we %all be able to obs]ve h[ ! wat] fl[s r\nd su* an ob/acle4 ,if ! air is fir/ driv5 out by ! fl[ ( ! cle> wat]1 & !n if ! jets ( col\r$ wat] are introduc$1 we see t ! l9es ( liquid fl[ are del9eat$ by col\r$ /reams or n>r[ b&s1 & t ^! /ream-l9es b5d r\nd & enclose ! ob/ruct+ object4 ,! space all r\nd ! %ip-%ap$ solid body is ?us cut up into tubes ( fl[ by /ream-l9es1 b ^! tubes ( fl[ are n[ no long] /raight1 & no long] ( equal wid? at all po9ts4 ,!y are n>r[] opposite ! middle "p ( ! ob/ruction ?an ne> ei!r end4 ,illu/ration3 ,,fig4 #bh4 ,at ?is po9t we mu/ make a digression to expla9 a fundam5tal law conc]n+ fluid fl[ 9 tubes4 ,suppose we h a uni=m horizontal metal tube1 ?r\gh :i* wat] is fl[+ 7see ,fig4 #bh74 ,at v>i\s po9ts along ! tube let v]tical glass pipes be ins]t$ to act z gauge or pressure-tubes4 ,!n :5 ! fluid fl[s along ! horizontal pipe x w /& up a c]ta9 height 9 ea* pressure-tube1 & ?is height w be a measure ( ! pressure 9 ! horizontal pipe at ! po9t :]e ! pressure-tube is ins]t$4 ,we %all notice t :5 ! wat] fl[s 9 ! horizontal pipe1 ! wat] 9 ! gauge-pipes /&s at diff]5t heights1 indicat+ a fall 9 pressure along ! horizontal pipe4 ,we also notice t a l9e jo9+ ! tops ( all ! liquid columns 9 ! pressure-pipes is a /raight1 slop+ l9e1 :i* is call$ ! hydraulic gradi5t4 ,?is exp]im5t proves to u t :5 fluid fl[s along a uni=m-section$ pipe !re is a uni=m fall or decrease 9 pressure along ! pipe4 ,! =ce :i* is driv+ ! liquid along ! horizontal pipe is measur$ by ! diff]5ce betwe5 ! pressures at its extreme ends1 & ! same is true ( any select$ l5g? ( ! horizontal pipe4 ,x w also be cle> t1 s9ce wat] is n compressible to any b ! v slighte/ ext5t1 ! quantity ( wat]1 reckon$1 say 9 gallons1 :i* passes p] m9ute across any section ( ! pipe mu/ be ! same4 ,illu/ration3 ,,fig4 #bi4 ,9 ! next place1 suppose we cause wat] to fl[ ?r\gh a tube :i* is n>r[] 9 "s places ?an 9 o!rs 7see ,fig4 #bi74 ,x w be readily admitt$ t 9 ?is tube also ! same quantity ( wat] w fl[ across e section1 wide or n>r[1 ( ! tube4 ,if1 h[ev]1 we ask--,:]e1 9 ?is case1 w !re be ! greate/ pressure8 x is c]ta9 t mo/ p]sons w\ld reply--,9 ! n>r[ portions ( ! tube4 ,!y w\ld ?9k t ! wat]-p>ticles pass+ ?r\gh ! tube resemble a cr[d ( p pass+ along a /reet :i* is con/rict$ 9 "s places l ! ,/r&4 ,! cr[d w\ld be mo/ tightly squeez$ toge!r1 & ! pressure ( p w\ld !re=e be great]1 9 ! n>r[ portions ( ! /reet4 ,9 ! case ( ! wat] fl[+ ?r\gh ! tube ( v>iable section ?is1 h[ev]1 is n ! case4 ,s f> f ! pressure be+ greate/ 9 ! n>r[ portions ( ! tube1 x c be %[n exp]im5tally t x is precisely at ^? places x is lea/4 ,?is c be demon/rat$ by ! tube %[n 9 ,fig4 #bi4 ,if wat] is all[$ to fl[ ?r\gh a tube con/rict$ 9 "s places1 & provid$ ) glass gauge-pipes at v>i\s po9ts to indicate ! pressure 9 ! pipe at ^? places1 x is f\nd t ! pressure1 z indicat$ by ! height ( ! wat] 9 ! gauge-glasses at ! n>r[ p>ts ( ! tube1 is less ?an t :i* x w\ld h at ^? places if ! tube 7 ( uni=m section & l5g?1 & pass$ ! same quantity ( wat]4 ,we c =mulate ?is fact "u a g5]al law :i* controls fluid motion also 9 o!r cases1 viz4 t :]e ! velocity ( ! liquid is greate/1 !re ! pressure is lea/4 ,x is evid5t1 s9ce ! tube is wid] 9 "s places ?an 9 o!rs1 & z a practically incompressible liquid is be+ pass$ ?r\gh x1 t ! spe$ ( ! liquid mu/ be great] 9 ! n>r[ portions ( ! tube ?an 9 ! wid] ones4 ,b exp]im5t %[s t aft] all[+ = :at may be call$ ! prop] hydraulic gradi5t ( ! tube1 ! pressure is lea/ 9 ^? places1 viz4 ! con/rict$ portions1 :]e ! velocity ( ! liquid is greate/4 ,?is g5]al pr9ciple is ( wide application 9 ! sci5ce ( hydraulics1 & x s]ves to enable u to int]pret aright _m p]plex+ facts met ) 9 physics4 ,we c1 9 ! next place1 ga!r toge!r ! v>i\s facts conc]n+ fluid fl[ :i* h be5 expla9$ above1 & apply !m to elucidate ! problems rais$ by ! passage ?r\gh wat] ( a %ip or a fi%4 ,let u consid]1 9 ! fir/ place1 a body totally subm]g$1 su* z a fi%1 a torp$o or a subm>9e boat1 & discuss ! "q :y a resi/ance is exp]i5c$ :5 an attempt is made to drag or pu% su* a body ?r\gh wat]4 ,! old-fa%ion$ notion 0 t ! wat] has to be pu%$ out ( ! way to make room = ! fi% to move =w>d1 & also has to be suck$ 9 to fill up ! cavity left beh9d4 ,mo/ p]sons :o h n be5 in/ruct$ 9 ! subject1 p]haps ev5 n[ h ! idea t ?is s-call$ 8head resi/ance0 is ! *ief cause ( ! resi/ance exp]i5c$ :5 we make a body ( any %ape move ?r\gh wat]4 ,a common assumption is also t ! object ( mak+ a %ip's b[s %>p is t !y may cut into ! wat] l a w$ge1 & m easily pu% x out ( ! way4 ,sci5tific inve/igation has1 h[ev]1 %[n t bo? ( ^! notions are errone\s4 ,! resi/ance felt 9 pull+ or pu%+ a boat ?r\gh ! wat] is n due to resi/ance (f]$ by ! wat] 9 virtue ( its in]tia4 ,no "p ( ?is resi/ance arises f ! ex]tion requir$ to displace ! wat] or pu% x out ( ! way4 ,! ,s*oolm5 ( ! ,middle ,ages us$ to discuss ! "q h[ x 0 t a fi% c\ld move ?r\gh ! wat]4 ,!y said ! fi% c\ld n move until ! wat] got out ( ! way1 & ! wat] c\ld n get out ( ! way until ! fi% mov$4 ,?is & simil> p]plexities 7 n remov$ until ! true !ory ( ! motion ( a solid ?r\gh a liquid _h be5 develop$4 ,briefly x may be said t !re are ?ree causes1 & only ?ree1 = ! resi/ance :i* we feel & h to ov]come :5 we attempt to drag a boat or %ip ?r\gh ! wat]4 ,^! are3 ,fir/1 sk9 friction1 due to ! friction betwe5 ! %ip-surface & ! wat]2 secondly1 eddy-resi/ance1 due to ! en]gy lo/ or tak5 up 9 mak+ wat] eddies2 & ?irdly1 wave-resi/ance1 due to en]gy tak5 up 9 mak+ surface-waves4 ,! sk9 friction & ! eddy-resi/ance bo? arise f ! fact t wat] is n a p]fect fluid4 ,! wave-resi/ance arises1 z we %all %[1 f ! unavoidable =mation ( waves by ! motion ( ! boat ?r\gh ! wat]4 ,9 ! case ( a :olly subm]g$ body1 l a fi%1 ! only resi/ance x has to ov]come is due to ! fir/ two causes4 ,! fi%1 progress+ ?r\gh ! wat] :olly "u ! surface1 makes no waves1 b ! wat] adh]es to its sk91 & !re is friction betwe5 !m z he moves4 ,also he creates eddies 9 ! wat]1 :i* require en]gy to produce !m1 & :5ev] me*anical "w has to be done1 z en]gy drawn (f f a mov+ body1 ?is implies ! exi/5ce ( a resi/ance to its motion :i* has to be ov]come4 ,accord+ly ,nature1 economical on all occasions 9 en]gy exp5diture1 has fa%ion$ ! fi% s z to r$uce ! p[] x has to exp5d 9 mov+ ?r\gh wat] z mu* z possible4 ,! fi% has a smoo? slipp]y sk94 7,we say 8z slipp]y z an eel407 ,x is n cov]$ ei!r ) fur or fea!rs1 b ) %9y scales1 s z to r$uce to a m9imum ! sk9 friction4 ,! fi% also is regul> & smoo? 9 outl9e4 ,x has no long e>s1 squ>e %\ld]s1 or project+ limbs or organs1 :i* by giv+ x an irregul> outl9e1 w\ld t5d to produce eddies 9 ! wat] z x moves along4 ,h5ce1 :5 we wi% to design a body to move quickly "u ! wat]1 we mu/ imitate 9 ^! respects ! /ructure ( a fi%4 ,accord+ly1 a ,:itehead torp$o1 t deadly in/rum5t employ$ 9 naval w>f>e1 is made smoo? & fi%-%ap$1 & a subm>9e boat is made cig>-%ap$ & z smoo? z possible1 = ! same reason4 ,if ! float+ object is p>tly above ! surface1 yet nev]!less1 z f> z conc]ns ! portion subm]g$1 !re is sk9 friction1 & ! production ( eddy-resi/ance4 ,h5ce1 9 ! con/ruction ( a rac+-ya*t1 ! greate/ c>e has to be tak5 to make its surface bel[ wat] ( poli%$ metal or v>ni%$ wood1 or o!r v smoo? mat]ial1 to dim9i% z f> z possible ! sk9 friction4 ,9 ! case ( bodies z regul> 9 outl9e z a %ip or fi%1 ! proportion ( ! driv+ p[] tak5 up 9 mak+ eddies 9 ! wat] is n l>ge1 & we may1 )\t s5sible error1 say t 9 _! case ! :ole resi/ance to motion is compris$ "u ! two heads ( sk9 friction & wave-mak+ resi/ance4 ,! proportion :i* ^! two causes be> to ea* o!r w dep5d ^u ! nature ( ! surface ( ! body :i* moves ov] ! wat]1 & its %ape & spe$4 ,at ?is po9t we may pause to notice t1 if we c\ld obta9 a p]fect fluid 9 practice1 x w\ld be f\nd t an object ( any %ape :olly subm]g$ 9 ! fluid c\ld be mov$ ab\t 9 any way )\t exp]i5c+ ! lea/ resi/ance4 ,?is !oretical d$uction is1 at fir/ sight1 s oppos$ to ord9>y preconceiv$ notions on ! subject1 t x des]ves a little att5tion4 ,x is difficult1 z already rem>k$1 = mo/ p :o h n c>efully /udi$ ! subject1 to rid _! m9ds ( ! idea t !re is a resi/ance to ! motion ( a solid ?r\gh a liquid aris+ f ! ef=t requir$ to pu% ! liquid out ( ! way4 ,b ?is notion is1 z already expla9$1 entirely errone\s4 ,9 ! light ( ! /ream-l9e !ory ( liquid motion1 x is easy to prove1 h[ev]1 ! tru? ( ! above /atem5t4 ,let u beg9 by suppos+ t a solid body ( regul> & symmetrical %ape1 say ( an oval =m 7see ,fig4 #cj71 is mov$ ?r\gh a fluid de/itute ( all /ick9ess or viscosity1 :i* !re=e does n adh]e to ! solid4 ,!n1 if ! solid is :olly subm]g$ 9 ?is fluid1 ! mutual action ( ! liquid & ! solid w be ! same1 :e!r we suppose ! liquid to be at re/ & ! solid to move ?r\gh x1 or ! solid body to be at re/ & ! liquid to fl[ pa/ x4 ,illu/ration3 ,,fig4 #cj4--,/ream-l9es r\nd an ovoid4 ,illu/ration3 ,,fig4 #ca4--,tube ( fl[ 9 a liquid4 ,if1 !n1 we suppose ! p]fect fluid to fl[ r\nd ! ob/acle1 x w di/ribute itself 9 a c]ta9 mann]1 & its motion c be del9eat$ by /ream-l9es4 ,!re w be no eddies or rotations1 because ! liquid is by assumption p]fect4 ,consid] n[ any two adjac5t /ream-l9es 7see ,fig4 #ca74 ,^! def9e a tube ( fl[1 repres5t$ by ! %ad$ portion1 :i* is n>r[] 9 ! middle ?an at ! ends4 ,h5ce ! liquid1 :i* we %all suppose also to be incompressible1 mu/ fl[ fa/] :5 go+ pa/ ! middle ( ! ob/acle :]e ! /ream-tubes are n>r[1 ?an at ! ends :]e ! /ream-tubes are wid]4 ,by ! pr9ciple already expla9$1 x w be cle> t ! pressure ( ! fluid w !re=e be less 9 ! n>r[ portion ( ! /ream-tube1 & f ! p]fect symmetry ( ! /ream-l9es x is evid5t !re w be great] & equal pressures at ! two ends ( ! imm]s$ solid4 ,! fl[ ( ! liquid pa/ ! solid subjects x1 9 fact1 to a numb] ( equal & balanc$ pressures at ! two ends :i* exactly equilibrate ea* o!r4 ,x is n q s easy to see at once t if ! solid body is n symmetrical 9 %ape ! same ?+ is true1 b x c be e/abli%$ by a /rict l9e ( reason+4 ,! result is to %[ t :5 a solid ( any %ape is imm]s$ 9 a p]fect liquid1 x _c be mov$ by ! liquid fl[+ pa/ x1 & correspond+ly w\ld n require any =ce to move x aga9/ & ?r\gh ! liquid4 ,9 %ort1 !re is no resi/ance to ! motion ( a solid ( any %ape :5 pull$ ?r\gh a p]fect or frictionless liquid4 ,:5 deal+ ) real liquids n entirely free f viscosity1 su* resi/ance z does exi/ is due1 z already m5tion$1 to sk9 friction & eddy =mation4 ,9 ! next place1 leav+ ! consid]ation ( ! movem5t ( :olly subm]g$ bodies ?r\gh liquids :e!r p]fect or imp]fect1 we %all proce$ to discuss ! important "q ( ! resi/ance (f]$ by wat] to ! motion ?r\gh x ( a float+ object1 su* z a %ip or swan4 ,we h 9 ?is case to take into consid]ation ! wave-mak+ prop]ties ( ! float+ solid4 ,we h already po9t$ out t to make a wave on wat] requires an exp5diture ( en]gy or ! p]=mance ( me*anical "w4 ,if a wave is made & travels away ov] wat]1 x c>ries ) x en]gy1 & h5ce x c only be creat$ if we h a /ore ( en]gy to draw ^u4 ,if we suppose t sk9 friction is abs5t1 & t ! %ip floats ^u a p]fect fluid1 x w\ld nev]!less be true t1 if ! mov+ object creates waves1 x w !reby r$uce its own movem5t & require ! application ( =ce to x to keep x go+4 ,we may say !re=e t if any float+ object creates waves on a liquid ov] :i* x moves1 ^! waves rob ! float+ body ( "s ( its en]gy ( motion4 ,! creation ( ! waves w br+ x to re/ 9 "t1 unless x is cont9ually urg$ =w>d by "s ext]nal & impress$ =ce1 & wave-g5]ation is a reason = a "p at lea/ ( ! resi/ance we exp]i5ce :5 we attempt to pu% x along4 ,accord+ly1 "o elem5t 9 ! problem ( design+ a %ip is t ( f9d+ a =m :i* w make z little wave-di/urbance z possible 9 mov+ ov] ! liquid4 ,x is comp>atively easy to f9d a %ape = a float+ solid :i* %all make a consid]able wave-di/urbance on ! wat] :5 x is pull$ ov] x1 b x is n q s easy to design a %ape :i* w n make waves1 or make b v small ones4 ,if we look c>efully at a ya*t glid+ along be=e a fre% breeze on a sea or lake surface :i* is n mu* ruffl$ by o!r waves1 x is possible to discov] t a %ip1 :5 go+ ?r\gh ! wat]1 creates f\r di/9ct sy/ems ( waves4 ,two ( ^! are v easy to see1 & two are m difficult to id5tify4 ,^! wave-sy/ems are call$ respectively ! oblique b[ & /]n waves1 & ! transv]se & re> waves4 ,we %all exam9e ea* sy/em 9 turn4 ,! mo/ important & easily obs]v$ ( ! f\r sets ( waves is ! oblique b[ wave4 ,x is mo/ easily se5 :5 a boy's boat skims ov] ! surface ( a pond1 & readily obs]v$ :5ev] we see a duck paddl+ along on ! wat]4 ,let any "o look1 = in/ance1 at a duck swimm+ on a pond4 ,he w see two tra9s ( little waves or ripples1 :i* are incl9$ at an angle to ! direction ( ! duck's l9e ( motion4 ,bo? tra9s are made up ( a numb] ( %ort waves1 ea* ( :i* ext5ds beyond or ov]laps its neighb\r 7see ,fig4 #cb74 ,illu/ration3 ,,fig4 #cb4--;,e*elon waves made by a duck4 ,h5ce1 f a common ,fr5* ^w1 ^! waves h be5 call$ e*elon waves1#ae & we %all s speak ( !m4 ,illu/ration3 ,,fig4 #cc4--;,e*elon waves made by a model ya*t4 ,on look+ at a boy's model ya*t 9 motion on ! wat]1 ! same sy/em ( waves w be se52 & on look+ at any real ya*t or /eam] 9 motion on smoo? wat]1 !y are q easily id5tifi$ 7see ,fig4 #cc74 ,! complete explanation ( ! =mation ( ^! b[ or e*elon waves is difficult to foll[1 b 9 a g5]al way _! =mation c be ?us expla9$3 ,suppose we h a flat piece ( wood1 :i* is held upright 9 wat]1 & to :i* we give a sudd5 pu%4 ,we %all notice t1 9 consequ5ce ( ! in]tia ( ! liquid1 x />ts a wave :i* travels away at a c]ta9 spe$ ov] ! surface ( ! wat]4 ,! sudd5 movem5t ( ! wood elevates ! wat] j 9 front ( x1 & ?is displacem5t =ms ! cre/ ( a wave :i* is !n h&$ on or propagat$ along ! surr\nd+ wat]-surface4 ,if two pieces ( wood are fa/5$ toge!r obliquely1 z 9 ,fig4 #cd1 & held 9 wat] p>tly subm]g$1 we %all f9d t :5 ?is wood is sudd5ly ?ru/ =w>d l a w$ge1 x />ts two oblique waves :i* move (f p>allel to ! incl9$ wood5 sides4 ,! b[s ( a %ip1 r\ghly speak+1 =m su* a w$ge4 ,illu/ration3 ,,fig4 #cd4 ,h5ce1 if we consid] ?is w$ge or ! b[s ( a %ip to be plac$ 9 /ill wat] & !n pu%$ sudd5ly =w>d1 !y w />t two incl9$ waves1 :i* w move (f p>allel to !mselves4 ,if we !n consid] ! w$ge to leap =w>d & repeat ! process1 two m incl9$ waves w be =m$ 9 front ( ! fir/2 & aga9 we may suppose ! process repeat$1 & a ?ird pair ( waves =m$4 ,! diff]5t positions ( ! %ip's b[s are %[n 9 ! diagram at #a1 #b1 & #c 9 ,fig4 #ce2 & c1 e1 & f are ! ?ree correspond+ sets ( e*elon$ waves4 ,= ! sake ( simplicity1 ! waves are %[n on "o side only4 ,if1 !n1 we imag9e ! %ip to move uni=mly =w>ds1 its b[s are always produc+ new incl9$ waves1 :i* move ) x1 & x is always1 s to speak1 leav+ ! old ones beh9d4 ,all ^! e*elon waves produc$ by ! b[ ( ! %ip are includ$ )9 two slop+ l9es :i* ea* make ) ! direction ( ! %ip's l9e ( movem5t1 an angle ( #ai #bh4af ,?is angle c be ?us set (f3 ,draw a circle 7see ,fig4 #cf71 & produce ! diamet] ,,bc ( ?is circle = a di/ance1 ,,ca1 equal to its own l5g?4 ,f ! end ,a ( ! produc$ diamet] draw a pair ( l9es1 ,,ad1 ,,ad1 call$ tang5ts1 to t\* ! circle4 ,!n ea* ( ^! l9es w make an angle ( #ai #bh ) ! diamet]4 ,if we suppose a %ip-to be plac$ at ! po9t m>k$ ,a 9 ! diagram 7see ,fig4 #cf71 all ! e*elon waves x makes w be includ$ )9 ^! l9es ,,ad1 ,,ad4 ,illu/ration3 ,,fig4 #ce4 ,moreov]1 ! angle ( ! l9es w n alt]1 :e!r ! %ip goes fa/ or sl[4 ,?is is easily se5 9 ! case ( a duck swimm+ on a lake4 ,?r[ bits ( bread to a duck s z to induce x to swim fa/] or sl[]1 & notice ! sy/em ( incl9$ or e*elon ripples made by ! duck's body z x swims4 ,x w be se5 t ! angle at :i* ! two l9es1 includ+ bo? ! tra9s ( e*elon ripples meet ea* o!r is n alt]$ z ! duck *anges its spe$4 ,illu/ration3 ,,fig4 #cf4 ,?is e*elon sy/em ( incl9$ waves is really only a "p ( a sy/em ( waves :i* is complet$ by a transv]se gr\p 9 ! re> ( ! vessel4 ,a draw+ has be5 giv5 by ,"l ,kelv91 9 8 lecture on 8,%ip ,waves10 ( ! complete sy/em ( ^! waves1 "p ( :i* is z repres5t$ by ! firm l9es 9 ,fig4 #cg4 ,?is complete sy/em is difficult to see 9 ! case ( a real %ip mov+ ov] ! wat]4 ,! incl9$ re> sy/em ( waves c sometimes be well se5 f ! deck ( a lake /eam]1 su* z ^? on ! l>ge ,swiss or ,italian lakes1 & may sometimes be photograph$ 9 a snap-%ot tak5 ( a boy's ya*t skimm+ along on a pond4 ,illu/ration3 ,,fig4 #cg4 ,9 addition to ! incl9$ b[ waves1 !re is a simil> sy/em produc$ by ! /]n ( a vessel1 :i* is1 h[ev]1 mu* m difficult to detect4 ,! o!r two wave-sy/ems produc$ by a %ip are g5]ally call$ ! transv]se waves4 ,!re is a sy/em ( waves ^: cre/-l9es are at "r angles to ! %ip1 & !y may be se5 9 pr(ile aga9/ ! side ( any %ip or ya*t z x moves along4 ,^! transv]se waves are really due to ! unequal pressures result+ f ! di/ribution ( ! /ream-l9es del9eat+ ! movem5t ( ! wat] pa/ ! %ip4 ,if we return aga9 to ! consid]ation ( ! fl[ ( a p]fect fluid r\nd an ovoid body1 x w be rememb]$ t x 0 %[n t1 9 consequ5ce ( ! fact t ! /ream-l9es are wid] ap>t ne> ! b[ & /]n ?an !y are opposite ! middle "p ( ! body1 ! pressure 9 ! fluid 0 great] ne> ! b[ & /]n ?an at ! middle4 ,:5 a body is n :olly subm]g$1 b floats on ! surface z does a %ip1 ^! excess pressures at ! b[ & /]n reveal !mselves by =c+ up ! wat]-surface opposite ! ends ( ! vessel & l[]+ x opposite ! middle4 ,?is may be se5 on look+ at any ya*t 9 pr(ile z x sails4 ,! ya*t appe>s to re/ on two cross-waves1 "o at ! b[ & "o at ! /]n1 & mid%ips ! wat] is depress$ 7see ,fig4 #ch74 ,illu/ration3 ,,fig4 #ch4 ,^! waves move ) ! ya*t4 ,if ! %ip is a long "o1 !n ea* ( ^! waves gives rise to a wave-tra92 & on look+ at a long %ip 9 motion1 x w be se5 t1 9 addition to ! incl9$ b[ wave-sy/em1 !re is a s]ies ( waves :i* are se5 9 pr(ile aga9/ ! hull4 ,illu/ration3 ,,fig4 #ci4 ,:5 a %ip goes at a v high spe$1 z 9 ! case ( torp$o-boat de/roy]s1 ! b[ ( ! vessel is g5]ally =c$ "r up on to ! top ( ! front transv]se waves1 & ! boat moves along ) its nose entirely out ( wat] 7see ,fig4 #ci74 ,9 fact1 ! boat is1 s to speak1 always go+ uphill1 ) its b[s re/+ on ! side ( a wave :i* advances ) x1 & its /]n foll[$ by ano!r wave1 :il/ beh9d x is left a cont9ually l5g!n+ trail ( waves1 :i* are produc$ by ^? :i* move ) ! boat4 ,! be/ way to see all ^! diff]5t gr\ps ( %ip-waves is to t[ a r l>ge model %ip )\t ma/s or sails--9 fact1 a m]e hulk--ov] smoo? wat] 9 a canal or lake4 ,let "o p]son c>ry a r long pole1 to ! end ( :i* a /r+ is ti$2 & by means ( ! /r+ let ! model %ip be pull$ ?r\gh ! wat]4 ,let ?is p]son run along ! banks ( ! canal or lake1 & t[ ! %ip /eadily ?r\gh ! wat] z f> z possible at a con/ant spe$4 ,let ano!r p]son1 provid$ ) a h& cam]a1 be r[$ 9 a boat aft] ! model1 & keep a few y>ds beh9d4 ,! second obs]v] w be able to photograph ! sy/em ( %ip-waves made by ! model1 & secure v>i\s photographs :5 ! model %ip is t[$ at diff]5t rates4 ,! e*elon & transv]se waves %\ld !n be cle>ly visible1 & if ! wat] is smoo? & ! light good1 x is n difficult to secure _m useful photographs4 ,by ?r[+ bits ( bread to ducks & swans disport+ !mselves on /ill wat]1 !y also may be induc$ to take active ex]cise 9 ! "r direction1 & expose !mselves & ! waves or ripples t !y make to ! l5s ( a h& cam]a or pocket kodak4 ,f a collection ( snap-%ot photographs ( ^! objects ! "y inve/igator w le>n mu* ab\t ! =m ( ! waves made by %ips1 & w see t !y are a necess>y accompanim5t ( ! movem5t ( e float+ object on wat]4 ,by conduct+ exp]im5ts ( ! above k9d "u su* conditions z w enable ! exact spe$ ( ! model to be det]m9$1 & ! resi/ance x exp]i5ces 9 mov+ ?r\gh ! wat]1 in=mation has be5 accumulat$ ( ! utmo/ value to %ipbuild]s4 ,our sci5tific k ( ! laws ( %ip-resi/ance we owe *iefly to ! lab\rs ( two great eng9e]s1 ,mr4 ,scott ,russell & ,mr4 ,william ,fr\de4 ,mr4 ,fr\de's "w 0 begun privately at ,torquay ab\t ! ye> #ahgj1 & 0 subsequ5tly cont9u$ by him = ! ,briti% ,admiralty4 ,mr4 ,fr\de 0 ! fir/ to %[ ! value & utility ( exp]im5ts made ) model %ips dragg$ ?r\gh ! wat]4 ,he con/ruct$ at ,torquay an exp]im5t tank ab\t #bjj feet 9 l5g?1 :i* 0 a sort ( cov]$ swimm+-ba?1 & he employ$ = 8 exp]im5ts model %ips made ( wood or p>aff9 wax1 ! latt] be+ *os5 because ! model c\ld be s easily cut to ! desir$ %ape1 & all ! *ips & ! model itself c\ld be melt$ up & us$ ov] aga9 = subsequ5t exp]im5ts4 ,)\t detail+ 9 hi/oric ord] 8 discov]ies1 suffice x to say t1 z ! outcome ( 8 "w1 ,mr4 ,fr\de 0 able to /ate two v important laws :i* relate to ! relative resi/ance exp]i5c$ :5 two models ( diff]5t sizes are dragg$ ?r\gh ! wat] at diff]5t spe$s4 ,! fir/ ( ^! relates to :at is call$ ! 8correspond+ spe$s40 ,suppose we h a real %ip #bej feet long1 & we make an exact model ( ?is %ip #aj feet long1 !n ! %ip is tw5ty-five times long] ?an ! model4 ,mr4 ,fr\de's law ( correspond+ spe$s is z foll[s3-- ,if ! above model & ! %ip are bo? made to move ov] /ill wat]1 ! %ip go+ five times z fa/ z ! model1 ! sy/em ( waves made by ! model w exactly reproduce on a small] scale ! sy/em ( waves made by ! %ip4 ,9 o!r words1 if we 7 to take a c\ple ( photographs1 "o ( ! %ip go+ at #bj miles an h\r1 & "o ( ! model "o tw5ty-fif? ( its size go+ at #d miles an h\r1 & r$uce ! two photographs to ! same size1 !y w\ld be exactly alike 9 e detail4 ,express$ 9 m precise language1 ! fir/ law ( ,fr\de is z foll[s3 ,:5 a %ip & a model ( x move ?r\gh smoo? wat] at su* spe$s t ! spe$ ( ! %ip is to ! spe$ ( ! model z ! squ>e root ( ! l5g? ( ! %ip is to ! squ>e root ( ! l5g? ( ! model1 !n ^! spe$s are call$ 8correspond+ spe$s40 ,at correspond+ spe$s ! wave-mak+ p[] ( ! model resembles t ( ! %ip on a r$uc$ scale4 ,if we call ,l & l ! l5g?s ( ! %ip & ! model1 & ,s & s ! spe$s ( ! %ip & ! model1 !n we h-- ,s_/s 7,l_/l7 :]e ,s & s are call$ correspond+ spe$s4 ,mr4 ,fr\de !n e/abli%$ a second law ( equal importance1 relat+ to t "p ( ! :ole resi/ance due to wave-mak+ exp]i5c$ by a %ip & a model1 or by two models :5 mov+ at correspond+ spe$s4 ,mr4 ,fr\de's second law is z foll[s3 ,if a %ip & a model are mov+ at 8correspond+ spe$s10 !n ! resi/ances to motion due to wave-mak+ are proportional to ! cube ( _! l5g?s4 ,to employ ! example giv5 above1 let ! %ip be #bej feet long & ! model #aj feet long1 !n1 z we h se51 ! correspond+ spe$s are z #e to #a1 s9ce ! l5g?s are z #be to #a4 ,if1 !re=e1 ! %ip is made to move at #bj miles an h\r1 & ! model at #d miles an h\r1 ! resi/ance exp]i5c$ by ! %ip due to wave-mak+ is to t exp]i5c$ by ! model z ! cube ( #be is to ! cube ( #a1 or 9 ratio ( #ae1fbe to #a4 ,9 symbols ! second law may be express$ ?us3 ,let ,r be ! resi/ance due to wave-mak+ exp]i5c$ by ! %ip1 & r t ( ! model :5 mov+ at correspond+ spe$s1 & let ,l & l be _! l5g?s z be=e2 !n-- ,r_/r ,l#c_/l#c ,be=e ^! laws c\ld be appli$ 9 ! design ( real %ips1 x 0 necess>y to make exp]im5ts to asc]ta9 ! sk9 friction ( diff]5t k9ds ( surfaces :5 mov+ ?r\gh wat] at v>i\s spe$s4 ,mr4 ,fr\de's exp]im5ts on ?is po9t 7 v ext5sive4 ,= example1 he %[$ t ! sk9 friction ( a clean copp] surface su* z =ms ! %ea?+ ( a %ip may be tak5 to be ab\t "o qu>t] ( a p\nd p] squ>e foot ( wett$ surface :5 mov+ at #fjj feet a m9ute4 ,?is is equival5t to say+ t a surface ( #d squ>e feet ( copp] mov$ ?r\gh wat] at ! rate ( #aj feet a second exp]i5ces a resi/+ =ce equal to ! weight ( #a lb4 due entirely to sk9 friction4 ,v r\ghly speak+1 ?is sk9 resi/ance increases z ! squ>e ( ! spe$4#ag ,?us at #bj feet p] second ! sk9 friction ( a surface ( #d squ>e feet ( copp] w\ld be #d lbs41 & at #cj feet p] second x w\ld be #i lbs4 ,any r\ghness ( ! copp] surface1 h[ev]1 greatly increases ! sk9 friction1 & 9 ! case ( a %ip ! accumulation ( b>nacles on ! copp] %ea?+ has an imm5se effect 9 l[]+ ! spe$ ( ! vessel by increas+ ! sk9 friction4 ,h5ce ! necessity = p]iodically clean+ ! %ip's bottom by scrap+ (f ^! cl++ gr[?s ( seawe$ & b>nacles4 ,mr4 ,fr\de also made _m exp]im5ts on surfaces ( p>aff9 wax1 because ( ?is mat]ial 8 %ip models 7 made4 ,x may suffice to say t ! sk9 friction 9 ?is case1 9 fre% wat]1 is su* t a surface ( #f squ>e feet ( p>aff9 wax1 mov+ at a spe$ ( #djj feet p] m9ute1 w\ld exp]i5ce resi/ance equal to ! weight ( #a lb4 ,!re are1 h[ev]1 c]ta9 corrections :i* h to be appli$ 9 practice to ^! rules1 dep5d+ ^u ! l5g? ( ! imm]s$ surface4 ,! mean spe$ ( ! wat] pa/ ! model or %ip-surface dep5ds on ! =m ( ! /ream-l9es next to x1 & x has already be5 %[n t ! velocity ( ! wat] next to ! %ip is n ! same at all po9ts ( ! %ip-surface4 ,x is great] ne> ! c5tre ?an at ! ends4 ,h5ce ! long] ! model1 ! less is ! mean resi/ance p] squ>e foot ( wett$ surface due to sk9 friction :5 ! model is mov$ at "s con/ant spe$ ?r\gh ! wat]4 ,! above explanations w1 h[ev]1 be suffici5t to enable ! read] to und]/& 9 a g5]al way ! problem to be solv$ 9 design+ a %ip1 especially "o int5d$ to be mov$ by /eam-p[]4 ,if a %ipbuild] accepts a contract to build a /eam]--say a pass5g]-/eam] = cross-,*annel s]vices--he is put "u obligation to provide a %ip capable ( travell+ at a /at$ spe$4 ,?us1 = in/ance1 he may und]take to gu>antee t ! /eam] %all be able to d #bj knots 9 smoo? wat]4 ,9 ord] to fulfil ?is contract he mu/ be able to asc]ta9 be=eh& :at eng9e-p[] to provide4 ,=1 if ! eng9e-p[] is insuffici5t1 he may fail to c>ry out 8 contract1 & ! %ip may be return$ on 8 h&s4 ,or if he goes to ! opposite extreme & supplies too l>ge a m>g9 ( p[]1 he may lose money on ! job1 or else he may aga9 violate 8 contract by provid+ an eng9e & boil] too extravagant 9 fuel4 ,x is 9 solv+ ! above k9d ( practical problem t ,mr4 ,fr\de's me?ods ( exp]im5t+ ) models 9 a tank are ( su* imm5se value4 ,! fir/ ?+ t ! naval ar*itect does 9 design+ a %ip is to prep>e a s]ies ( draw+s1 %[+ ! =m ( ! hull ( ! vessel4 ,f ^! draw+s a model is con/ruct$ exactly to scale4 ,9 ,engl&1 foll[+ ,mr4 ,fr\de's practice1 ^! models are usually made ( p>aff9 wax1 ab\t #ab or #ad feet long & #a in* 9 ?ickness4 ,9 ! ,unit$ ,/ates wood is us$4 ,^! models are con/ruct$ ) elaborate c>e & by ! aid ( special ma*9]y1 & are g5]ally #aj or #ab feet 9 l5g?1 & "s prop] fraction ( ! l5g? ( ! real vessel !y repres5t4 ,! models are !n plac$ 9 a tank & exp]im5ts are made1 ! object ( :i* is to asc]ta9 ! =ce or 8pull0 requir$ to drag ! model ?r\gh ! wat] at v>i\s spe$s4 ,! tank belong+ to ! ,briti% ,admiralty is at ,hasl>1 ,gosport1 ne> ,portsm\?1 & ! exp]im5ts are n[ conduct$ !re by ,mr4 ,e4 ,edmund ,fr\de1 :o cont9ues ! sci5tific "w & inve/igations ( 8 di/+ui%$ fa!r1 ,mr4 ,william ,fr\de4 ,?is ,admiralty tank at ,hasl> is #djj feet 9 l5g?4 ,! well-kn[n firm ( %ipbuild]s1 ,messrs4 ,d5ny ,bros41 ( ,dumb>ton1 ,scotl&1 h also a private exp]im5tal tank ( ! same k9d4 ,! ,gov]nm5t ( ! ,unit$ ,/ates ( ,am]ica h a simil> tank at ,wa%+ton1 ! ,italian ,gov]nm5t h "o at ,spezzia1 & ! ,russian ,admiralty has also made "o4 ,^! tanks resemble l>ge swimm+-ba?s1 :i* are ro($ ov] 7see ,fig4 #dj74 ,illu/ration3 ,,fig4 #dj4--;,an exp]im5tal tank = te/+ %ip models 7,wa%+ton74#ah ,ov] ! wat]-surface is arrang$ a pair ( rails1 on :i* runs a light c>riage or plat=m4 ,?is c>riage is drawn along by a rope atta*$ to a /eam-eng9e1 :i* moves at a v uni=m rate1 & its spe$ c be exactly asc]ta9$ & automatically record$4 ,?is mov+ c>riage has a rod or lev] dep5d+ f x1 to :i* ! model %ip is atta*$4 ,! pull on ?is rod is exactly regi/]$ on a mov+ /rip ( pap] by v delicate record+ me*anism4 ,! exp]im5t is conduct$ by plac+ ! model at "o end ( ! tank1 & tak+ a run at kn[n & con/ant spe$ to ! o!r end4 ,! exp]im5tali/ is ?us able to discov] ! total resi/ance :i* x is necess>y to ov]come 9 pu%+ ! model %ip at a c]ta9 kn[n spe$ ?r\gh ! wat]4 ,! imm]s$ surface ( ! model be+ measur$ & ! necess>y calculations made1 he c !n d$uct f ! total resi/ance ! resi/ance due to sk9 friction1 & ! residue gives ! resi/ance due to wave-mak+4 ,suppose1 !n1 t ! exp]im5t has be5 p]=m$ ) a model ( a %ip yet to be built1 ! run be+ tak5 at a 8correspond+ spe$40 ,! obs]vations w give ! wave-mak+ resi/ance ( ! model1 & f ,mr4 ,fr\de's second law ! wave-mak+ resi/ance ( ! real %ip is pr$ict$4 ,add+ to ?is ! calculat$ sk9-friction resi/ance ( ! real %ip1 we h ! pr$et]m9$ actual total %ip-resi/ance at ! /at$ spe$4 ,= ! sake ( giv+ precision to ^! ideas1 x may be well to give an outl9e ( ! calculations = a real %ip1 z giv5 9 a pamphlet by ,mr4 ,ar*ibald ,d5ny4#ai ,! tank at ! ,lev5 %ipy>d1 con/ruct$ by ,messrs4 ,d5ny ,bros4 = _! own exp]im5ts1 is #cjj feet long1 #bb feet wide1 & #aj feet deep1 & conta9s #aejj tons ( fre% wat]4 ,at ea* end are two %all[] p>ts :i* s]ve z docks = balla/+ & trimm+ models4 ,z an example ( ! use ( ! tank 9 pr$ict+ ! p[] requir$ to drive a %ip ( c]ta9 design ?r\gh ! wat]1 ,mr4 ,a4 ,d5ny gives ! foll[+ figures3 ,! %ip to be built 0 #bdj feet 9 l5g?1 & f ! draw+s a model 0 con/ruct$ #ab feet 9 l5g?1 or "o-tw5tie? ! size4 ,x 0 !n requir$ to pr$et]m9e ! p[] requir$ to drive ! %ip ?r\gh ! wat] at a spe$ ( #ac knots4 ,a knot1 be x rem>k$1 is a spe$ or velocity ( #a nautical mile an h\r1 or #fjhj feet p] h\r4 ,x w be se5 t ?is is n f> f #ajj feet p] m9ute4 ,by ,fr\de's fir/ law1 ! correspond+ spe$ = ! #ab-;foot model is !re=e-- #ac #fjhj_/fj 7#ab_/bdj7 #cjf feet p] m9ute ,! model 0 accord+ly dragg$ ?r\gh ! tank at a spe$ ( ne>ly #e feet p] second1 &1 aft] d$uct+ f ! total obs]v$ pull ! resi/ance due to ! calculat$ sk9 friction ( ! model1 x 0 f\nd t ! resi/ance to ! motion ( ! model at ?is spe$ due to wave-mak+ 0 #ajh lb4 ,h5ce1 by ,fr\de's second law1 ! wave-mak+ resi/ance ( ! %ip 0 pr$et]m9$ to be-- #ajh 7#bdj_/ab7c #dj_/ci #hhej lbs4 ,! la/ fraction #dj_/ci is a correct+ factor 9 pass+ f fre% wat] to salt wat]4 ,! surface ( ! propos$ %ip 0 #aj1bhj squ>e feet1 & ! sk9 friction 0 kn[n to be #aja lb4 p] squ>e foot at a spe$ ( #ace knots4 ,h5ce ! total sk9 resi/ance ( ! %ip w\ld be-- #aj1bhj #aja #dj_/ci #aj1fbj lbs4 ,add+ to ?is1 ! #hhej lbs4 = wave-mak+ resi/ance1 we h a total resi/ance ( #ai1dgj lbs4 pr$et]m9$ z ! total pressure requir$ to be ov]come 9 mov+ ! %ip at a spe$ ( #ace knots4 ,h5ce1 s9ce #a horse-p[] is def9$ to be a p[] :i* ov]comes a resi/ance ( #cc1jjj lbs4 mov$ #a foot p] m9ute1 x is easy to see t #ai1dgj lbs4 ov]come at a rate ( #ace knots repres5ts a p[] (-- 7#ai1dgj #ace #fjhj7_/7cc1jjj #fj7 #haj horse-p[] ,b n[1 9 ! case ( a screw-driv5 /eam]1 a "p ( ! p[] is lo/ 9 m]ely *urn+ up ! wat]1 & a "p 9 int]nal frictional losses 9 ! eng9e & screw-%aft4 ,x is n f> f ! tru? to say t #ej p] c5t4 ( ! appli$ eng9e-p[] is lo/ 9 useless wat]-*urn+4 ,h5ce1 = ! above /eam]1 an actual p[] ( at lea/ #afjj ,h4,p4 w\ld h to be appli$ to ! screw-%aft4 ,to all[1 h[ev]1 = ! loss ( p[] 9 friction1 & to all[ a m>g9 = em]g5cies1 x w\ld be usual to provide = su* a /eam] eng9es ( at lea/ #cjjj indicat$ horse-p[]4 ,ea* %ipbuild] has1 h[ev]1 at call a mass ( data :i* enable him1 f actual measur$ mile trials1 to det]m9e ! rates betwe5 ! calculat$ driv+ horse-p[] & ! indicat$ horse-p[] ( ! eng9es1 & s enable him1 9 ! light ( exp]i5ce1 to provide 9 any new %ip ! exact am\nt ( /eam-p[] necess>y to produce ! requir$ spe$4 ,z an in/ance ( h[ accurately ?is c be done by ! aid ( ! tank exp]im5ts1 ,mr4 ,a4 ,d5ny gives an example drawn f exp]i5ce 9 build+ ! well-kn[n paddle-/eam]s ,pr9cess ,joseph9e & ,pr9cess ,h5riette = ! ,belgian ,gov]nm5t ,dov] to ,o/5d fa/ mail-/eam] s]vice4 ,! spe$ gu>ante$ be=e ! boats 7 built 0 #bj knots4 ,! e/imate 0 made = #ba knots1 & ! actual results ( trials on ! measur$ mile1 :5 ! %ips 7 built1 %[$ t ea* did #baa knots on prolong$ & sev]e te/4 ,! read]1 !re=e1 _c fail to see h[ important are ^! me?ods1 laws1 & rese>*es ( ,mr4 ,fr\de4 ,! above-describ$ process = te/+ models is be+ cont9ually conduct$ 9 ! case ( all new battle%ips & cruis]s = ! ,briti% ,navy1 & also is pursu$ by ! naval con/ructors ( o!r nations4 ,9 connection ) ! ext5sive programme ( battle%ip con/ruction :i* has be5 c>ri$ out ( late ye>s1 ,sir ,william ,:ite1 ! late em95t ,*ief ,director ( ,naval ,con/ruction1 /ates t x is n too mu* to say t ^! me?ods ( inve/igation & exp]im5t h plac$ 9 ! h&s ( ! naval ar*itect an in/rum5t ( imm5se p[] = guid+ him safely & prev5t+ co/ly mi/akes4 ,sir ,william ,:ite has decl>$ t x w\ld h be5 impossible to proce$ ) ! same c]ta9ty 9 battle%ip design1 7 x n = ! aid af=d$ by ^! me?ods4 ,mr4 ,fr\de 0 n cont5t1 h[ev]1 ) exp]im5ts made ) models4 ,he asc]ta9$ by actual trials ! total =ce requir$ to drive an actual %ip ?r\gh ! wat] at v>i\s spe$s1 & obta9$ f o!r exp]im5ts valuable data :i* %[$ ! proportion 9 :i* ! total resi/ance (f]$ to ! %ip 0 divid$ betwe5 ! sk9 friction & ! wave-mak+ resi/ance4 ,!n he made exp]im5ts on a %ip ( #aaeg tons1 viz4 ,h4,m4,s4 ,greyh\nd4 ,?is vessel 0 t[$ by ano!r vessel ( #cjgh tons1 viz4 ,h4,m4,s4 ,active1 by means ( a t[-rope & a dynamomet]1 :i* enabl$ ! exact 8pull0 on ?is haws] to be asc]ta9$ :5 ! ,greyh\nd 0 t[$ at c]ta9 spe$s4 ,! foll[+ are "s ( ! results obta9$3-- ,spe$ 9 knots ,/ra9 9 tons ( ,h4,m4,s4 ,greyh\nd4 on t[+-rope4 #d knots #jf tons #f 0 #ad 0 #h 0 #be 0 #aj 0 #dg 0 #ab 0 #ij 0 ,x w be se5 t ! total resi/ance increases v rapidly ) ! spe$1 v>y+ 9 a high] ratio ?an ! squ>e ( ! spe$4 ,9 addition1 ! indicat$ horse-p[] ( ! eng9e ( ! ,greyh\nd 0 tak5 :5 be+ self-driv5 at ! above spe$s1 & x 0 f\nd t only #de p] c5t4 ( ! indicat$ horse-p[] ( ! eng9es 0 us$ 9 propell+ ! %ip1 ! rema9+ #ee p] c5t4 be+ wa/$ 9 eng9e & %aft friction & 9 useless *urn+ ( ! wat] by ! screw4 ,x is an important ?+ to "k h[ ?is total resi/ance is divid$ betwe5 sk9 friction & wave-mak+ resi/ance4 ,mr4 ,r4 ,e4 ,fr\de has k9dly furni%$ ! au?or1 ?r\gh ! int]m$iation ( ,sir ,william ,:ite1 ) "s figures obta9$ f exp]im5ts at ,hasl>1 %[+ ! proportion ( ! :ole %ip-resi/ance :i* is due to sk9 friction = v>i\s classes ( %ips go+ at c]ta9 spe$s4 ,at full spe$4 ,at #aj knots4 ,battle%ips #ee p] c5t4 #gi p] c5t4 ,cruis]s #ee 0 #hd 0 ,torp$o-boat de/roy]s #dc 0 #hj 0 ,! above table gives ! p]c5tage :i* ! sk9 friction =ms ( ! total resi/ance1 & ! rema9d] is1 ( c\rse1 wave-mak+ & eddy-resi/ance4 ,! curves %[n 9 ,fig4 #da 7tak51 by k9d p]mission ( ! editor1 f an article by ,mr4 ,e4 ,h4 ,t5nyson-,d',eync\rt1 9 ,cassi]'s ,magaz9e = ,novemb]1 #aija7 give1 9 a diagrammatic =m1 an idea ( ! mann] 9 :i* ! two pr9cipal s\rces ( %ip-resi/ance v>y ) ! spe$4 ,illu/ration3 ,,fig4 #da4--7,reproduc$1 by p]mission1 f ,cassi]'s ,magaz9e47 ,x w be se5 t :5 a %ip is go+ at a relatively sl[ spe$1 ! great] portion ( ! :ole resi/ance is due to sk9 friction1 b :5 go+ at a high spe$1 ! great] portion ( ! resi/ance is due to wave-mak+4 ,h5ce ! moral is t %ips & boats int5d$ to move at a high spe$ mu/ be s fa%ion$ z to r$uce to a m9imum ! wave-mak+ p[]4 ,9 g5]al1 ! naval ar*itect has to consid] _m o!r matt]s besides spe$4 ,9 battle%ip design he has to consid] /ability1 p[] ( c>ry+ guns & arm\r1 & v>i\s o!r qualities4 ,9 pass5g]-/eam]s he has to take into consid]ation capacity = pass5g]s & freight1 also /ead9ess & sea-go+ qualities2 & all ^! ?+s limit & control ! design4 ,!re is "o class ( vessel1 h[ev]1 9 :i* ev]y?+ is sacrific$ to spe$1 & t is 9 rac+-ya*ts4 ,h5ce1 9 ! design ( a rac+-ya*t1 ! ar*itect has mo/ scope = consid]ations :i* be> *iefly ^u ! removal ( all limitations to spe$4 ,a little exam9ation1 !re=e1 ( ! evolution ( ! mod]n rac+-ya*t %[s h[ ! pr9ciples we h endeav\r$ to expla9 h _h full sway 9 det]m9+ ! pres5t =m ( su* boats4 ,att5tion has *iefly be5 direct$ to ?is matt] 9 connection ) ! int]national ya*t race = ! possession ( ! ,am]ica ,cup4 ,9 #ahea a ya*t nam$ ! ,am]ica cross$ ! ,atlantic & made h] appe>ance at ,c[es to compete = a cup giv5 by ! ,royal ,ya*t ,squadron4 ,up to t "t ,briti% ya*ts _h be5 design$ ) full bluff b[s & a tap]+ run aft4 ,^! boats 7 good sea-boats1 b _! wave & eddy mak+ p[]s 7 consid]able4 ,! ,am]ica 0 con/ruct$ ) v f9e l9es & a %>p b[1 & 0 a great advance on exi/+ types ( ya*t4 ,9 ! race :i* ensu$ ! ,am]ica won ! cup1 & c>ri$ x (f to ! ,unit$ ,/ates4 ,s9ce t date !re has be5 an int]mitt5t b /eady ef=t on ! "p ( ,briti% ya*tsm5 to recov] ! trophy1 s f>1 h[ev]1 )\t success4 ,illu/ration3 ,,am]ica1 #ahea4 ,,vigilant1 #ahic4 ,,puritan1 #ahhe4 ,,def5d]1 #ahie4 ,,volunte]1 #ahhg4 ,,columbia1 #ahii4 ,unit$ ,/ates ya*ts ent]$ = ! ,am]ica ,cup race1 #ahea-ahii4 7,,fig4 #db47 ,illu/ration3 ,,g5e/a1 #ahhe4 ,,valkyrie ,,iii41 #ahie4 ,,?i/le1 #ahhg4 ,,%amrock1 #ahii4 ,,valkyrie ,,ii41 #ahic4 ,,%amrock ,,ii41 #aija4 ,,fig4 #db4--;,briti% ya*ts ent]$ = ! ,am]ica ,cup race1 #ahhe-aija4 ,9 a v int]e/+ article 9 ,h>mswor?'s ,magaz9e1 9 #aija1 ,mr4 ,e4 ,goodw9 has trac$ ! gradual evolution ( ! mod]n ya*t1 su* z ,%amrock ,,ii4 or ! ,columbia1 f ! ,am]ica4 ,no d\bt ! me?ods ( 8measurem5t0 9 =ce at ! "t1 or ! dim5sions :i* det]m9e :e!r ! boat c ent] = ! ,cup race or n1 h _h "s influ5ce 9 settl+ ! %ape4 ,! read]1 h[ev]1 w see1 on comp>+ ! outl9es ( "s ( ! compet+ ya*ts z %[n 9 ,fig4 #db1bj t !re has be5 a gradual t5d5cy to r$uce ! und]wat] surface z mu* z possible1 & also to remove ! wave-mak+ t5d5cy by ov]hang+ ! b[s4 ,! only rule n[ 9 =ce re/rict+ ! ya*t size = ! ,cup race is t x mu/ n be m ?an #ij feet 9 l5g? :5 measur$ on ! wat]-l9e4 ,9 ord] t ! ya*t may h /ability1 & be able to c>ry a l>ge sail-surface1 x mu/ h a c]ta9 dep? ( imm]s$ hull4 ,?is is ess5tial also to prev5t ! boat f mak+ leeway :5 sail+ ) ! w9d abeam4 ,b consi/5tly ) ?is object1 ! two great aims ( ! ya*t-build] are1 fir/1 to r$uce z mu* z possible ! sk9 friction by mak+ ! ya*t-surface smoo? & highly poli%$4 ,?us mod]n rac+-ya*ts are n always built ( wood1 b v (t5 ( "s metal1 su* z bronze1 /eel1 or alum9ium alloys1 :i* admit ( a v high poli%4 ,?is hull-surface is burni%$ z mu* z possible be=e ! race1 to r$uce to a m9imum ! sk9 friction4 ,!n 9 ! second place1 ! design] aims at fa%ion+ ! =m ( ! b[ ( ! ya*t s z to r$uce z mu* z possible its wave-mak+ qualities4 ,a f9e type ( mod]n ya*t glides ?r\gh ! wat] ) h>dly any p]ceptible b[ wave at mod]ate spe$s4 ,?us ! foll[+ extract f ! ,*icago ,record] ( ,septemb] #d1 #aija1 respect+ ,sir ,?omas ,lipton's ya*t1 ,%amrock ,,ii41 dur+ h] trials = ! ,cup race1 %[s h[ m>k$ a feature ?is is 9 ! case ( a ya*t ( ! be/ mod]n type3-- 8,) h] own]1 design]1 build]1 manag]1 & sailmak] on bo>d1 ! ya*t ,%amrock ,,ii4 sail$ h] sev5? trial race to-day (f ,s&y ,hook4 ,al?\gh at times !re 0 n m ?an a ?ree-knot air1 at no "t did ! ya*t act sluggi%ly4 8,%e slipp$ ?r\gh ! wat] at an amaz+ly good rate "u ! influ5ce ( h] great ma9sail & light sails4 ,! wat] 0 smoo?1 b ev5 :5 press$ to a spe$ ( #i knots ! ya*t made a v small wave at ! b[1 & left an absolutely clean wake40 ,we may say1 !re=e1 t ! ideal =m ( ya*t is "o :i* w\ld travel ?r\gh ! wat] )\t mak+ any wave at all at b[ or /]n4 ,?is condition c1 h[ev]1 only be rea*$ approximately1 b ! cle> recognition ( ! pr9ciple has enabl$ ya*ts to be design$ ) va/ly great] spe$ p[]s ?an 9 ! old days ( bluff b[s & tap]+ bodies4 ,be=e pass+ away f ! subject ( waves made by %ips1 x is desirable to ref] a little m 9 detail to ! complicat$ wave-sy/em made by a %ip 9 motion4 ,?is has be5 mo/ c>efully elucidat$ by ,"l ,kelv91 :o1 9 ?is z 9 s _m o!r matt]s1 is our great tea*]4 ,"l ,kelv9 has %[n t if a small float+ body is t[$ ?r\gh ! wat] at a uni=m spe$1 x orig9ates a sy/em ( waves1 ea* "o ( :i* is ( ! =m %[n 9 ,fig4 #dc4 ,! :ole sy/em ( waves =m$ is repres5t$ 9 ,fig4 #cg1 :]e ! position ( ! %ip or mov+ object is at ! po9t m>k$ ,a4 ,! key to a correct compreh5sion ( ?is %ip wave-sy/em is to be f\nd 9 ! fact expla9$ 9 ,*apt] ,i41 t a gr\p ( wat] waves on an indef9itely ext5d$ wat] surface advances at half ! spe$ ( a s+le wave4 ,x has already be5 %[n t :5 a s+le wave-di/urbance is made ^u wat] x gradually develops itself into a gr\p ( waves4 ,! s+le wave :5 creat$ causes a di/urbance on wat] :i* ext5ds bo? =w>ds & backw>ds4 ,z ! wave moves =w>d ! wave-di/urbance is always gr[+ 9 front & dy+ away beh9d1 & ! wave-gr\p !re=e moves =w>d1 b ! c5tre or limits ( ! gr\p move ) only half ! velocity ( a s+le wave4 ,illu/ration3 ,,fig4 #dc4 ,n[ consid] ! %ip orig9ally at ,b 7see ,fig4 #cf71 & let u suppose ! %ip to make a small j]k =w>d4 ,?is op]ation is l plung+ a /one into ! wat]1 & x />ts a wave-sy/em4 ,b if ! %ip moves =w>d ) a uni=m spe$1 by ! "t ! %ip has rea*$ ! po9t ,a1 ! end ( ! wave-gr\p w h rea*$ a po9t ,c1 su* t ,c is halfway betwe5 ,b & ,a4 ,! movem5t ( ! %ip1 h[ev]1 orig9ates a gr\p ( waves1 & ! velocity ( a wave on wat] is dep5d5t ^u its wave-l5g?1 z already expla9$1 s t ! great] ! wave-l5g? ! great] ! velocity4 ,h5ce ! conditions t det]m9e ! =m ( ! wave-sy/em r\nd ! %ip are3 7#a7 t ! head ( ! procession goes =w>d ) ! spe$ ( ! %ip2 7#b7 t !re is an end or limit to ! transv]se sy/em ( waves beh9d1 :i* moves =w>d ) half ! spe$ ( ! %ip2 7#c7 ! incl9ation ( ! wave at any po9t to ! direction ( motion ( ! %ip mu/ be su* t its velocity1 9 its own direction1 is consi/5t ) ! wave-l5g? at t place4 ,^! g5]al conditions det]m9e ! =m ( ! wave-gr\p z %[n 9 ,fig4 #cg2 b ! detail$ pr$et]m9ation ( ! exact =m ( ! oblique & re> wave _c be made )\t ! employm5t ( ma!matical reason+ ( a some:at advanc$ "*4 ,= ! purposes ( ! g5]al read] x w be suffici5t to note t ?is procession ( ev]-ext5d+ waves1 :i* l5g!ns backw>ds beh9d a %ip1 requires en]gy to produce x4 ,?is en]gy mu/ be suppli$ f ! %ip1 & ! wave-production con/itutes !re=e a cause ( resi/ance to motion :i* is felt & has to be ov]come 9 keep+ ! spe$ ( ! %ip con/ant4 ,9 close connection ) ?is subject is ! f9e inve/igation made ab\t ! ye> #ahcd by ano!r em95t eng9e]1 ,mr4 ,scott ,russell1 on ! motion ( canal-boats4 ,8 rese>*es 7 communicat$ to ! ,royal ,society ( ,ed9burgh4 ,x has already be5 expla9$ t :5 a wave is />t$ 9 a canal1 ! wave-l5g? be+ l>ge comp>$ ) ! dep? ( ! canal1 !n ! velocity ( ! long wave is ! same z t atta9$ by a /one 9 fall+ ?r\gh air a di/ance equal to half ! dep? ( ! canal4 ,scott ,russell made ! int]e/+ discov]y t x is only :5 ! spe$ ( a canal-boat is less ?an t ( a long wave 9 ! canal t ! boat leaves beh9d x a procession ( waves4 ,! position ( ! boat is !n on ! re>w>d side ( ! fir/ wave4 ,z already m5tion$1 ! boat leaves beh9d x a trail ( waves1 & ! re> ( ?is procession travels =w>d at half ! spe$ ( ! boat4 ,if ! spe$ ( ! boat is great] ?an t ( ! longe/ free wave 9 t canal1 x _c make any procession ( waves1 & !n !re w\ld be no sy/em ( ev]-l5g!n+ waves beh9d x1 b only "o wave or hummock travell+ along "u ! boat4 ,"l ,kelv9 describes1 9 8 lecture on 8,%ip ,waves10#ba h[ ?is important discov]y 0 9 fact made by a horse4 ,! horse belong$ to "o ,william ,h\/on1 & its daily duty 0 to drag a canal-boat on ! ,glasg[ & ,ardrossan ,canal4 ,on "o occasion ! horse took fright & gallop$ (f1 & ,h\/on1 be+ an obs]vant man1 notic$ t :5 once ! horse _h atta9$ a c]ta9 spe$ ! tractive resi/ance evid5tly became less5$1 & ! boat 0 dragg$ along m easily & )\t wa% beh9d x4 ,accord+ly1 he />t$ a sy/em ( light canal-boats--or fly-boats1 z !y 7 call$--ea* #fj feet long1 & drawn by two horses at #g1 #h1 or #i miles an h\r4 ,! horses 7 :ipp$ up & made to gallop1 & soon dragg$ ! boat up on to ! top ( its own wave1 :]eupon x w5t along mu* m easily1 & )\t a sy/em ( /]n waves4 ,mr4 ,scott ,russell in/itut$ a se>*+ inve/igation into ?is effect 9 #ahcg at ! bridge ( ,h]mi/on1 on ! ,=? & ,clyde ,canal1 at a place :]e !re 0 a /raight run ( #aejj feet4 ,! dep? ( ! canal wat] 0 #d to #e feet1 & ! spe$ ( ! long wave 0 accord+ly #ab feet p] second1 or #h miles an h\r4 ,exp]im5ts 7 made1 among/ o!rs1 ) a boat call$ ,rai?1 ! weight ( :i* 0 #aj1bci lbs41 or #e tons4 ,?is boat 0 t[$ along ! canal1 & ! 8pull0 on ! t[-rope measur$ by means ( an in/rum5t call$ a dynamomet]4 ,x 0 f\nd by ,mr4 ,scott ,russell t ! pull or =ce requir$ to drag ! boat did n increase ) ! spe$ regul>ly1 b fell (f 9 a m>k$ mann] :5 ! spe$ ( ! boat rea*$ #i miles p] h\r4 ,?is is %[n by ! foll[+ table3-- ,,scott ,,russell',s ,,exp]im5ts ,,on ,,canal-,,boats4 ,tractive =ce 9 p\nds ,spe$ ( boat 9 miles appli$ to boat4 p] h\r4 #aab #dgb #bfa #eib #bge #fai #bej #ijd #bfi #ajdh ,= ano!r boat-weigh+ #ab1egi lbs41 or #f tons1 ! results obta9$ 9 ! same mann] 7 z foll[s3-- ,tractive =ce 9 p\nds4 ,spe$ 9 miles p] h\r4 #bej #fai #ejj #geg #djj #heb #bhj #ijd ,?is la/ exp]im5t %[s1 9 a v rem>kable mann]1 ! way 9 :i* ! =ce requir$ to drag ! boat falls (f z ! critical spe$ ( #i miles an h\r is rea*$4 ,"h1 !n1 we h ! outl9es ( ! pro( fir/ giv5 by ,mr4 ,scott ,russell1 t ! tractive =ce und]goes a sudd5 dim9ution :5 ! spe$ ( ! boat 9 a canal approximates to or j exce$s t ( ! long wave 9 t p>ticul> dep? ( wat]4 ,if pass5g] traffic on canals _h n be5 de/roy$ by ! adv5t ( railways1 we %\ld1 no d\bt1 h se5 ext5sive applications ( ! pr9ciple discov]$ s curi\sly by ! aid ( an al>m$ horse1 & s skilfully inve/igat$ by a celebrat$ eng9e]4 ,! :ole !ory ( ! trail ( waves made by a canal-boat is only compreh5sible if x is cle>ly se5 t a wat]-surface wave has a c]ta9 velocity det]m9$ by its wave-l5g?4 ,if ! wave-spe$ is small1 ! waves are %ort4 ,z ! spe$ increases ! waves get long]4 ,or ! matt] may be put 9 ano!r way4 ,we may say t j z a p5dulum has a c]ta9 rate ( vibration dep5d+ on its l5g?1 s a wat] wave has a c]ta9 frequ5cy1 & !re=e1 a c]ta9 spe$ ( propagation dep5d5t ^u ! wave-l5g?1 or %orte/ di/ance f "o wave-cre/ to ! next4 ,:5 a boat moves along a canal ! waves x makes move ) x1 & ! fir/ wave ( all moves ) ! spe$ ( ! boat4 ,h5ce ! wave-l5g? mu/ accommodate itself to t spe$4 ,z ! spe$ ( ! boat increases t[>ds t ( ! free 8long wave10 ! wave-l5g? gets great] & great]1 & :5 ! boat-spe$ is equal to t acquir$ by a heavy body1 say a /one 9 fall+ ?r\gh half ! dep? ( ! canal1 !n !re is only "o wave1 & ! boat rides up on t "o4 ,! next wave is practically s f> beh9d t x is non-exi/5t1 & ! boat ceases to be foll[$ by any trail ( waves1 or 8wa%40 ,,*apt] ,,iii4 ,,waves ,,& ,,ripples ,,9 ,,! ,,air4 ,leav+ ! consid]ation ( waves & ripples on a wat]-surface1 we pass on to discuss ! subject ( waves & ripples 9 ! air4 ,ne>ly e "o is aw>e1 9 a g5]al way1 t s\nd is due to a di/urbance creat$ 9 ! atmosph]e4 ,few1 h[ev]1 are fully acqua9t$ ) ! nature ( ! movem5ts 9 ! air :i* excite our s5se ( he>+1 & to :i* we owe1 n only ! pleasures ( conv]sation & ! enjoym5t ( all ! s\nds 9 nature1 b ^? delights ( music :i* are among/ ! pure/ =ms ( pleasure we possess4 ,9 ! fir/ place1 x is necess>y to demon/rate ! fact t 9 a place :]e !re is no air !re c be no s\nd4 ,be=e y on ! table is a brass plate cov]$ ) a glass dome4 ,"u ! dome is a piece ( clockwork1 :i*1 :5 set 9 action1 /rikes a gong4 ,?is clockwork is susp5d$ by silk /r+s f a frame to keep x out ( contact ) ! plate4 ,! plate is 9 connection1 by a pipe1 ) an air-pump d[n/airs1 & f ! space "u ! dome we c at pleasure remove ! air4 ,be=e s do+1 h[ev]1 ! clockwork %all be set 9 motion1 s t y w !n see ! hamm] /rik+ ! gong1 & y also he> ! s\nd4 ,if n[ we exhau/ ! air1 ! s\nd rapidly dies away1 & :5 a fairly p]fect vacuum has be5 made1 :il/ y see ! hamm] cont9u+ to p\nd ! bell1 y notice t no s\nd at all rea*es y\r e>s4 ,turn+ a tap1 ,i let 9 ! air1 & once m ! r+ ( ! bell peals =?4 ,! exp]im5t %[s conclusively t s\nd is convey$ to u ?r\gh ! air1 & t if we isolate a s\nd+ body by remov+ ! air ar\nd x1 all transmission ( s\nd is /opp$4 ,ev5 r>efy+ ! air greatly weak5s ! s\nd1 = x is notic$ t an explod+ pi/ol or crack] does n create ! same int5sity ( s5sation 9 ! e> at ! top ( a v high m\nta9 z x does 9 ! valley bel[4 ,we h !n to %[1 9 ! next place1 t a sub/ance :i* is emitt+ s\nd is 9 a rapid /ate ( vibration1 or to-&-fro movem5t4 ,tak+ a tun+-=k 9 my h&1 ,i /rike its prongs aga9/ ! table1 & y he> x fa9tly s\nd+4 ,y\r unassi/$ vision w n1 h[ev]1 enable y to see t ! prongs are 9 rapid motion4 ,if1 h[ev]1 ,i hold x aga9/ a pi?-ball susp5d$ by a silk fibre1 y see by ! viol5t b\nc+ ( ! ball t ! prongs mu/ be 9 en]getic vibration4 ,ano!r exp]im5t ( ! same k9d1 :i* y c y\rselves repeat1 is to elicit a s\nd f a small table-gong by /rik+ x ) ! hamm]4 ,!n hold ne> ! surface ( ! metal a small ball ( wood or cork1 to :i* a susp5d+ ?read has be5 ti$4 ,! ball w keep jump+ f ! gong-surface 9 a mann] :i* w conv9ce y t ! latt] is 9 a /ate ( viol5t agitation4 ,! mode & ext5t ( ?is movem5t 9 a s\nd-emitt+ body mu/ next be m ?or\ghly exam9$4 ,let me expla9 ! means by :i* ,i %all make ?is analysis4 ,on ! prong ( a tun+-=k1 ,t 7see ,fig4 #dd71 is fix$ a small mirror1 ,m1 & a ray ( light is reflect$ f an electric lant]n on to ?is mirror4 ,! ray is !n reflect$ back aga9 on to a sort ( cubical box1 ,c1 ! sides ( :i* are cov]$ ) look+-glass1 & f9ally x falls ^u ! scre54 ,! mirrors are s arrang$ t if ! cubical mirror is at re/ & ! =k also1 a bright spot ( light is se5 ^u ! scre54 ,if ! =k is set 9 vibration1 !n ! spot ( light moves up & d[n s rapidly t x =ms a v]tical b> or l9e ( light ^u ! scre54 ,! cubical mirror is c>ri$ ^u an axis1 & c be set 9 rotation4 ,if ! =k is at re/ & ! cubical mirror revolves1 !n ! spot ( light m>*es horizontally across ! scre51 & :5 ! motion ( ! mirror is suffici5tly rapid x =ms a horizontal & brilliant b& ( light4 ,if1 !n1 ^! two motions are p]=m$ at ! same "t1 ! tun+-=k be+ set 9 vibration & ! cubical mirror 9 rotation1 we f9d t ! spot ( light on ! scre5 executes a wavy motion1 & we see 9 consequ5ce a s9u\s bright l9e ^u ! wall4 ,illu/ration3 ,,fig4 #dd4 ,we h "h two pr9ciples involv$1 :i* x may be bett] to expla9 a little m 9 detail4 ,an impression made ^u ! eye la/s = ab\t ! t5? "p ( a second4 ,h5ce1 if a lum9\s po9t or bright object moves suffici5tly rapidly1 we cease to be able to foll[ its movem5t1 & we receive on our eyes m]ely ! effect ( a lum9\s l9e ( light4 ,e boy sees ?is :5 he :irls r\nd a light$ squib or /ick ) a flam+ end4 ,9 ! next place1 notice t two indep5d5t movem5ts at "r angles comb9e into :at is call$ a resultant motion4 ,?us ! v]tical up-&-d[n motion ( ! spot ( light 9 our exp]im5t1 comb9$ ) its uni=m horizontal movem5t1 results 9 ! production ( a wavy motion4 ,= ! sake ( ^? :o wi% to repeat ! exp]im5t1 a few little h9ts may be giv54 ,! revolv+ cubical mirror is a some:at exp5sive piece ( app>atus1 b f\nd 9 e well-appo9t$ physical laboratory4 ,a *eap sub/itute1 h[ev]1 may be made by firmly /ick+ on to ! sides ( a wood5 box pieces ( ?9 look+-glass4 ,! box is !n to be susp5d$ by a /r+4 ,if ! /r+ is twi/$1 ! box may be set sp9n+ l a jo9t ( meat roa/+ be=e ! fire4 ,an ord9>y magic lant]n may be us$ to provide a p>allel beam ( light4 ,9 lecture demon/rations x is necess>y to employ ! electric arc lamp1 & to make use ( an arrangem5t ( l5ses to create ! requir$ p[]ful p>allel beam ( light4 ,!n z reg>ds ! =k4 ,we are employ+ "h a r elaborate contrivance call$ an electrically driv5 tun+-=k1 b = home demon/ration x is suffici5t to make use ( a s+le piece ( /\t /eel clock-spr+1 or any o!r flexible & highly temp]$ piece ( /eel4 ,?is mu/ be fix$ to a block ( wood z a support1 & to its end mu/ be fa/5$ ) c>e a small piece ( lead1 to :i* is atta*$ a fragm5t ( ?9 silv]$ glass ( ! k9d call$ a galvanomet] mirror1 :i* may be procur$ ( any sci5tific in/rum5t mak]4 ,! position ( ?is vibrat+ spr+ mu/ be su* t1 if ! spr+ vibrates alone1 x w reflect ! ray ( light on to "o face ( ! cubical mirror1 & !nce on to a :ite wall1 & create a v]tical b> ( light1 :i* becomes a spot ( light :5 ! spr+ is at re/4 ,x is possible to pur*ase v small concave mirrors ab\t half an in* 9 diamet]1 made ( glass silv]$ at ! back4 ,if "o ( ^! c be procur$1 !n !re is no ne$ to employ an optical lant]n2 ) an ord9>y table-lamp1 or ev5 a c&le z a s\rce ( light1 x is easy to focus a bright spot ( light ^u ! scre51 :i* effects ! desir$ purpose ( mak+ evid5t ! motion ( ! spr+4 ,be=e we dismiss ! exp]im5t1 let me say "o or two m words ab\t x4 ,y notice :5 x is proce$+ t ! lum9\s wavy l9e is a regul> & symmetrical "o4 ,?is %[s u t ! motion ( ! prong ( ! =k is simil>ly regul>4 ,?is k9d ( backw>ds-&-=w>ds motion is call$ an h>monic motion1 or a simple p]iodic motion4 ,x is v simil> to ! k9d ( movem5t execut$ by ! pi/on ( a /eam-eng9e z x oscillates to & fro4 ,! exact nature ( ! wavy l9e ( light y see ^u ! scre5 c be del9eat$ by a l9e drawn z foll[s3 ,on a %eet ( pap] describe a circle1 & divide its circumf]5ce into twelve equal p>ts 7see ,fig4 #de74 ,?r\gh ! c5tre & ?r\gh ea* ( ^! po9ts on ! circumf]5ce draw p>allel l9es4 ,divide up a l5g? ( ! l9e drawn ?r\gh ! c5tre into twelve equal p>ts1 & numb] ^! divisions #a to #ab4 ,numb] also ! po9ts on ! circumf]5ce ( ! circle4 ,?r\gh ! twelve po9ts on ! horizontal l9e erect p]p5dicul>s4 ,make a dot at ! int]section ( ! p]p5dicul>1 or ord9ate1 z x is call$1 drawn ?r\gh po9t #a on ! horizontal l9e1 & ! horizontal ?r\gh po9t #a on ! circumf]5ce ( ! circle4 ,d ?is = all ! twelve int]sections1 & !n c>efully draw a smoo? curve ?r\gh all ^! po9ts4 ,we obta9 a wavy curve1 :i* is call$ a s9e curve1 or simple h>monic curve1 & is ! same =m ( curve z t exhibit$ on ! scre5 9 ! exp]im5t ) ! tun+-=k & spot ( light4 ,! piece ( ! curve drawn z above is call$ "o wave-l5g? ( ! h>monic curve4 ,illu/ration3 ,,fig4 #de4--;,a simple h>monic curve4 ,9 our case ! tun+-=k is mak+ "o hundr$ complete vibrations 7to & fro7 p] second4 ,h5ce ! p]iodic "t1 or "t occupi$ by "o complete wave1 is ! hundr$? "p ( a second4 ,to realize :at ?is small int]val ( "t means1 x is suffici5t to rememb] t ! hundr$? "p ( a second is to "o second z ! duration ( ?is lecture 7"o h\r7 is to f\r days & nights4 ,! prongs ( a s\nd+ tun+-=k or ! surface ( a gong or a bell1 :5 /ruck1 are !re=e 9 rapid motion4 ,we c !n proce$ to an exp]im5t fitt$ to indicate ! diff]5ce betwe5 ^? motions 9 s\nd+ bodies :i* create musical tones1 & ^? :i* create m]e noises or vocal s\nds4 ,i h on ! table be=e me a b5t brass tube provid$ ) a m\?piece at "o end1 & ! o!r end ( ! tube is cov]$ ov] ) a v ?9 piece ( %eet indi>ubb] ti$ on l ! cov] ( a jam-pot4 ,to ! out] surface ( ?is indi>ubb] is cem5t$ a v small1 light silv]$-glass mirror4 ,! same arrangem5ts are made z 9 ! case ( ! previ\s exp]im5t1 & ! ray ( light f a lant]n is reflect$ f ! little mirror on to ! revolv+ cubical mirror1 & !nce on to ! scre54 ,sett+ ! cubical mirror 9 rotation1 we h a l9e ( bright light ^u ! scre54 ,if1 !n1 my assi/ant s+s or speaks into ! m\?piece1 ! motion ( ! indi>ubb] sets 9 vibration ! little atta*$ mirror4 ,?is mirror is n atta*$ to ! c5tre ( ! membrane1 b a little to "o side4 ,h5ce y c easily und]/& t :5 ! indi>ubb] is bulg$ 9 or out1 ! atta*$ mirror is m or less tilt$1 & ! spot ( light is displac$ up or d[n on ! scre54 ,9 ?is mann] ! movem5ts ( ! spot imitate ^? ( ! diaphragm4 ,h5ce ! =m ( ! bright l9e on ! scre5 is an indication ( ! k9d ( movem5t ! diaphragm is mak+4 ,let u !n1 9 ! fir/ place1 s+ into ! tube :il/ ! cubical mirror is uni=mly rotat$4 ,if my assi/ant s\nds a full pure note1 y w see t ! /raight l9e ( light in/antly ca/s itself into a wavy =m1 :i* is n1 h[ev]1 q ( ! same %ape z 9 ! case ( ! tun+-=k4 ,"h ! zigzag l9e resembles ! outl9e ( saw-tee? 7see ,frontispiece74 ,if he v>ies ! l\dness ( 8 s\nd1 y see ! height ( ! tee? alt]1 be+ great] ! l\d] 8 note4 ,if he *anges ! tone1 s++ a bass or a treble note1 y obs]ve t1 correspond+ to a high or treble note1 ! waves are %ort1 & correspond+ to a deep or bass note1 ! waves are long4 ,accord+ly1 ! %ape ( ! l9e ( light ^u ! scre5 gives u exact in=mation z to ! nature ( ! movem5t ( ! indi>ubb] diaphragm1 viz4 :e!r x is mov+ 9 & out1 sl[ly or quickly1 mu* or little4 ,aga91 suppose1 in/ead ( s++ into ! tube1 my assi/ant speaks a few words4 ,if1 = in/ance1 he repeats 9 a l\d tone ! simple b famili> n>rative ( 8,old ,"m ,hubb>d10 y w see t1 correspond+ to ea* ^w ( ! s5t5ce1 ! l9e ( light ^u ! scre5 b5ds itself into a peculi> irregul> =m1 & ea* p>ticul> ^w is z x 7 writt5 9 l9es ( fire ^u ! wall4 ,notice h[ c]ta9 s\nds1 su* z b & p & also t are repres5t$ by v high not*es or tee? 9 ?is l9e ( light4 ,^! s\nds are call$ explosive consonants1 & if y exam9e ! mann] 9 :i* !y are made by y\r m\?1 y w notice t x consi/s 9 clos+ ! m\? by ! lips or tongue plac$ betwe5 ! tee?1 & !n sudd5ly )draw+ ! ob/ruction s z to all[ ! air f ! lungs to ru% =cibly out4 ,h5ce ! air outside1 & 9 ?is case ! diaphragm1 receives a sudd5 bl[1 :i* is repres5t$ by ?is tall too? or not* 9 ! lum9\s b&4 ,! exp]im5t tea*es u t :]eas musical tones are caus$ by c]ta9 v regul> & uni=m vibrations ( ! s\nd+ body1 vocal s\nds & noises are caus$ by v irregul> movem5ts4 ,also t l\d s\nds are creat$ by l>ge motions1 & feeble ones by small motions4 ,aga91 t ! diff]5ce betwe5 tones 9 music is a diff]5ce 9 ! rate ( vibration ( ! s\nd+ body4 ,we may inf] also t ! diff]5ce betwe5 ! quality ( s\nds is connect$ ) ! =m ( ! wave-motion made by !m4 ,hav+ e/abli%$ ^! facts1 we mu/1 9 ! next place1 proce$ to notice a little m closely ! nature ( an air wave4 ,x w be necess>y to rem9d y ( c]ta9 qualities possess$ n only by ! air we brea!1 b by all gases z well4 ,"h is a cyl9d] ) a closely fitt+ pi/on1 & a tap at ! bottom ( ! tube4 ,if ,i close ! tap & try to =ce d[n ! pi/on1 ,i feel "s resi/ance1 :i* increases z ! pi/on is pu%$ =w>d4 ,if ! pressure is remov$1 ! pi/on flies back to its old position1 z if !re 7 a spr+ und]nea? x4 ,! air 9 ! tube is an ela/ic sub/ance1 & x resi/s compression4 ,at con/ant temp]ature ! volume into :i* ! air is squeez$ is inv]sely z ! pressure appli$4 ,! air1 !re=e1 possesses ela/icity ( bulk1 z x is call$1 & x resi/s be+ made to occupy a small] volume4 ,aga91 ! air possesses in]tia1 & :5 x is set 9 motion x cont9ues to move l any o!r heavy body1 aft] ! mov+ =ce is )drawn4 ,we h1 !re=e1 pres5t 9 x ! two ess5tial qualities = ! production ( a wave-motion1 z expla9$ 9 ! fir/ lecture4 ,! air resi/s compression 9 virtue ( ela/icity1 & :5 x is all[$ to exp& aga9 back1 x p]si/s 9 motion 9 virtue ( in]tia4 ,let u consid] next ! process ( production ( a v simple s\nd1 su* z an explosion4 ,suppose a small quantity ( gun-cotton to be detonat$4 ,x causes a s\nd1 & !re=e an air wave4 ,! process by :i* ?is wave is made is z foll[s3 ,! explosion ( ! gun-cotton sudd5ly creates a l>ge quantity ( gas1 :i* adm9i/]s to ! air a v viol5t outw>d pu% or bl[4 ,9 consequ5ce ( ! in]tia ( ! air1 x _c respond ev]y:]e in/antly to ?is =ce4 ,h5ce a c]ta9 sph]ical lay] ( air is compress$ into a small] volume4 ,?is lay]1 h[ev]1 almo/ imm$iately exp&s aga91 & 9 s do+ x compresses ! next out] lay] ( air & r>efies itself4 ,!n1 aga91 ! second lay] 9 exp&+ compresses a ?ird1 & s on4 ,accord+ly1 a /ate ( compression is h&$ on f lay] to lay]1 & ea* /ate ( compression is foll[$ by "o ( r>efaction4 ,! individual air-p>ticles are caus$ to move to & fro 9 ! direction ( ! radii ( ! sph]e ( :i* ! s\rce ( explosion is ! c5tre4 ,h5ce we h :at is call$ a sph]ical longitud9al wave produc$4 ,ea* air-p>ticle sw+s backw>ds & =w>ds 9 ! l9e ( propagation ( ! wave4 ,! actual motion ( ea* air-p>ticle is exce$+ly small4 ,! spe$ ) :i* ?is zone ( compression travels outw>ds1 is call$ ! velocity ( ! s\nd wave1 & ! ext5t to :i* ea* air-p>ticle moves backw>ds & =w>ds is call$ ! amplitude ( ! wave4 ,suppose1 9 ! next place1 t in/ead ( a m]ely transitory s\nd l an explosion1 we h a cont9u\s musical s\nd1 we h to inquire :at !n w be ! description ( air-movem5t execut$4 ,! exp]im5ts %[n already w h conv9c$ y t1 9 ! case ( a musical s\nd1 ea* air-p>ticle mu/ repeat ! same k9d ( motion aga9 & aga94 ,! precise nature ( ! displacem5t c be be/ illu/rat$ by ! use ( two models4 ,be=e y is plac$ a frame to :i* are slung a s]ies ( golf-balls susp5d$ by ?reads 7see ,fig4 #d1 ,*apt] ,i474 ,betwe5 ea* pair ( balls !re is a spiral brass spr+1 :i* ela/ically resi/s bo? compression & ext5sion4 ,y w see t ! r[ ( balls & spr+s1 !re=e1 has simil> prop]ties to ! air4 ,9 virtue ( ! spr+s x resi/s compression & expansion1 & 9 virtue ( ! mass or in]tia ( ! balls any ball1 if displac$ & all[$ to move back1 ov]%oots its position ( equilibrium because x p]si/s 9 motion4 ,! r[ ( balls1 !re=e1 resi/s ext5sion & compression 9 consequ5ce ( ! ela/icity ( ! spr+s1 & ea* ball p]si/s 9 movem5t 9 consequ5ce ( ! in]tia ( ! ball4 ,if we !n adm9i/] a little pat to ! fir/ ball1 y w see a wave-motion run along ! l9e ( balls4 ,ea* ball 9 turn moves to & fro a little way1 & its movem5t is h&$ on to its neighb\rs4 ,we h "h an example ( a longitud9al wave-motion :i* resembles t ( ! air :5 x is trav]s$ by a s\nd wave4 ,ano!r model :i* is ( a m elaborate "* %[s u ! sort ( motion made 9 a tube :5 a s\nd wave due to a cont9u\s musical s\nd is pass+ along x4 ,x consi/s ( a glass disc :i* is black5$1 & has ! pa9t remov$ along c]ta9 exc5tric circul> l9es4 ,?is disc is made to revolve 9 front ( a wide slit 9 a piece ( metal4 ,by means ( an optical lant]n we project on to ! scre5 an image ( ! slit1 :i* y see is cross$ by c]ta9 bright b>s ( light1 cr[d$ toge!r at "s places & m spac$ ap>t at o!rs4 ,:5 ! disc revolves1 ^! b>s ( light ea* move to & fro successively1 & ! result is t ! cr[d$ place moves along1 or is displac$4 ,a wave ( compression is propagat$ along ! slit1 & ! localities :]e ! b>s ( light are compress$ or exp&$ cont9ually *ange _! place4 ,if we imag9e ! air 9 a tube to be divid$ into slices1 repres5t$ by ^! b>s ( light1 ! motion ( ! model exactly repres5ts ! motion ( ! air 9 ! tube :5 x is trav]s$ by a s]ies ( s\nd waves4 ,! di/ance f "o place ( greate/ compression to ! next is call$ ! wave-l5g? ( ! s\nd wave4 ,h5ce1 al?\gh a s\nd su* z t ( an explosion may consi/ 9 ! propagation ( a s+le lay] ( compression1 ! production ( a cont9u\s musical note involves ! transf]5ce ( a s]ies ( equidi/ant compressional zones1 or waves4 ,^! models w h assi/$ y1 ,i tru/1 to =m a cle> idea ( ! nature ( a s\nd wave 9 air4 ,x is some?+ v diff]5t1 9 fact1 f a wave on ! surface ( wat]1 b x is *>act]iz$ by ! same g5]al qualities ( wave-motion4 ,x is a /ate ( longitud9al p]iodic motion 9 a r[ ( p>ticles1 :i* is h&$ on f "o to ano!r4 ,ea* p>ticle ( air oscillates 9 ! l9e ( propagation ( ! wave1 & moves a little way backw>ds & =w>ds on ei!r side ( its undi/urb$ position4 ,x w be se51 !re=e1 t a solit>y s\nd wave is a /ate ( air-compression :i* travels along 9 ! o!rwise /ation>y air4 ,! air is squeez$ m tightly toge!r 9 a c]ta9 region1 & successive lay]s ( air take up ?is condition4 ,9 ! case ( wat]-surface waves ! wave is a region ( elevation at :i* ! wat] is rais$ above ! g5]al or av]age level1 & ?is elevat$ region is transf]r$ f place to place on o!rwise /ation>y wat]4 ,9 ! case ( an air-wave tra9 we h simil> regions ( compression foll[+ ea* o!r at di/ances1 x may be1 ( a fraction ( an in* or ( sev]al feet4 ,?us 9 ! case ( ord9>y spee* or song1 ! waves are f #b to #h feet 9 l5g?1 t is1 f "o compress$ region to ! next4 ,9 ! case ( a :i/le1 ! wave-l5g? may be #a or #b in*es1 :il/ ! deepe/ note ( an organ produces a s\nd ( :i* ! wave-l5g? is ab\t #cb feet4 ,z 9 e o!r in/ance ( wave-motion1 air waves may diff] f ea* o!r 9 ?ree respects4 ,fir/1 9 wave-l5g?2 secondly1 9 amplitude2 & ?irdly1 9 wave-=m4 ,! fir/ det]m9es :at we call ! tone1 i4e4 :e!r ! s\nd is high or l[1 treble or bass2 ! second det]m9es ! int5sity ( ! s\nd1 :e!r fa9t or l\d2 & ! ?ird det]m9es its quality1 or1 z ! ,g]mans expressively call x1 ! s\nd-col\r 7,klangf>be74 ,we recognize at once a diff]5ce betwe5 ! s\nd ( a v[el1 say ah1 sung by diff]5t p]sons to ! same note ( ! piano & ) ! same l\dness4 ,!re is a p]sonal elem5t1 an individuality1 ab\t voices :i* at once arre/s our att5tion1 ap>t altoge!r f ! tone or l\dness4 ,?is s\nd-quality is det]m9$ by ! =m ( ! wave-motion1 t is1 by ! nature ( ! movem5t ( ! air-p>ticle dur+ its little excursion to & fro 9 :i* x takes "p 9 produc+ a zone ( compression or r>efaction 9 ! air & s =ms a s\nd wave4 ,we h next to discuss ! spe$ ) :i* ?is air-compression is propagat$ ?r\gh ! air4 ,e "o kn[s t x is n in/antane\s4 ,we see ! fla% ( a gun at a di/ance1 & a second or s aft]w>ds we he> ! bang4 ,we notice t ! ?und] is he>d (t5 long aft] ! lightn+ fla% is se54 ,x w\ld take too long to describe ! exp]im5ts :i* h be5 made to det]m9e precisely ! spe$ ( s\nd waves4 ,suffice x to say t all ! be/ exp]im5ts %[ t ! velocity ( a s\nd wave 9 air1 at ! temp]ature ( melt+ ice1 or at #j ,c4 #cb ,fahr41 is v ne>ly #ajhg feet p] second1 or #cc1acf c5timetres p] second4 ,?is is equival5t to #gda miles p] h\r1 or m ?an t5 times ! spe$ ( an express tra94 ,at ?is rate a s\nd wave w\ld take #d h\rs to cross ! ,atlantic ,ocean1 #af h\rs to g half r\nd ! _w or to ! antipodes1 & "s #b m9utes to cross f ,dov] to ,calais4 ,an opportunity ( obs]v+ ?is spe$ ( s\nd waves on a gigantic scale occurr$ ab\t #bj ye>s ago on ! occasion ( a great volcanic eruption ne> ,java4 ,if y op5 ! map ( ,asia & look = ,java & ,sumatra 9 ! ,asiatic ,ar*ipelago1 y w easily f9d ! ,sunda ,/rait1 & on a good map y w see a small isl& m>k$ call$ ,krakatoa4 ,?is isl& possesses1 or r did possess1 a volcano :i*1 until ! ye> #ahhc1 _h n be5 kn[n to be 9 eruption4 ,9 t ye>1 h[ev]1 x aga9 bur/ into activity1 & aft] prelim9>y w>n+s a f9al /up5d\s outbur/ occurr$ on ,augu/ #bg1 #ahhc4 ,! ro> ( ?is volcanic explosion 0 probably ! l\de/ noise ev] he>d ^u ?is e>?4 ,! p5t-up volcanic gases & vap\rs bur/ =? f "s subt]ranean prison ) su* appall+ p[] t !y creat$ an air wave :i* n only encircl$ ! e>?1 b rev]b]at$ to & fro sev5 times be=e x f9ally fad$ away4 ,! zone ( compress$ air =m+ ! mighty air wave z x pass$ f po9t to po9t on ! e>?'s surface1 caus$ an increase ( atmosph]ic pressure :i* left its record on all ! self-regi/]+ b>omet]s1 & ?us enabl$ its /eps to be trac$4 ,a dilig5t exam9ation ( ^! records1 z collect$ 9 a celebrat$ ,report ( ! ,royal ,society ^u ! ,eruption ( ,krakatoa1 %[$ exactly ! mann] 9 :i* ?is great air wave exp&$4 ,/>t+ f ,krakatoa at #aj a4m4 on ! #bg? ( ,augu/1 #ahhc1 ! air wave sp$ outw>ds 9 a circle ( ev]-increas+ diamet] until1 by #g p4m4 on ! same day1 or #i h\rs lat]1 x =m$ a girdle embrac+ ! :ole _w4 ,?is /up5d\s circul> air wave1 #bd1jjj miles 9 circumf]5ce1 !n contract$ aga91 & 9 #i h\rs m _h cond5s$ itself at a po9t 9 ! nor!rn region ( ,s\? ,am]ica1 :i* is ! antipodes ( ,krakatoa4 ,x !n reb\nd$1 &1 exp&+ once m1 j l a wat] wave reflect$ f ! side ( a circul> tr\gh1 return$ on its own /eps1 s t #cf h\rs aft]w>ds x _h aga9 rea*$ ! po9t f :5ce x set out4 ,aga9 & aga9 x p]=m$ ! same d\ble j\rney1 b ea* "t weak] ?an be=e1 until1 aft] sev5 times1 ! e*oes ( ?is mighty air wave _h completely di$ away4 ,?is is no fancy picture1 b a sob] record ( fact obta9$ f ! infallible records ( self-regi/]+ air-pressure-measur+ in/rum5ts4 ,b we h evid5ce t ! actual s\nd ( ! explosion 0 he>d1 #d h\rs aft] x happ5$1 on ! o!r side ( ! ,indian ,ocean1 by human e>s1 & we h 9 ?is an in/ance ( ! measurem5t ( ! velocity ( s\nd on ! l>ge/ scale on :i* x 0 ev] made4 ,!re are _m curi\s & int]e/+ facts connect$ ) ! transmission ( a s\nd wave ?r\gh air1 affect+ ! di/ance at :i* s\nds c be he>d4 ,! spe$ ( s\nd 9 air is mu* influ5c$ by ! temp]ature ( ! air & by w9d4 ,! spe$ ( s\nd increases ) ! temp]ature4 ,= e degree ,fahr5heit above ! melt+-po9t ( ice 7#cb ,fahr47 ! spe$ is increas$ by "o foot p] second4 ,a m accurate rule is z foll[s3 ,take ! temp]ature ( ! air 9 degrees ,c5tigrade1 & add to ?is numb] #bgc4 ,9 o!r words1 obta9 ! value ( #bgc t :]e t is ! temp]ature ( ! air4 ,!n ! velocity ( s\nd 9 feet p] second at ?is temp]ature is equal to ! value ( ! expression-- #ajij77bgc t7_/#bgc7 ,!re is "o po9t 9 connection ) ! velocity ( propagation ( a s\nd wave :i* %\ld n be left )\t elucidation4 ,x has be5 expla9$ t ! velocity ( a wave 9 any m$ium is num]ically giv5 by ! numb] obta9$ by divid+ ! squ>e root ( ! ela/icity ( ! m$ium by ! squ>e root ( its d5sity4 ,! numb] repres5t+ ! ela/icity ( a gas is num]ically ! same z t repres5t+ its absolute pressure p] squ>e unit ( surface4 ,! volume ela/icity ( ! air may !re=e be measur$ by ! absolute pressure x ex]ts on a unit ( area su* z #a squ>e foot4 ,at ! e>?'s surface ! pressure ( ! air at #j ,c4 is equal to ab\t #baafd lbs4 p] squ>e foot4 ,! absolute unit ( =ce 9 me*anics is t =ce :i* communicates a velocity ( #a foot p] second to a mass ( #a lb4 aft] act+ ^u x = #a second4 ,if we all[ a mass ( #a lb4 to fall f re/ "u ! action ( gravity at ! e>?'s surface1 x acquires aft] #a second a velocity ( #cbb feet p] second4 ,h5ce ! =ce usually call$ 8a pressure ( #a lb40 is equal to #cbb absolute units ( =ce4 ,accord+ly1 ! atmosph]ic pressure at ! e>?'s surface is #baafd #cbb #fh1adh absolute units ( =ce 9 t sy/em ( measurem5t 9 :i* ! foot1 p\nd1 & second are ! fundam5tal units4 ,! absolute d5sity ( ! air is ! mass ( #a cubic foot3 #ac cubic feet ( air at ! freez+-po9t1 & :5 ! b>omet] /&s at #cj in*es1 weigh ne>ly #a lb4 ,m exactly1 #a cubic foot ( air "u ^! conditions weighs #jjhjgbh lb4 avoirdupois4 ,if1 !n1 we divide ! numb] repres5t+ ! absolute pressure ( ! air by ! numb] repres5t+ ! absolute d5sity ( air1 we obta9 ! quoti5t #hdd1afh2 & if we take ! squ>e root ( ?is1 we obta9 ! numb] #iabf4 ,! above calculation 0 made fir/ by ,newton2 & he 0 unable to expla9 h[ x 0 t ! velocity ( ! air wave1 calculat$ 9 ! above mann] f ! g5]al =mula = wave-spe$1 gave a value = ! velocity1 viz4 #iabf1 :i* 0 s mu* less ?an ! obs]v$ velocity ( s\nd1 viz4 #ajij feet p] second at #j ,c4 ,! true explanation ( ?is diff]5ce 0 fir/ giv5 by ! celebrat$ ,fr5* ma!matician ,laplace4 ,he po9t$ out t 9 air1 z 9 all o!r gases1 ! ela/icity1 :5 x is compress$ sl[ly1 is less ?an t :5 x is compress$ quickly4 ,a gas1 :5 compress$1 is heat$1 & if we give ?is heat "t to escape1 ! gas resi/s ! compression less ?an if ! heat /ays 9 x4 ,h5ce air is a little m resili5t to a v sudd5 compression ?an to a sl[ "o4 ,laplace %[$ t ! ratio ( ! ela/icity "u sudd5 compression 0 to t "u sl[ compression 9 ! same ratio z ! quantities ( heat requir$ to raise a unit mass ( air #a ,c4 "u con/ant pressure & "u con/ant volume4 ,?is ratio is call$ 8! ratio ( ! two specific heats10 & is a numb] close to #ada4 ,h5ce ! velocity1 z calculat$ above1 mu/ be correct$ by multiply+ ! numb] #hdd1afh by ! numb] #ada1 & !n tak+ ! squ>e root ( ! product4 ,:5 ?is calculation is made1 we obta91 z a result1 ! numb] #ajia1 :i* is exactly ! obs]v$ value ( ! velocity ( s\nd 9 feet p] second at #j ,c4 & "u atmosph]ic pressure4 ,! velocity ( s\nd is mu* affect$ by w9d or movem5t ( ! air4 ,s\nd travels fa/] ) ! w9d ?an aga9/ x4 ,h5ce ! pres5ce ( w9d di/orts ! %ape ( ! s\nd wave by mak+ portions ( x travel fa/] or sl[] ?an ! re/4 ,^! two facts expla9 h[ x happ5s t l\d s\nds are sometimes he>d at great di/ances f ! s\rce1 b n he>d at places close by4 ,illu/ration3 ,,fig4 #dg 7reproduc$ by p]mission ( proprietors ( ,k74--,map ( ,s\? ( ,engl&1 %[+ places 7black dots7 at :i* s\nd ( fun]al guns 0 he>d1 ,febru>y #a1 #aija4 ,consid] ! case ( a l\d s\nd made ne> ! surface ( ! e>?4 ,if ! air 7 all at re/1 & ev]y:]e at ! same temp]ature1 ! s\nd waves %\ld spread out 9 hemisph]ical =m4 ,b if1 z is g5]ally ! case1 ! temp]ature ne> ! gr\nd is high] ?an x is up above1 !n ! "p ( ! wave ne> ! e>? travels m quickly ?an t 9 ! high] regions ( ! air4 ,x foll[s t ! s\nd wave w h its direction alt]$1 & in/ead ( proce$+ ne> ! e>? 9 a direction p>allel to ! gr\nd1 x w be elevat$1 s z to /rike 9 an upw>d direction4 ,aga91 x may be br\ght d[n by meet+ ) a curr5t ( air :i* bl[s aga9/ ! l[] portion & s ret>ds t to a great] ext5t ?an x does ! upp] "p4 ,s x comes to pass t a s\nd wave may1 z x 71 8play leap-frog0 ov] a c]ta9 di/rict1 be+ lift$ up & !n let d[n aga92 & p]sons 9 t region w n he> ! s\nd1 al?\gh o!rs fur!r (f w d s4 ,a v /rik+ in/ance ( ?is occurr$ on ! occasion ( ! fun]al procession ( our late belov$ ,que5 ,victoria ( bless$ memory4 ,! body 0 convey$ across ! ,sol5t on ,febru>y #a1 #aija1 betwe5 l9es ( battle%ips :i* fir$ salutes ) big guns4 ,arrangem5ts 7 made to det]m9e ! greate/ di/ance ! s\nd ( ^! guns 0 he>d4 ,9 a v int]e/+ article 9 ,k = ,june1 #aija1 ,dr4 ,c4 ,davison has collect$ ! results ( obs]vation f eighty-f\r places1 "s ( :i* are indicat$ 9 ! map 7see ,fig4 #dg71 tak51 by k9d p]mission ( ! editor ( ,k1 f t j\rnal4 ,obs]vations 7 receiv$ f places z f> di/ant z ,ald]ton 7,suffolk71 #aci miles f ! ,sol5t4 ,at sev]al places ! s\nd ( ! guns 0 l\d en\gh to make w9d[s %ake4 ,?is occurr$ at ,longfield 7#ef miles71 ,sutton 7#eh miles71 & ,ri*mond ,hill 7#fa miles74 ,b :il/ !re is cle> evid5ce t ! s\nd ( ! guns 0 he>d ev5 at ,pet]bor\gh 7#abe miles71 mo/ curi\s to say1 ! s\nd 0 h>dly he>d at all 9 ! neighb\rhood ( ! ,sol5t4 ,! ne>e/ place f :i* any record 0 receiv$ 0 ,horley1 9 ,surrey 7#ej miles74 ,h5ce x appe>s evid5t t ! s\nd 0 lift$ up soon aft] leav+ ! ,sol5t1 & pass$ "r ov] ! heads ( obs]v]s ne>1 travell+ 9 ! high] air = a consid]able di/ance1 probably #dj or #ej miles1 & 0 !n deflect$ d[n aga91 & rea*$ obs]v]s on ! e>?'s surface at mu* great] di/ances4 ,an exam9ation ( ! w9d-*>ts = t day makes x tol]ably cle> t ?is 0 due to ! mann] 9 :i* ! w9d 0 bl[+ at ! "t4 ,dr4 ,davison1 loc4 cit41 says-- 8,n[1 on ,febru>y #a1 ! w9d at places to ! we/ ( ,spi!ad 0 g5]ally light1 & f ! we/ or ne>ly s1 ?\gh ne> ,lyndhur/ !re 0 a fre% breeze f ab\t ,w4,n4,w4 or ,n4,w4 ,at ,portsm\?1 aga91 ! w9d is describ$ z f ! %ore4 ,on ! o!r h&1 _m ( my correspond5ts at great di/ances f ,spi!ad /ate t ! w9d1 :5 s5sible1 0 s\!rly 9 direction4 ,?us ! s\nd-rays 7 fir/ ( all refract$ by contr>y w9ds ov] ! heads ( obs]v]s betwe5 #aj & #de miles1 & 7 aft]w>ds br\ght d[n aga9 by fav\rable upp] curr5ts1 s t ! reports 7 cle>ly audible beyond #ej miles & up to #adj miles f ,spi!ad1 & 7 s l\d at a di/ance ( #hd miles t lab\r]s 9 ! fields put d[n _! spades & li/5$40 ,! same explanation has be5 giv5 ( ! extraord9>y diff]5ces t are f\nd at v>i\s times 9 ! di/ance at :i* ligh?\se fog-horns are he>d by %ips at sea4 ,!re is 9 ?is case1 h[ev]1 ano!r possible explanation1 due to :at is call$ int]f]5ce ( s\nd waves1 ! explanation ( :i* w be giv5 pres5tly4 ,! late ,pr(essor ,tyndall1 :o 0 an au?ority on ?is subject1 0 ( op9ion t 9 "s /ates ( ! atmosph]e !re exi/$ :at he call$ 8ac\/ic opacity10 ! air be+ non-uni=m 9 temp]ature & moi/ure2 & ?r\gh ?is v irregul> m$ium1 s\nd waves1 :5 pass+1 lo/ a great deal ( _! int5sity by int]nal reflection1 or eclipses1 j z light is /opp$ :5 pass+ ?r\gh a non-homog5e\s m$ium l cru%$ ice or glass4 ,at ea* surface a little ( ! light is wa/$ by irregul> reflection1 & s ! m$ium1 ?\gh compos$ ( fragm5ts ( a transp>5t sub/ance1 is m or less opaque 9 ! mass4 ,on ! subject ( s\nd-signals z coa/-w>n+s1 "s exce$+ly int]e/+ in=mation has rec5tly be5 suppli$ by ,mr4 ,e4 ,price-,edw>ds 7see ,j\rnal ( ! ,society ( ,arts1 vol4 #ej1 p4 #cae1 #aijb74 ,! ,ligh?\se ,bo>ds ( diff]5t c\ntries provide ! means = mak+ l\d w>n+ s\nds at v>i\s ligh?\ses1 z a sub/itute = ! light :5 fog comes on4 ,! di/ance at :i* ^! s\nds c be he>d1 & ! di/ance-trav]s+ p[] ( v>i\s k9ds ( s\nds1 h be5 ! subject ( elaborate inve/igations4 ,! in/rum5t :i* has be5 f\nd to be ! mo/ effective 9 produc+ v p[]ful s\nd waves is call$ a sir54 ,x consi/s ( a tube or horn1 hav+ at ! bottom a fix$ disc ) slits 9 x4 ,outside ?is disc is ano!r movable "o :i* revolves aga9/ ! fir/1 & :i* also has slits 9 x4 ,:5 ! second disc revolves1 ! passage way into ! horn is op5$ & clos$ int]mitt5tly & sudd5ly1 z ! slits 9 ! discs co9cide or n4 ,air or /eam "u a pressure ( #aj to #dj lbs4 on ! squ>e in* is bl[n into ! horn1 & ! rapid int]ruption ( ?is bla/ by ! revolv+ slits causes x to be cut up into puffs :i*1 :5 suffici5tly frequ5t1 give rise to a v l\d s\nd4 ,! air "u pressure is admitt$ to a back *amb] & awaits an opportunity to escape1 & ?is is giv5 to x :5 ! revolv+ disc moves into su* a position t ! slits 9 ! fix$ & mov+ disc come opposite ea* o!r4 ,9 comp>ative trials ( diff]5t s\nd-produc+ in/rum5ts1 no?+ has yet be5 f\nd to surpass ?is sir5 z a produc] ( p5etrat+ s\nds4 ,x has be5 f\nd v important t ! frequ5cy ( ! note giv5 by ! sir5 %\ld co9cide ) ! fundam5tal tone ( ! trumpet or horn4 ,z w be expla9$ 9 ! next lecture1 e column ( air 9 a tube has a p>ticul> natural "t-p]iod ( oscillation4 ,suppose1 = in/ance1 t = a c]ta9 l5g? ( trumpet-tube ?is is second4 ,!n ! sir5 ) t trumpet w be mo/ effective if ! int]ruptions ( ! air-bla/ are #ajj p] second4 ,"l ,rayleigh has also %[n t ! %ape ( ! m\? ( ! trumpet is important1 & t ?is %\ld n be circul> z usual1 b elliptical or oval1 ! %orte/ diamet] ( ! ellipse be+ "o qu>t] ( ! longe/ "o4 ,also t ! m\? %\ld occupy su* a position t ! long] axis is v]tical4 ,moreov]1 he consid]s t ! %ort axis ( ! oval %\ld n exce$ half ! wave-l5g? ( ! s\nd be+ emitt$4 ,) a trumpet-m\? ( su* a %ape1 ! s\nd is prev5t$ to "s ext5t f be+ project$ up & d[n1 b diffus$ bett] lat]ally--a result :i* is desir$ 9 coa/ s\nd-signals4 ,! in=mation accumulat$ z reg>ds ! di/ances at :i* s\nds c be he>d is v briefly z foll[s3-- ,fir/ z reg>ds w9d4 ,! direction ( ! w9d has a mo/ rem>kable influ5ce on ! di/ance at :i* a giv5 l\d s\nd c be he>d4 ,9 "o in/ance1 ! noise ( a sir5 0 he>d #bj miles 9 calm wea!r2 :]eas1 ) an oppos+ w9d1 x 0 n he>d m ?an #a mile away4 ,x has be5 f\nd t = calm wea!r a l[-pit*$ note is bett] 9 c>ry+ p[] ?an a high note1 b 9 r\gh wea!r ! opposite is ! case4 ,"o ?+ t has be5 notic$ by all :o h exp]im5t$ ) ?is subject is ! curi\s occurr5ce ( 8areas ( sil5ce40 ,t is to say1 a c]ta9 sir5 w be well he>d close to its position4 ,!n a little f>!r (f ! s\nd w be lo/1 b on go+ f>!r away /ill x is he>d aga94 ,_m !ories h be5 advanc$ to acc\nt = ?is1 b none are completely satisfactory4 ,x is1 h[ev]1 a well-e/abli%$ effect1 & "o ) :i* x behoves all m>9]s to be acqua9t$4 ,"o curi\s fact is ! v great p[] t c be absorb$ 9 creat+ a l\d sir5 note4 ,?us 9 "o case1 a sir5 giv+ a high note 0 f\nd to absorb z mu* z #fjj horse-p[] :5 ! note 0 s\nd$ cont9u\sly4 ,! mo/ /rik+ & 9 "o s5se ! mo/ disappo9t+ ?+ ab\t ^! l\d s\nds is ! small di/ance :i* !y travel 9 c]ta9 /ates ( ! w9d4 ,z a g5]al result1 x has be5 f\nd t ! mo/ effective s\nd = coa/-w>n+s is "o hav+ a frequ5cy ( #ajj1 or a wave-l5g? ( ab\t #aj feet4 ,:5 deal+ ) ! subject ( waves 9 g5]al1 x 0 po9t$ out t ! velocity ( a wave dep5d$ ^u ! ela/icity & ! d5sity ( ! m$ium 9 :i* x 0 be+ propagat$4 ,9 ! case ( a s\nd wave 9 air or any o!r gas1 ! spe$ ( wave-transmission is proportional to ! squ>e root ( ! ela/icity ( ! gas1 & inv]sely proportional to ! squ>e root ( ! d5sity4 ,at ! same temp]ature ! ela/icity ( a gas may be tak5 to be ! same z its pressure4 ,h5ce1 at ! same pressure1 ! spe$ ( s\nd-wave transmission ?r\gh diff]5t gases v>ies inv]sely z ! squ>e root ( _! d5sities4 ,an example w make ?is cle>4 ,if we take ! d5sity ( hydrog5 gas to be unity 7 #a71 !n ! d5sity ( oxyg5 is #af4 ,! ratio ( ! d5sities is !re=e #a to #af1 & ! squ>e roots ( ! d5sities are z 7#a7 to 7#af71 or z #a to #d4 ,accord+ly1 ! velocity ( s\nd waves 9 hydrog5 gas is to t 9 oxyg5 gas z #a is to 4 ,9 o!r words1 s\nd travels f\r times fa/] 9 hydrog5 ?an x does 9 oxyg5 at ! same temp]ature & pressure4 ,! foll[+ table %[s ! velocity ( s\nd 9 diff]5t gases at ! melt+-po9t ( ice 7 #j ,c47 & atmosph]ic pressure 7 #gfj mm4 b>omet]74 ,gas4 ,velocity4 ,hydrog5 #dafc feet p] second ,c>bonic oxide #aajf 0 0 ,air #ajij 0 0 ,oxyg5 #ajda 0 0 ,c>bonic acid #hef 0 0 ,accord+ly1 we see t ! light] ! gas ! fa/] s\nd travels 9 x1 pressure & temp]ature be+ ! same4 ,if ! atmosph]e we brea! consi/$ ( hydrog5 in/ead ( a mixture ( oxyg51 nitrog51 & _m o!r gases1 a clap ( ?und] w\ld foll[ a fla% ( lightn+ mu* m quickly ?an x does 9 our pres5t air1 suppos+ ! /orms to be at ! same di/ance4 ,"u pres5t circum/ances1 if #bj seconds elapse betwe5 ! fla% & ! peal1 x indicates t ! /orm is ab\t #d miles away1 b if ! atmosph]e 7 ( hydrog51 = a /orm at ! same di/ance ! ?und] w\ld foll[ ! lightn+ 9 ab\t #e seconds4 ,furni%$ ) ^! facts ab\t ! propagation ( air waves1 x is n[ possible to po9t out "s int]e/+ consequ5ces4 ,x w be 9 y\r recollection t 9 ! fir/ *apt] x 0 po9t$ out t a wave on wat] c\ld be reflect$ by a h>d surface1 & t x c\ld be refract$1 or b5t1 :5 x pass$ f a region :]e x 0 mov+ quickly to "o :]e x 0 mov+ m sl[ly4 ,x w be necess>y n[ to prove exp]im5tally t ! same ?+s c be done ) s\nd1 9 ord] t a body ( pro( may be built up 9 y\r m9ds conv9c+ y t ! ext]nal cause ( s\nd-s5sation mu/ be a wave-motion 9 ! air4 ,9 ! fir/ place1 ,i mu/ describe to y1 some:at 9 detail1 ! nature ( ! arrangem5ts we %all employ = produc+ & detect+ ! s\nd waves :i* w be us$ 9 ^! exp]im5ts4 ,x w\ld n d to rely ^u ! e> z a detector because y _c all be s plac$ z to he> ! s\nds :i* w be produc$1 & we %all1 !re=e1 employ a peculi> k9d ( flame1 call$ a s5sitive flame1 to act z a detector4 ,if ord9>y coal-gas /or$ 9 a gasomet] is burnt at a small jet "u consid]able pressure1 we are able to produce a tall flame ab\t #ah to #bd in*es 9 height4 ,! jet us$ is "o ) a /eatite top & small p9-hole gas exit ab\t in* 9 diamet]4 ,! pressure ( gas mu/ be equal to ab\t #aj in*es ( wat]1 & x _c be drawn /raight (f ! h\se gas-pipes1 b mu/ be suppli$ f a special gasomet] or gasbag "u a pressure suffici5t to make a flame #ah in*es or s 9 height4 ,if ! pressure is too great1 ! flame ro>s2 if ! pressure is slightly r$uc$1 ! flame c be made to burn quietly & =m a tall re$-l flame 7,a1 ,fig4 #dh74 ,?is flame1 :5 prop]ly adju/$1 is curi\sly s5sitive to %rill1 *irp+ s\nds4 ,y may %\t or talk l\dly ne> x1 & x takes no notice ( y\r voice1 b if y *irrup or :i/le 9 a %rill tone1 or cl9k y\r keys or a few co9s 9 y\r h&1 ! flame at once %ort5s itself to ab\t #f or #g in*es 9 height1 & becomes possess$ ( a peculi>ly ragg$ edge1 :il/ at ! same "t x ro>s 7,b1 ,fig4 #dh74 ,:5 9 adju/m5t1 ! cl9k ( a c\ple ( co9s 9 ! h& w affect ?is s5sitive flame on ! o!r side ( ! room4#bb ,! flame is also v s5sitive to a %rill :i/le or bird-call4 ,x w be cle> to y1 f previ\s explanations1 t ! flame responds1 !re=e1 to v %ort air waves =m+ high notes4 ,! p>ticul> flame ,i %all n[ use responds ) great read9ess to air waves ( #a in* to in* 9 l5g?4 ,illu/ration3 ,,fig4 #dh4--;,a s5sitive flame3 ,a1 quiesc5t2 ,b1 ro>+4 ,x may be well to expla9 t ! s5sitive portion ( ! flame is ! root1 j :]e x em]ges f ! burn]1 & x is ! action ( ! s\nd wave 9 ?r[+ ?is portion ( ! flame into vibration :i* is ! cause ( its curi\s behavi\r4 ,if y ?9k :at ! action mu/ be1 y w easily see t ! op]ation ( ! s\nd wave is to ?r[ ! p>ticles ( ! gas1 j z !y escape f ! hole 9 ! jet1 into vibration 9 a direction transv]se or at "r angles to ! direction ( _! movem5t 9 ! flame4 ,! gas molecules are1 :5 unact$ ^u by ! s\nd wave1 ru%+ out ( ! jet1 9 an upw>d direction4 ,:5 ! s\nd wave imp+es on !m !y are1 s to speak1 caught1 & caus$ to rock to & fro 9 a direction across ! flame4 ,! comb9ation ( ^! two motions results 9 a spread+ action on ! flame1 s t in/ead ( be+ a ?9 lance-l %ape1 x becomes m blunt1 /umpy1 & ragg$ at ! sides4 ,! flame acts1 !re=e1 z a detector ( c]ta9 s\nds4 ,x is a v s5sitive k9d ( e> :i* li/5s & responds to ! slighte/ :isp] if only utt]$ 9 c]ta9 tones1 b is deaf to all o!r s\nds4 ,its great use to u is t x ackn[l$ges ! pres5ce ( air waves ( %ort wave-l5g?1 & %[s at once :5 x is imm]s$ 9 a /ream ( air waves or ripples ( v %ort wave-l5g?4 ,9 addition to ?is1 ,i am provid$ ) a :i/le giv+ a v %rill or high note1 :i* is bl[n /eadily by a curr5t ( air suppli$ "u con/ant pressure f a res]voir4 ,if ! :i/le is set 9 action1 y w at once see ! s5sitive flame dip d[n & ackn[l$ge ! pres5ce ( ! air-waves s5t out by ! :i/le4 ,! air waves s5t out by ?is :i/le proce$1 ( c\rse1 9 all directions1 b = our pres5t purpose we require to create :at ,i may call a beam ( s\nd4 ,y all "k ! action ( a magnify+-glass1 or l5s1 ^u a ray ( light4 ,:at boy is !re :o has n1 at "s "t or o!r1 amus$ himself by conc5trat+ ! rays ( ! sun by a burn+-glass1 & by br++ !m to a focus set light to a piece ( pap]1 or burnt 8 own or companion's h&8 ,9 ?is case we use a piece ( glass call$ a l5s1 :i* is ?ick] 9 ! middle ?an at ! edges1 to conv]ge p>allel rays ( light to a po9t or focus4 ,we also use su* a l5s 9 our optical lant]n to r5d] ! div]g+ rays f an electric lamp p>allel1 & s make a p>allel beam ( light4 ,i %all def] = a mom5t an explanation ( ?is action1 & simply say "h t x is possible to con/ruct a s\nd-l5s1 :i* op]ates 9 ! same mann] on rays ( s\nd4 ,i h _h su* a s\nd-l5s con/ruct$ = our pres5t exp]im5ts1 & x is made z foll[s3-- ,x is possible to buy small balloons made ( v ?9 mat]ial call$ collodion1 ?is latt] consi/+ ( gun-cotton dissolv$ 9 e!r & alcohol1 & !n p\r$ out on a glass plate & all[$ to dry4 ,if "o ( ^! balloons is pur*as$1 x is possible ) great dext]ity to cut f x two sph]ical segm5ts or sauc]-%ap$ pieces4 ,^! h !n to be cem5t$ ) siccot9e to a wood5 r+ hav+ two small pipes op5+ into x 7see ,fig4 #di74 ,by means ( ^! pipes we c inflate ! l5s-%ap$ bag s =m$ ) a heavy gas call$ c>bonic acid gas1 made by p\r+ /rong acid ^u m>ble or *alk4 ,! result ( ^! op]ations1 all ( :i* require consid]able skill ( h&1 is to furni% u ) a s\nd-l5s consi/+ ( a collodion film 9 ! %ape ( a magnify+-glass1 or d\ble convex l5s1 fill$ ) c>bonic acid gas heavi] ?an ! air4 ,! s\nd-l5s s made is fix$ up aga9/ a hole 9 a glass scre5 ( ! same size z ! l5s1 & on "o side ( ! l5s is plac$ ! :i/le1 & on ! o!r side ! s5sitive flame4 ,^! h to be adju/$ s t ! :i/le ,w1 ! c5tre ( ! l5s ,l1 & ! jet ( ! flame ,f are 9 "o /raight horizontal l9e p]p5dicul> to ! glass plate4 ,illu/ration3 ,,fig4 #di4--;,a s\nd-l5s focuss+ a div]g5t beam ( air waves4 ,! di/ance ( ! :i/le f ! l5s has !n to be adju/$ s z to produce on ! o!r side a ne>ly p>allel beam ( s\nd4 ,9 o!r words1 ! :i/le mu/ be plac$ 9 ! focus ( ! l5s4 ,a rule = do+ ?is is z foll[s3 ,if ! balloon f :i* ! segm5ts ( collodion 7 cut 0 ne>ly sph]ical1 & _h a diamet] ( #h in*es1 !n ! :i/le mu/ be plac$ at slightly less ?an #h in*es f ! side ( ! l5s next to x4#bc ,! exact di/ance1 h[ev]1 w h to be f\nd by trial1 b x is some:]e ne> ! po9t s det]m9$4 ,! s5sitive flame %\ld be ab\t #d or #e feet away f ! l5s on ! o!r side ( ! scre54 ,^! arrangem5ts hav+ be5 made & ! :i/le set 9 action1 x w be f\nd t ! flame responds vigor\sly :5 x is plac$ on ! axis-l9e ( ! l5s1 b if mov$ a few in*es to "r or left ( ?is l9e1 x w cease to fl>e4 ,?is %[s u t we h =m$ a beam ( s\nd1 & ) "s little c>e x is possible to make ?is a ne>ly p>allel beam1 s t :5 plung$ 9 ?is /ream ( air waves ! flame dips1 b by remov+ x j outside ! /ream ( s\nd x no long] fl>es4 ,i h f\nd x n difficult1 :5 us+ a s\nd-l5s #f or #g in*es 9 diamet]1 to make a beam ( s\nd f a :i/le "s #aj in*es wide at ab\t #d feet f ! l5s4 ,suppos+ ! s\nd-l5s & s5sitive flame s adju/$1 x is !n necess>y = our purpose to provide a s\nd-prism1 made 9 ! foll[+ mann]3 ,a z9c box is made 9 w$ge =m1 & ! two incl9$ sides are cut out1 & ^! w9d[s are cov]$ ) ?9 collodion film4 ,! box has two pipes connect$ ) x1 by means ( :i* x c be fill$ ) c>bonic acid gas4 ,provid$ ) ?is app>atus1 x is n[ possible to %[ y a s]ies ( exp]im5ts :i* w leave no d\bt 9 y\r m9ds t ! ext]nal ag5cy :i* creates 9 u ! s5sation ( s\nd is a wave-motion 9 ! air we brea!4 ,let me1 9 ! fir/ place1 %[ y t a s\nd-beam c be reflect$4 ,we adju/ our s5sitive flame & set ! :i/le 9 action1 & create1 z describ$1 by ! l5s1 a beam ( s\nd4 ,at a little di/ance1 say a c\ple ( feet1 outside ! p>allel beam we place ! s5sitive flame1 &1 be+ %elt]$ f ! direct action ( ! :i/le1 x rema9s p]fectly quiesc5t4 ,tak+ a %eet ( glass 9 my h&1 ,i hold x at an angle ( #de 9 ! s\nd-beam1 & y see ! flame at once ro>s4 ,! beam has be5 reflect$ on to ! flame1 b a v small angul> movem5t ( ! glass is suffici5t to reflect ! s\nd-ray pa/ ! flame )\t t\*+ x1 & ! flame !n exhibits no agitation4 ,a few exp]im5ts ( ?is k9d ) ! flame 9 v>i\s positions are suffici5t to %[ t ! s\nd-beam is reflect$ by ! glass 9 accordance ) ! law ( reflection ( wave-motion1 viz4 t ! angle ( incid5ce is equal to ! angle ( reflection4 ,we c 9 ! same way reflect ! s\nd-beam by a wood5 bo>d1 a piece ( c>dbo>d1 a look+-glass1 or a %eet ( metal4 ,we c reflect x f a wet du/]1 b n v well f a dry h&k]*ief4 ,if we place ! flame 9 ! direct beam1 x is easy to %[ t all ! above good reflectors ( s\nd are opaque to a s\nd-ray1 & ca/ an ac\/ic %ad[4 ,9 fact1 ,i c prev5t ! flame f ro>+ by m]ely int]pos+ my h& 9 front ( x4 ,a wet du/] is f\nd to be opaque to ^! s\nd waves1 b a dry l95 h&k]*ief is fairly transp>5t4 ,! collodion film us$ 9 mak+ ! l5s & prism is also exce$+ly transp>5t to ^! %ort air waves4 ,we may !n g "o /ep fur!r1 & %[ t ^! air waves are capable ( refraction4 ,x w be 9 y\r remembrance t1 9 speak+ ( wat] ripples1 x 0 %[n by exp]im5t t1 :5 wat] ripples pass$ ov] a b\nd>y betwe5 two regions1 9 "o ( :i* !y travell$ m quickly ?an 9 ! o!r1 a b5d+ ( ! direction ( ripple-motion took place4 ,we c %[ precisely ! same ?+ ) ^! air waves4 ,! collodion prism has be5 fill$ ) a heavy gas call$ c>bonic acid4 ,?is gas is ab\t half z heavy aga9 z air1 & x is ?is heavy & poison\s gas :i*1 by accumulat+ 9 old wells or brew]s' vats or 9 coal-m9es aft] an explosion1 causes ! dea? ( any man or liv+ animal imm]s$ 9 x4 ,x has already be5 expla9$ t ! velocity ( s\nd waves 9 diff]5t gases v>ies inv]sely z ! squ>e root ( _! d5sity4 ,h5ce ! spe$ ( a s\nd wave 9 c>bonic acid gas w be less ?an t 9 air 9 ! ratio ( ! squ>e roots ( ! d5sities ( ^! gases4 ,! d5sity ( c>bonic acid gas is to t ( air z #aeeb is to #a4 ,! squ>e root ( #aeeb is #abdf1 or ne>ly #a4 ,accord+ly1 ! spe$ ( a s\nd wave 9 c>bonic acid gas is to ! spe$ 9 air z #d is to #e4 ,a s\nd wave 9 air w !re=e travel #e feet or #e in*es 9 ! same "t t x travels #d feet or #d in*es 9 c>bonic acid gas4 ,let u n[ consid] :at mu/ happ5 if a s\nd wave falls obliquely ^u ! face ( our c>bonic acid prism4 ,illu/ration3 ,,fig4 #ej4--,! refraction ( a wave by a prism4 ,let ,,abc be ! prism 7see ,fig4 #ej7 repres5t$ 9 plan1 & let ab1 ab1 ab1 be a tra9 ( s\nd waves advanc+ aga9/ ! face ,,ac4 ,z soon z ! left end b ( ! wave ab t\*es ! face ,,ac1 & ent]s ! c>bonic acid gas1 its spe$ w beg9 to be ret>d$1 & 9 ! "t tak5 by ! "r end a to move 9 air f a to c1 ! left end w h mov$ 9 c>bonic acid gas1 by a less di/ance1 bd1 ! di/ances ca & db1 be+ 9 ! ratio ( #e to #d4 ,h5ce x is cle> t ! wave-front ab w be swung r\nd1 & :5 ! wave has :olly ent]$ ! prism1 its direction ( motion w h be5 b5t r\nd to ! left4 ,! same ?+ w happ5 at em]g5ce4 ,! "r end1 e1 ( ! wave ef gets out into ! air :il/ ! left end1 f1 is /ill 9 c>bonic acid4 ,accord+ly1 9 ! "t tak5 = ! end f to move to h1 ! end e w h mov$ a great] di/ance1 9 ! ratio ( #e to #d1 to g1 & !re=e we h aga9 a b5d+ r\nd ( ! wave-direction4 ,x is evid5t1 !re=e1 t ?is unequal ret>d+ ( ! two sides ( ! wave w result 9 a refraction1 or b5d+1 ( ! wave-direction1 & t :]eas ! s\nd-ray 0 proce$+1 be=e ent]+ ! prism1 9 ! direction ( ! arr[ on ! "r h&1 x is alt]$1 aft] pass+ ?r\gh ! prism1 s z to be travell+ 9 ! direction ( ! arr[ on ! left-h& side4 ,! d\ble b5d+ ( ! s\nd-ray is !re=e caus$ by1 & is evid5ce ( ! fact t1 ! s\nd wave travels m sl[ly 9 c>bonic acid gas ?an x does 9 air4#bd ,let u1 !n1 br+ ^! /atem5ts to ! te/ ( exp]im5t4 ,we aga9 />t 9 action ! :i/le ,w1 & place ! s5sitive flame 9 ! l9e ( ! l5s-axis1 & notice h[ viol5tly ! flame fl>es 7see ,fig4 #ea74 ,! flame is n[ at a di/ance ( #d feet f ! l5s4 ,i move ! flame #a foot to ! left h&1 & x is n[ outside ! beam ( s\nd1 & rema9s quiesc5t4 ,! prism ,p1 previ\sly fill$ ) c>bonic acid gas1 is !n ins]t$ betwe5 ! s\nd-l5s & ! flame1 & close to ! =m]4 ,:5 prop]ly plac$1 ! s5sitive flame ,f imm$iately dips & ro>s4 ,x w be abundantly evid5t to y t ?is c only arise because ! prism has b5t r\nd ! s\nd-beam1 & deflect$ x on to ! flame4 ,b if ! beam is b5t r\nd1 !n x foll[s t if ! flame is n[ mov$ back to ! c5tral position ,f1 ! prism rema9+ 9 front ( ! l5s1 t ! flame w n n[ ro>1 & ?is we f9d to be ! case4 ,if1 h[ev]1 ! prism is !n remov$1 ! flame at once bur/s into a ro>4 ,illu/ration3 ,,fig4 #ea4--,! refraction ( a s\nd-ray4 ,?is exp]im5t proves to demon/ration t we c refract waves ( s\nd j z we c refract ripples on wat]4 ,hav+ reg>d to :at we h n[ se51 ,i d n ?9k y w h any difficulty 9 see+ h[ x is t ! biconvex s\nd-l5s1 fill$ ) c>bonic acid gas1 is able to r5d] div]g5t s\nd-rays p>allel2 9 o!r words1 c conv]t a sph]ical s\nd wave into a plane s\nd wave4 ,consid] :at ! effect really mu/ be4 ,let ! s\nd-l5s be repres5t$ 9 section by ,,ab 7see ,fig4 #di71 & let ,w be ! :i/le s5d+ out sph]ical s\nd waves1 repres5t$ by ! dott$ l9es4 ,:5 ! sph]ical wave meets ! l5s1 ! c5tral portion ( ! wave passes into a ret>d+ m$ium1 :il/ ! "r & left w+s ( ! wave are /ill 9 air4 ,h5ce1 z be=e1 ! w+s ga9 on ! c5tre4 ,aga91 at em]g5ce ! w+s em]ge be=e ! c5tre ( ! wave1 & h5ce aga9 ! w+s ga9 on ! c5tre4 ,aft] complete em]g5ce ! sph]ical wave-surface has be5 flatt5$ out & made into a plane wave4 ,h5ce ! s\nd-rays div]g+ f ! :i/le are r5d]$ p>allel or ev5 conv]g5t1 provid$ t ! :i/le is prop]ly plac$ ) reg>d to ! l5s4 ,y w see1 !re=e1 t we c use a gas d5s] ?an ! air1 conta9$ 9 a transp>5t bag or vessel ( collodion1 z ! means ( *ang+ ! =m & direction ( s\nd waves4 ,we c make l5ses & prisms ( c>bonic acid gas :i* act on rays ( s\nd j z d l5ses & prisms ( glass on rays ( light4 ,!re is1 h[ev]1 "o great diff]5ce betwe5 ! op]ation ( a c>bonic acid prism on rays ( s\nd1 & t ( a glass or o!r prism on rays ( light4 ,9 ! lectures on !r waves x w be made cle> to y t :at we call light really consi/s 9 waves 9 a m$ium kn[n z ! !r4 ,b :5 su* light waves are propagat$ ?r\gh a transp>5t mat]ial l glass1 ! spe$ ( transmission dep5ds on ! wave-l5g?1 j z 9 ! case ( wat] waves4 ,b z reg>ds s\nd waves !re is no diff]5ce betwe5 ! velocity ( propagation or spe$ ) :i* waves ( diff]5t wave-l5g?s move4 ,h5ce a bass note travels j z fa/ z a treble note1 & ! s\nd waves f a flute h a spe$ ( ! same value z t f a trumpet or bassoon4 ,if x 7 n s1 x w\ld be impossible = u to he> music or song at a di/ance1 because ! notes w\ld arrive all 9 ! wrong ord]1 & ! mo/ famili> melody w\ld be unrecognizable4 ,x foll[s f ?is t air waves1 no matt] :at _! wave-l5g?1 are equally refract$ on pass+ f "o m$ium to ano!r ( diff]5t d5sity4 ,we %all see lat] on t ?is is n ! case ) waves ( light & !r waves g5]ally4 ,9 ! case ( mo/ transp>5t sub/ances ! !r waves :i* con/itute light are transmitt$ ) diff]5t velocities1 ! long] waves mov+ fa/] ?an ! %ort] ones4 ,h5ce we h ! famili> result ( ! decomposition ( a ray ( :ite light into its diff]5t con/itu5ts by a glass prism4 ,we _c1 h[ev]1 p]=m a simil> exp]im5t on a complex s]ies ( waves ( s\nd by means ( a c>bonic acid prism4 ,9 o!r words1 a s\nd-prism refracts1 b does n disp]se s\nd waves ( v>i\s wave-l5g?s4 ,"o ?+1 h[ev]1 %\ld be po9t$ out be=e dismiss+ ?is exp]im5t1 & t is t to %[ successfully ! exp]im5t ) ! prism1 ! l5g? ( ! s\nd waves us$ mu/ be small comp>$ ) ! dim5sions ( ! prism4 ,! reason = ?is is t o!rwise !re w\ld be too mu* b5d+ ( ! waves r\nd ! ob/acle4 ,:5 a tra9 ( waves1 no matt] :e!r waves 9 air or waves 9 wat]1 meets ) an imp]vi\s body1 !re is always a c]ta9 b5d+ ( ! waves r\nd x1 :i* is te*nically call$ diffraction4 ,we may see ?is effect on a l>ge scale :5 sea waves1 roll+ 91 pass by "s l>ge rock /&+ up l an isl& out ( ! wat]4 ,! waves meet x1 pass r\nd x1 &1 s to speak1 embrace x & cont9ue on ! o!r side4 ,if !re is to be any calm wat] on ! leew>d side1 ! isl& mu/ be l>ge comp>$ ) ! l5g? ( ! waves4 ,! same ?+ holds good ) reg>d to air waves4 ,9 ord] t an object may =m an ac\/ic or s\nd-%ad[1 x is necess>y t ! con/ruction %all be l>ge comp>$ ) ! l5g? ( ! wave4 ,?us ! h& held 9 front ( ! m\? does n mu* ob/ruct ! waves ( ! speak+ voice1 because ^! waves are ab\t #b to #d feet long4 ,b z y h se5 :5 us+ s\nd waves only #a in* long1 ! h& w =m a v well-m>k$ s\nd-%ad[1 z %[n by its effect :5 held betwe5 a :i/le & a s5sitive flame4 ,9 ord] to complete our pro( t ! ag5cy :i* affects our e>s z s\nd is really due to air waves1 x is necess>y to be able to %[ t we c produce int]f]5ce ) air waves1 z 9 ! case ( waves on wat]4 ,! nature ( ! effect call$ int]f]5ce by :i* "o wave is made to annihilate ano!r has be5 already fully expla9$4 ,i w n[ endeav\r to exhibit to y ! int]f]5ce ( two s\nd-wave tra9s 9 an exp]im5t due to ,"l ,rayleigh1 ! app>atus = :i* he has k9dly l5t to me4 ,x consi/s1 z y see1 ( a /&1 to :i* is fix$ a jet1 f :i* we =m a tall s5sitive flame4 ,beh9d ! flame is plac$ a %eet ( glass1 :i* is held v]tically1 b c be slid t[>ds or f ! flame4 ,at a little di/ance we place a bird-call1 or sort ( :i/le1 :i* produces1 :5 bl[n ) air1 a note s %rill z to be inaudible to human e>s4 ,! air-vibrations s g5]at$ are at ! rate ( #cc1jjj p] second1 :i* is beyond ! limit ( audition4 ,h5ce1 ev5 :5 bl[n /rongly1 y he> no s\nd f ?is appliance4 ,x produces1 h[ev]1 z y c see1 a v viol5t effect ^u ! s5sitive flame4 ,h5ce ?is flame he>s a note :i* we _c he>1 & x sugge/s t p]haps "s animals or insects may h a range ( he>+ q beyond ! limits fix$ = our human e>s4 ,su* be+ ! case1 y w see t if ! glass plate is plac$ beh9d ! flame at a c]ta9 di/ance1 ! flame at once /ops fl>+ & becomes quiesc5t4 ,if1 h[ev]1 ! plate is mov$ to or f ! flame by a v small di/ance equal to ab\t ! "o-twelf? "p ( an in*1 ! tall flame at once drops 9 height & beg9s to fl>e4 ,if we move ! plate /eadily backw>ds by equal small di/ances1 we f9d ! flame alt]nately quiesc5t & wav+4 ,! explanation ( ?is effect is t x is due to ! int]f]5ce betwe5 ! direct & reflect$ s\nd-rays4 ,! waves ( air are turn$ back :5 !y meet ! glass 9 su* a mann] t ! cre/s ( ! arriv+ waves are made to co9cide ) ! holl[s ( ! reflect$ waves1 or1 to speak m correctly1 ! zones ( cond5sation ( "o are co9cid5t ) ! places ( r>efaction ( ! o!r4 ,:5 ! glass is adju/$ s t ?is happ5s1 all air-wave motion j 9 front ( x is de/roy$1 & h5ce ! s5sitive detect+ flame rema9s quiesc5t4 ,if1 h[ev]1 ! glass is mov$ ne>] to or fur!r f ! flame1 !n ! cond5sations ( ! reflect$ wave may be made to fall 9 ! same places z ! cond5sations ( ! arriv+ wave1 & 9 t case ! di/urbance is d\bl$1 & n de/roy$4 ,illu/ration3 ,,fig4 #eb4 ,a little model may be made :i* w help ! read] to grasp ?is po9t4 ,cut out a piece ( pap] 9 ! =m %[n 9 ,fig4 #eb to repres5t a wave4 ,b5d back ! pap] on itself at ! dott$ l9e ab1 & let "o half repres5t ! arriv+ wave1 & ! o!r ! reflect+ wave4 ,x w be se5 t 9 ?is case ! cre/s ( ! incom+ wave are oblit]at$ by ! holl[s ( ! return+ wave4 ,if1 h[ev]1 ! pap] is b5t back at cd1 !n ! cre/s ( ! reflect$ & incid5t waves conspire1 & !re is no int]f]5ce4 ,:5ev] we c produce int]f]5ce 9 ?is mann] betwe5 two sets ( s\nd-rays1 or light-rays1 or rays ( any o!r k9d1 we h ! /ronge/ possible pro( t we are conc]n$ ) a wave-motion2 because 9 no o!r way t we c und]/& is x possible t a de/ruction ( s\nd by s\nd c take place by1 s to speak1 sup]impos+ two s\nd-rays1 or a de/ruction ( light by br++ toge!r two rays ( light4 ,we may1 !n1 conclude our discussion ( ?is "p ( our subject by exam9+ ! mann] 9 :i* vibrat+ bodies communicate a diff]5t =m ( wave to ! air4 ,z already expla9$1 we are by our e>s enabl$ to appreciate ! fact t ! air is ?r[n into a wave-motion1 & t ?is wave-motion may consi/ ( waves ( great or small wave-l5g?1 & great or small amplitude4 ,b we are able to d some?+ m--we are able to detect a diff]5ce betwe5 ! =m ( two waves1 s t if repres5t$ by a wavy l9e ( light1 z y h se51 ! nature ( ! outl9e ( t l9e impresses itself ^u our consci\sness4 ,no?+ is m rem>kable ?an ! extraord9>y delicacy ( ! e> 9 ?is respect4 ,among/ all our scores ( fri5ds & acqua9tances we recognize ea* by a quality ( voice :i* we speak ( z h>%1 melodi\s1 sympa!tic1 rasp+1 p5etrat+1 or cle>4 ,?is is n altoge!r a matt] ( enunciation or vocalization1 = if diff]5t p]sons pron\nce correctly ! same v[el-s\nd1 we c detect a great diff]5ce betwe5 _! voices4 ,we h1 !n1 to ask :]e9 ?is diff]5ce consi/s :5 consid]$ ) respect simply to :at goes on outside ( u 9 ! air4 ,great light 0 ?r[n on ?is by ! inv5tion & p]fection ( ! phonograph & telephone1 & also a m rec5t & wond]ful inv5tion1 v>i\sly call$ ! micro-phonograph or telegraphone4 ,y h all he>d a phonograph speak1 or s+1 or reproduce music4 ,9 its orig9al =m ! ,edison phonograph consi/$ ( a cyl9d] cov]$ ) t9foil1 aga9/ :i* press$ lightly a /eel po9t atta*$ to ! c5tre ( a metal disc4 ,9 its mod]n =m1 z improv$ by ,edison1 ,bell1 ,ta9t]1 & o!rs1 x is a f> m p]fect in/rum5t = record+ & reproduc+ s\nd4 ,x n[ consi/s ( a cyl9d] cov]$ ) a composition simil> to v h>d soap4 ,?is cyl9d] is c>ri$ on a metal drum1 & caus$ to revolve by clockwork sl[ly & v uni=mly4 ,a metal arm c>ries an ela/ic metal disc call$ a receiv+ diaphragm1 & to ! back ( ?is is atta*$ a v delicate cutt+-tool l a small *isel4 ,by means ( a screw ! *isel & diaphragm are made to travel along ! cyl9d]1 & if no vibration is giv5 to ! disc ! tool cuts a spiral on ! record+ cyl9d]1 :i* is a clean groove ) smoo? bottom pl\gh$ out ( ! s(t composition4 ,if1 h[ev]1 we speak or s+ to ! diaphragm1 ! air waves cause x to vibrate1 & ?is makes ! tool cut a furr[1 ! bottom ( :i* is irregul>1 ! undulations correspond+ exactly to ! movem5ts ( ! diaphragm4 ,?us1 if we c\ld look at ! section ( ! furr[1 we %\ld see x undulat+ l a m9iature swit*back railway1 ea* up-&-d[n correspond+ ) "o vibration ( ! diaphragm4 ,9 ?is mann] we /ore up a record ( air waves on ! h>d-soap cyl9d]4 ,9 ! next place1 to reproduce ! s\nd1 ano!r diaphragm ) a trumpet m\?piece has at its back a little po9t$ lev] or set ( lev]s1 "o extremity re/+ ^u ! bottom ( ! irregul> furr[4 ,!n1 if ! cyl9d] is s set t ?is reproduc+ diaphragm travels ov] ! record cut by ! receiv+ diaphragm1 we h a motion communicat$ to x :i* is ! exact facsimile ( t :i* produc$ ! furr[4 ,accord+ly1 ! reproduc+ diaphragm gives back to ! air impulses :i* reproduce ! same wave-tra9s1 & !re=e ! same spee* or song1 z t :i* creat$ ! record4 ,we may 9 ?is mann] record any human utt]ance & receive x aga91 ^w-p]fect1 mon?s or ye>s aft] x 0 made4#be ,! action ( ! phonograph leads u to inquire h[ a disc ( metal or o!r ela/ic mat]ial responds to a]ial vibrations :i* fall ^u x1 & ,i %all conclude ?is lecture by %[+ y "o exp]im5t ( a k9d to illu/rate ?is po9t1 :i*1 ?\gh n v easy to p]=m1 is c]ta9ly "o ( ! mo/ attractive t c be %[n4 ,!re is on ! table a brass tube1 ( a %ape some:at l a squ>e-%\ld]$ funnel1 & ov] ! small] end is loosely slipp$ a wide indi>ubb] tube ) a m\?piece4 ,x is ess5tial t ! indi>ubb] tube %all n fit tightly1 b %all be support$ s t an air space exi/s all r\nd betwe5 x & ! brass funnel tube4 ,! latt] may be c>ri$ on a wood5 /&4 ,! wid] end ( ! funnel mu/ h a diamet] ( ab\t #b in*es1 & ! lip mu/ be q smoo?4 ,! int]ior ( ! funnel %\ld be black5$4 ,a soap solution has !n to be prep>$ z = bl[+ soap-bubbles4 ,a good =mula = mak+ ?is solution is giv5 by ,pr(essor ,v]non ,boys1 9 8 book1 8,soap ,bubbles & ! ,=ces :i* m\ld !m10 & is z foll[s3 ,fill a clean /opp]$ bottle ?ree-qu>t]s full ( s(t wat]4 ,add "o-=tie? "p ( its weight ( oleate ( soda1 :i* w probably float on ! wat]4 ,leave x until x is dissolv$4 ,!n ne>ly fill up ! bottle ) ,price's glyc]9e1 & %ake well4 ,leave ! bottle /opp]$ = a week 9 a d>k place4 ,!n syphon (f ! cle> liquid f ! scum at ! top4 ,add "o or two drops ( /rong ammonia to e p9t ( ! liquid4 ,d n w>m or filt] ! liquid1 & keep x c>efully f exposure to ! air4 ,d n expose ! liquid to ! air m ?an necess>y2 b 9 bl[+ a bubble p\r out a little ( ! liquid into a sauc]4 ,9 default ( ?is good solution a sub/itute may be f\nd by dissolv+ bits ( cle> yell[ soap 9 s(t wat]2 b ?is soapy wat] does n yield films :i* la/ s long z ^? made ) ! ,plateau solution above describ$4 ,by dipp+ ! wide end ( ! funnel tube into "s ( ! soap solution plac$ 9 a sauc]1 x is easy to cov] ! end ) a flat soap film :i* w la/ a consid]able "t4 ,?is tube has !n to be fix$ 9 front ( an electric arc or lime-light lant]n1 s t a p[]ful p>allel beam ( light c be direct$ on to ! film by a small flat mirror or look+-glass4 ,a l5s is also plac$ s z to focus an image ( ! film on to a scre54 ,9 f9d+ ! "r position = ! l5s1 x is a great help to place a piece ( :ite c>d ) "s bold black lett]s ^u x ov] ! brass funnel 9 ! place :i* w be occupi$ ) ! soapy film1 & to focus ?is s z to obta9 a %>p image ( ! lett]s on ! scre54 ,:5 ! soap film is !n sub/itut$ = ! c>d1 we %\ld h on ! scre5 a reflection ( ! film surface1 :i* at fir/ w appe> z a pat* ( :ite light ^u ! scre54 ,if we all[ ! film to /& = a few seconds1 x beg9s to get ?9n] at ! upp] "p ?an at ! bottom1 & ! image on ! scre5 w exhibit gorge\s b&s ( r$ & gre51 call$ int]f]5ce col\rs1 :i* are due1 l ! col\rs on a soap-bubble1 to ! int]f]5ce ( ! rays ( light reflect$ f ! inn] & out] surfaces ( ! film4 ,if ! exp]im5t is skilfully p]=m$1 ! appe>ance on ! scre5 w !n be v beautiful4 ,we %all h a pat* ( light :i* exhibits b&s ( col\rs1 becom+ m int5se ! long] ! film /&s1 & t[>ds ! end hav+ some:at ! appe>ance ( an unusually lovely sunset4 ,j be=e ?is condition ( ! film is rea*$1 if we s+ g5tly into ! m\?piece ( ! indi>ubb] tube1 ! soap film w be ?r[n into vibration4 ,! image on ! scre5 w exhibit a set ( regul>ly arrang$ conc5tric /ation>y ripples1 :i* w alt] 9 appe>ance ) e *ange 9 ! note sung4 ,! exp]im5t requires "s c>e & practice to p]=m x prop]ly1 & %\ld n be attempt$ 9 public )\t _m rehe>sals2 b :5 well %[n x is a mo/ effective & int]e/+ exp]im5t4 ,we see1 !re=e1 t s delicate an object z a /ret*$ soap-film c take up ! vibrations ( ! air & be itself ?r[n into vibration4 ,! reason is t ! soap-film1 z already expla9$ 9 ! fir/ lecture1 resi/s /ret*+1 & behaves l a %eet ( ela/ic indi>ubb]4 ,h5ce1 z ea* air wave falls ^u x1 ! film is alt]nately pu%$ out & pull$ 91 b be+ held at ! edges1 x c only accommodate itself by /ret*+4 ,we h1 !re=e1 set up 9 ! film a set ( /ation>y waves simil> to ^? set up on a rope fix$ at "o end :5 ! loose end is regul>ly j]k$ up & d[n by ! h&4 ,! exp]im5t %[s u cle>ly ! way 9 :i* an ela/ic disc is set 9 vibration :5 compressional waves fall ^u x1 & 9 ! next lecture we %all proce$ to discuss ! vibrations ( ?is k9d :i* give rise to musical effects4 ,,*apt] ,,iv4 ,,s\nd ,,& ,,music4 ,our discussion ( waves & ripples 9 ! air w\ld be v incomplete if we left x )\t any fur!r ref]5ce to ! diff]5ce betwe5 ^? motions 9 ! air :i* con/itute noise or s\nd1 & ^? to :i* we owe ! pleasure-produc+ effects ( musical tones4 ,i propose1 !re=e1 to devote our "t to-day to a brief exposition ( ! prop]ties & modes ( production ( ^? air-vibrations :i* give rise to ! class ( s5sations we call music4 ,suffici5t has already be5 said to make x cle> to y t "o ess5tial diff]5ce betwe5 s\nd or noise & music1 z f> z reg>ds ! ev5ts tak+ place outside ( our own organism1 is t1 9 ! fir/ case1 we h a m or less irregul> motion 9 ! air1 &1 9 ! second1 a rhy?mical movem5t1 con/itut+ a tra9 ( air waves4 ,! great] pleasure we exp]i5ce f ! latt] is1 no d\bt1 p>tly due to _! rhy?mic "*4 ,we d]ive satisfaction f all regul>ly repeat$ muscul> movem5ts1 su* z ^? involv$ 9 danc+1 skat+1 & r[+1 & ! agreeable s5sation we enjoy 9 _! p]=mance is p>tly due to _! p]iodic or cyclical "*4 ,9 ! same way1 our e>s are satisfi$ by ! uni=mly repeat$ & su/a9$ vibrations proce$+ f an organ-pipe or tun+-=k 9 action1 b we are irritat$ & annoy$ by ! s5sations set up :5 irregul> vibrations ( ! air due to ! bray ( a donkey or ! scree* ( a p>rot fall ^u !m4 ,be=e1 h[ev]1 we c advance fur!r 9 an analysis ( ! nature ( musical s\nds1 two ?+s mu/ be cle>ly expla9$4 ,! fir/ ( ^! is ! mean+ ( ! t]m natural p]iod ( vibration1 & ! second is ! nature ( ! effect call$ resonance4 ,y see be=e y ?ree small brass balls susp5d$ by /r+s4 ,"o /r+ is #a foot long1 ! second #d feet1 & ! ?ird #i feet4 ,^! susp5d$ balls are call$ simple p5dulums4 ,tak+ 9 my h&s ! balls atta*$ to ! #a-;foot & ! #d-;foot /r+s1 ,i )draw !m a little way f _! positions ( re/ & let !m g4 ,!y vibrate l p5dulums1 b1 z y see1 ! #a-;foot p5dulum makes two sw+s 9 ! "t t ! #d-;foot makes "o sw+4 ,repeat+ ! exp]im5t ) ! #a-;foot & ! #i-;foot p5dulum1 we f9d t ! %ort "o n[ makes ?ree sw+s 9 ! "t ! long "o makes "o sw+4 ,! inf]5ce imm$iately foll[s t ^! p5dulums1 ^: respective l5g?s are #a1 #d1 & #i feet1 make _! sw+s f side to side 9 times :i* are respectively 9 ! ratio ( #a1 #b1 & #c4 ,aga91 if we )draw any ( ! p5dulums f its position ( re/ & let x sw+1 we %all f9d t 9 any /at$ p]iod ( "t1 say #a m9ute1 x executes a c]ta9 def9ite numb] ( oscillations :i* is peculi> to itself4 ,y might imag9e t1 by )draw+ x m or less f its position ( re/1 & mak+ x sw+ ov] a l>g] or small] di/ance1 y c\ld make ^! sw+s p] m9ute m or less z y please4 ,b y w\ld f9d1 on try+ ! exp]im5t1 t ?is is n ! case1 & t1 provid$ ! arc ( vibration is n too great1 ! "t ( "o complete sw+ to & fro is ! same :e!r ! sw+ be l>ge or small4 ,9 sci5tific language ?is is call$ ! iso*ronism ( ! p5dulum1 & is said to h be5 discov]$ by ,galileo 9 ! ,ca!dral at ,pisa1 :5 wat*+ ! sw+s ( a *&eli] die away1 :il/ c\nt+ _! numb] by ! beats ( 8 pulse4 ,?is p]iodic "t ( vibration1 :i* is indep5d5t ( ! amplitude ( vibration1 provid$ ! latt] is small1 is call$ ! natural "t ( vibration ( ! p5dulum1 or its free p]iodic "t4 ,9 ! case ( ! simple p5dulum ! free p]iodic "t is proportional to ! squ>e root ( ! l5g? ( ! p5dulum4 ,accord+ly1 a %ort p5dulum makes m sw+s p] m9ute ?an a long "o1 & ?is rate ( sw++ is q indep5d5t ( ! weight ( ! bob4 ,we c1 ( c\rse1 take hold ( ! bob ) our h& & =ce x to vibrate 9 any p]iod we please1 & ?us produce a =c$ vibration2 b a free vibration1 or "o :i* is un=c$1 has a natural "t-p]iod ( its own4 ,9 ord] t any body may vibrate :5 displac$ & !n set free1 two conditions mu/ exi/4 ,9 ! fir/ place1 !re mu/ be a controll+ =ce t5d+ to make ! sub/ance return to its orig9al position :5 displac$4 ,9 ! second place1 ! ?+ mov$ mu/ h mass or in]tia1 & :5 displac$ & all[$ to return x mu/ 9 consequ5ce ov]%oot ! m>k1 & acquire a displacem5t 9 an opposite direction4 ,9 ! case ( ! p5dulum ! ela/ic control or re/or+ =ce is ! weight ( ! bob1 :i* makes x always try to occupy ! l[e/ position4 ,we c1 h[ev]1 make a p5dulum ( ano!r k9d4 ,"h1 = in/ance1 is a heavy ball susp5d$ by a spiral spr+ 7see ,fig4 #ec74 ,if ,i pull ! ball d[n a little1 & !n let x g1 x jumps up & d[n1 & executes v]tical vibrations4 ,! ela/ic control "h is ! spr+ :i* resi/s ext5sion4 ,9 ?is in/ance1 also1 !re is a natural free "t ( vibration1 indep5d5t ( ! ext5t ( ! motion1 b dep5d5t ^u ! weight ( ! ball & ! /iffness ( ! spr+4 ,illu/ration3 ,,fig4 #ec4 ,a good illu/ration ( ! above pr9ciples may be f\nd 9 ! con/ruction ( a clock or a wat*4 ,a clock conta9s a p5dulum :i* vibrates 9 a c]ta9 fix$ "t4 ,! arrangem5ts we call ! 8works0 ( a clock are only a contrivance = c\nt+ ! sw+s1 & record+ !m by ! 8h&s0 ( ! clock4 ,ow+1 h[ev]1 to ! friction ( ! 8works10 ! p5dulum w\ld soon come to re/1 & h5ce we h a ma9spr+ or 8weights0 :i* apply a little pu% to ! p5dulum at ea* sw+1 & keep x go+4 ,9 a wat* !re is no p5dulum1 b !re is a 8balance-:eel & hair-spr+10 or a :eel :i* has a spiral spr+ atta*$ to x1 s t x c sw+ backw>ds & =w>ds ?r\gh a small angle4 ,! s-call$ 8escapem5t0 is a means by :i* ! sw+s are c\nt$1 & a little impulse giv5 to ! :eel to keep x sw++4 ,! wat* 8keeps "t0 if ?is hair-spr+ is ( ! "r degree ( /iffness1 & ! balance-:eel ( ! "r weight & size4 ,?us a clock c be made to g fa/] or sl[] by slightly alt]+ ! l5g? ( its p5dulum1 & ! wat* by slightly *ang+ ! /iffness ( its hair-spr+4 ,x may be not$ 9 pass+ t our legs1 9 walk+1 sw+ l p5dulums1 & e p>ticul> l5g? ( leg has its own natural "t ( vibration1 s t !re is a c]ta9 spe$ at :i* ea* p]son c walk :i* causes him or h] ! lea/ am\nt ( fatigue1 because x corresponds ) ! natural free or un=c$ p]iod ( vibration ( ! leg consid]$ z a p5dulum4 ,we n[ pass on to notice ano!r v important matt]4 ,if we h any p5dulum1 or mass susp5d$ by a spr+1 hav+ !re=e a c]ta9 natural p]iod ( vibration1 we c set x 9 motion by adm9i/]+ to x small repeat$ bl[s or pu%es4 ,if ! int]val betwe5 ^! impulses corresponds ) ! natural "t-p]iod ( oscillation1 x w be f\nd t quickly a v l>ge sw+ is accumulat$ or produc$4 ,if1 on ! o!r h&1 ! int]val betwe5 ! bl[s does n correspond ) ! natural "t ( vibration1 !n _! effect 9 produc+ vibration is comp>atively small4 ,?is may be illu/rat$ ) great ease by means ( ! ball susp5d$ by a spr+4 ,suppose t by means ( an indi>ubb] puff-ball ,i make a little puff ( air aga9/ ! susp5d$ ball4 ,! small impulse produces h>dly any visible effect4 ,let ?is puff be repeat$ at int]vals ( "t equal to t ( ! natural free p]iod ( vibration ( ! susp5d$ ball4 ,!n we f9d t1 9 ! c\rse ( a v few puffs1 we h caus$ a v consid]able vibration or sw+ to take place 9 ! heavy ball4 ,if1 h[ev]1 ! puffs ( air come irregul>ly1 !y produce v little effect 9 sett+ ! ball 9 motion4 ,9 ! same mann] a p5dulum1 consi/+ ( a heavy block ( wood1 may be set sw++ ov] a consid]able range by a v few prop]ly tim$ taps ( ! f+]4 ,we may notice ano!r in/ance ( ! effect ( accumulat$ impulses :5 walk+ ov] a plank laid across a dit*4 ,if we tread 9 "t ) ! natural vibration-p]iod ( ! flexible plank1 we %all f9d t v soon we produce oscillations ( a dang]\sly l>ge ext5t4 ,:]eas1 if we are c>eful to make ! "t ( our /eps or movem5t disagree ) t ( ! plank1 ?is w n be ! case4 ,x is = ?is reason t soldi]s cross+ a susp5sion bridge are (t5 made to break /ep1 le/ ! /eady tramp ( arm$ m5 %\ld happ5 to set up a p]il\s /ate ( vibration 9 ! bridge4 ,x is n untru?ful to say t a boy ) a pea-%oot] c\ld 9 "t break d[n ,*>+ ,cross ,railway ,bridge ov] ! ,?ames4 ,if we suppose a pea %ot aga9/ "o ( ! sections ( ?is iron bridge1 !re is no d\bt t x w\ld produce an inf9itesimal displacem5t ( ! bridge4 ,also !re is no "q t ! bridge1 be+ an ela/ic & heavy /ructure1 has a natural free "t ( vibration4 ,h5ce1 if pea aft] pea 7 %ot at ! same place at int]vals ( "t exactly agree+ ) ! free "t-p]iod ( vibration ( ! bridge1 ! effects w\ld be cumulative1 & w\ld 9 "t increase to an am\nt :i* w\ld endang] ! /ructure4 ,impracticable & undesirable z x might be to c>ry out ! exp]im5t1 x is nev]!less c]ta9ly true1 t a boy ) a pea-%oot]1 giv5 suffici5t pati5ce & suffici5t peas1 c\ld 9 "t break d[n an iron gird] bridge by ! accumulation ( prop]ly tim$ b inf9itely small bl[s4 ,! au?or _h an in/ance ( ?is be=e him n long ago4 ,he 0 at a place :]e v l>ge ma/s 7 be+ erect$4 ,"o ( ^! ma/s1 ab\t #ej feet long1 0 re/+ on two great blocks ( wood plac$ "u ea* end4 ,?is ma/ 0 a f9e beam ( timb]1 squ>e 9 section1 & ea* side ab\t #b feet wide4 ,! ma/1 !re=e1 lay l a bridge on its t]m9al supports4 ,/&+ or jump+ on ! middle ( ?is great beam produc$ h>dly any visible deflection4 ,! writ]1 h[ev]1 plac$ 8 h& on ! c5tre ( ! log & press$ x g5tly4 ,repeat+ ?is pressure at int]vals1 discov]y 0 soon made ( ! natural "t-p]iod ( vibration1 & by repeat+ ! pressures at ! "r mom5t x 0 f\nd t l>ge oscillations c\ld be accumulat$4 ,if he _h v5tur$ to proce$ f> ) ?is op]ation1 x is c]ta9 t1 ) prop]ly tim$ impulses1 x w\ld h be5 possible1 by m]ely apply+ ! pressure ( "o h&1 to break 9 half ?is great wood5 ma/4 ,we h con/ant occasion 9 me*anical "w to notice t :]eas "o pull or pu% ( great vig\r w n create "s desir$ displacem5t ( an object1 a numb] ( v small hits1 or prop]ly tim$ pu%es or pulls1 w a*ieve ! requisite result4 ,we might summ>ize ! =ego+ facts by say+ t x is a maxim 9 deal+ ) bodies capable ( any k9d ( free vibration t impulses1 h[ev] small1 w create oscillations ( any requir$ magnitude1 if only appli$ at int]vals equal to ! natural free p]iod ( vibration ( ! body 9 "q4 ,we c illu/rate ^! pr9ciples by a few exp]im5ts :i* h special ref]5ce to musical in/rum5ts4 ,if we fa/5 "o end ( a rope to a fix$ support1 we f9d we c produce a wave or pulse 9 ! rope by j]k+ ! free end up & d[n ) ! h&4 ,! spe$ ) :i* a pulse or wave travels along a rope dep5ds ^u its weight p] unit ( l5g?1 or1 say1 on ! numb] ( p\nds x weighs p] y>d1 & on ! t5sion or pull on ! rope4 ,! tight] ! rope1 ! quick] x travels2 & = ! same t5sion ! heavi] ! rope1 ! sl[] x travels4 ,x is n difficult to %[ t ! spe$ ) :i* ! pulse travels is measur$ by ! squ>e root ( ! quoti5t ( ! t5sion ( ! rope by its weight p] unit ( l5g?1 or1 z x may be call$1 ! d5sity ( ! rope4 ,we h already expla9$ t1 9 a m$ium su* z air1 a wave ( compression is propagat$ at a spe$ :i* is measur$ by ! squ>e root ( ! quoti5t ( ! air-pressure1 or ela/icity1 by its d5sity4 ,9 exactly ! same way ! hump t is =m$ on a rope by giv+ "o end ( x a j]k1 runs along at a spe$ :i* is measur$ by ! squ>e root ( ! quoti5t ( ! /ret*+ =ce1 or t5sion1 by ! d5sity4 ,! propagation ( a pulse or wave along a /r+ is mo/ easily %[n = lecture purposes by fill+ a long indi>ubb] tube ) s&1 & !n hang+ x up by "o end4 ,! tube s load$ has a l>ge weight p] unit ( l5g?1 & accord+ly1 if we give "o end a j]k a hump is creat$ :i* travels along r sl[ly1 & ( :i* ! movem5t c easily be wat*$4 ,we may sometimes see a canal-boat driv] give a j]k ( ?is k9d to ! end ( 8 horse-rope1 to make x cle> "s ob/acle su* z a po/ or bu%4 ,if we d ?is ) a rope fix$ at "o end1 we %all notice t :5 ! hump rea*es ! end x is reflect$ & returns ^u itself4 ,if we repres5t by ! lett] l ! l5g? ( ! rope1 & by t ! "t requir$ to travel ! d\ble di/ance !re & back f ! free end1 !n ! quoti5t ( #bl by t is obvi\sly ! velocity ( ! wave4 ,b we h /at$ t ?is velocity is equal to ! squ>e root ( ! t5sion ( ! rope 7call x e7 by ! weight p] unit ( l5g?1 say m4 ,h5ce cle>ly-- #bl_/t 7e_/m72 or t #bl 7m_/e7 ,suppos+1 !n1 t ! j]ks ( ! free end are giv5 at int]vals ( "t equal to t1 or to ! "t requir$ = ! pulse to run along & back aga91 we %all f9d ! rope ?r[n into s-call$ /ation>y waves4 ,if1 h[ev]1 ! j]ks come twice z quickly1 !n ! rope c accommodate itself to !m by divid+ itself into two sections1 ea* ( :i* is 9 sep>ate vibration2 & simil>ly x c divide itself into ?ree1 f\r1 five1 or six1 or m sections 9 /ation>y vibration4 ,! rope1 !re=e1 has n only "o1 b _m natural free p]iods ( vibration1 & x c adapt itself to _m diff]5t frequ5cies ( j]k+1 provid$ ^! are integ] multiples ( its fundam5tal frequ5cy4 ,! above /atem5ts may be v easily v]ifi$ by ! use ( a l>ge tun+-=k & a /r+4 ,let a light cord or silk /r+ be atta*$ to "o prong ( a l>ge tun+-=k :i* is ma9ta9$ 9 motion electrically z pres5tly to be expla9$4 ,! o!r end ( ! cord passes ov] a pulley1 & has a little weight atta*$ to x4 ,let ! tun+-=k be set 9 vibration1 & v>i\s weights atta*$ to ! opposite end ( ! cord4 ,x is possible to f9d a weight :i* applies su* a t5sion to ! cord t its "t ( free vibration1 z a :ole1 agrees ) t ( ! =k4 ,! cord is !n ?r[n into /ation>y vibration4 ,?is is be/ se5 by ?r[+ ! %ad[ ( ! cord ^u a :ite scre51 :5 x w appe> z a grey sp9dle-%ap$ %ad[4 ,! c5tral po9t ,a ( ! sp9dle is call$ a v5tral po9t1 or anti-node1 & ! /ation>y po9ts ,n are call$ ! nodes 7see ,fig4 #ed74 ,next let ! t5sion ( ! /r+ be r$uc$ by remov+ "s ( ! weight atta*$ to ! end4 ,:5 ! prop] adju/m5t is made1 ! cord w vibrate 9 two segm5ts1 & h a node at ! c5tre4 ,ea* segm5t vibrates 9 "t ) ! tun+-=k1 b ! "t ( vibration ( ! :ole cord is d\ble t ( ! =k4 ,simil>ly1 by adju/+ ! t5sion1 we may make ! cord vibrate 9 ?ree1 f\r1 or m sections1 con/itut+ :at are call$ ! h>monics ( ! /r+4 ,! /r+1 !re=e1 9 any p>ticul> /ate z reg>ds t5sion & l5g?1 has a fundam5tal p]iod 9 :i* x vibrates z a :ole1 b x c also divide itself into sections1 ea* ( :i* makes two1 ?ree1 f\r1 or m times z _m vibrations p] second4 ,illu/ration3 ,,fig4 #ed4 ,9 ! case ( a viol9 or piano /r+1 we h an example ( ! same action4 ,9 play+ ! viol91 ! effective l5g? ( ! /r+ is alt]$ by plac+ ! f+] ^u x at a c]ta9 po9t1 & !n sett+ ! /r+ 9 vibration by pass+ along x a b[ ( horsehair cov]$ ) ros94 ,! /r+ is set 9 vibration z a :ole1 & also 9 sections1 & x !re=e yields ! s-call$ fundam5tal tone1 accompani$ by ! h>monics or ov]tones4 ,e viol9i/ kn[s h[ mu* ! tone is affect$ by ! po9t at :i* ! b[ is plac$ across ! /r+1 & ! reason is t ! po9t :]e ! b[ t\*es ! /r+ mu/ always be a v5tral po9t1 or anti-node1 & x !re=e det]m9es ! h>monics :i* %all occur4 ,ano!r good illu/ration ( ! action ( prop]ly int]mitt5t small impulses 9 creat+ vibrations may be f\nd 9 ! foll[+ exp]im5t ) two electrically controll$ tun+-=ks3 ,a l>ge tun+-=k1 ,f 7see ,fig4 #ed71 has fix$ betwe5 its prongs an electro-magnet1 ,e1 or piece ( iron surr\nd$ ) silk-cov]$ wire4 ,:5 an electric curr5t f a batt]y1 ,b1 trav]ses ! wire x causes ! iron to be magnetiz$1 & x !n attracts ! prongs & pulls !m toge!r4 ,! circuit ( ! batt]y is complet$ ?r\gh a little spr+y piece ( metal atta*$ to "o ( ! prongs :i* makes contact ) a fix$ screw4 ,! arrangem5t is su* t :5 ! prongs fly ap>t ! circuit is complet$ & ! curr5t fl[s1 & !n ! curr5t magnetizes ! iron1 & ?is 9 turn pulls ! prongs toge!r1 & breaks ! circuit4 ,! =k1 !re=e1 ma9ta9s itself 9 vibration :5 once x has be5 />t$4 ,x is call$ an electrically driv5 tun+-=k4 ,"h are two su* =ks1 9 e way id5tical4 ,"o ( ! =ks is self-driv51 b ! curr5t ?r\gh its own electro-magnet is made to pass also ?r\gh ! electro-magnet ( ! o!r =k1 :i* is1 !re=e1 n self-driv51 b controll$ by ! fir/4 ,if1 !n1 ! fir/ =k is />t$1 ! electro-magnet ( ! second =k is trav]s$ by int]mitt5t electric curr5ts hav+ ! same frequ5cy z ! fir/ =k1 & ! electro-magnet ( ! second =k adm9i/]s1 !re=e1 small pulls to ! prongs ( ! second =k1 ^! pulls correspond+ to ! p]iodic "t ( ! fir/ =k4 ,if1 z at pres5t1 ! =ks are id5tical1 & ,i />t ! fir/ "o1 or ! driv+ =k1 9 action x w1 9 a few seconds1 cause ! second =k to beg9 to s\nd4 ,let me1 h[ev]1 affix a small piece ( wax to ! second =k4 ,i h n[ alt]$ its prop] p]iod ( vibration by slightly weight+ ! prongs4 ,y n[ see t ! fir/ =k is unable to set ! second =k 9 action4 ,! electro-magnet is op]at+ z be=e1 b its impulses d n come at ! "r "t1 & h5ce ! second =k does n beg9 to move4 ,if we weight ! two =ks equally ) wax1 we c aga9 tune !m 9 sympa?y1 & !n once aga9 !y w control ea* o!r4 ,illu/ration3 ,,fig4 #ee4--;,an exp]im5t on resonance4 ,all ^! cases1 9 :i* "o set ( small impulses at prop] int]vals ( "t create a l>ge vibration 9 ! body on :i* !y act1 are said to be in/ances ( resonance4 ,a m p]fect illu/ration ( ac\/ic resonance may be br\ght be=e y n[4 ,be=e me1 on ! table1 is a tall glass cyl9drical j>1 & ,i h 9 my h& a tun+-=k1 ! prongs ( :i* make #bef vibrations p] second :5 /ruck 7see ,fig4 #ee74 ,if ! =k is />t$ 9 action1 y at a di/ance w he> b little s\nd4 ,! prongs ( ! =k move ?r\gh ! air1 b !y d n set x 9 v great oscillatory movem5t4 ,let u calculate1 h[ev]1 ! wave-l5g? ( ! waves giv5 out by ! =k4 ,f ! fundam5tal =mula1 wave-velocity wave-l5g? frequ5cy2 & kn[+ t ! velocity ( s\nd at ! pres5t temp]ature ( ! air is ab\t #aabf feet p] second1 we see at once t ! l5g? ( ! air wave produc$ by ?is =k mu/ be ne>ly #dd feet1 because #dd #bef #aabfd4 ,h5ce ! qu>t] wave-l5g? is ne>ly #aa foot1 or1 say1 #a foot #a in*4 ,i hold ! =k ov] ?is tall j>1 & p\r wat] into ! j> until ! space betwe5 ! wat]-surface & ! top ( ! j> is a little ov] #a foot1 & at t mom5t ! s\nd ( ! =k becomes mu* l\d]4 ,! column ( air 9 ! j> is #aa foot 9 l5g? & ?is res\nds to ! =k4 ,y w h no difficulty 9 see+ ! reason = ?is 9 ! light ( previ\s explanations4 ,! air column has a c]ta9 natural rate ( vibration1 :i* is su* t its fundam5tal note has a wave-l5g? f\r times ! l5g? ( ! column ( air4 ,9 ! case ( ! rope fix$ at "o end & j]k$ up & d[n at ! o!r s z to make /ation>y vibrations1 ! l5g? ( ! rope is "o qu>t] ( ! wave-l5g? ( its /ation>y wave4 ,?is is easily se5 if we rememb] t ! fix$ end mu/ be a node1 & ! end mov$ up & d[n mu/ be an anti-node1 or v5tral segm5t1 & ! di/ance betwe5 a node & an anti-node is "o qu>t] ( a wave-l5g?4 ,accord+ly ! vibrat+ column ( air 9 ! j> also has a fundam5tal mode ( vibration1 su* t ! l5g? ( ! column is "o qu>t] ( a wave-l5g?4 ,h5ce ! vibrat+ prongs ( ! #bef-p]iod tun+-=k1 :5 held ov] ! #aa foot long column ( air1 are able to set ! air 9 great vibratory movem5t1 = ! impulses f ! prongs come at exactly ! "r "t4 ,accord+ly1 ! l\d s\nd y he> :5 ! =k is held ov] ! j> proce$s1 n s mu* f ! =k z f ! column ( air 9 ! j>4 ,! prongs ( ! =k give little bl[s to ! column ( air1 & ^! be+ at int]vals equal to ! natural "t-p]iod ( vibration ( ! air 9 ! j>1 ! latt] is soon set 9 viol5t vibration4 ,we c1 9 ! next place1 pass on n[ to discuss "s matt]s connect$ ) ! !ory ( music4 ,:5 regul> air-vibrations or wave-tra9s fall ^u ! e> !y produce ! s5sation ( a musical tone1 provid$ t _! frequ5cy lies betwe5 ab\t #dj p] second & ab\t #djjj4 ,! l[e/ note 9 an organ usually is "o hav+ #cb vibrations p] second1 & ! highe/ note 9 ! or*e/ra is t ( a piccolo flute1 giv+ #dgeb vibrations p] second4 ,we c appreciate z s\nd vibrations ly+ betwe5 #af & #cb1jjj1 b ! great] portion ( ^! high frequ5cies h no musical "*1 & w\ld be describ$ z :i/les or squeaks4 ,:5 "o note has twice ! frequ5cy ( ano!r x is call$ ! octave ( ! fir/4 ,?us our range ( musical tones is compris$ )9 ab\t sev5 octaves1 or )9 ! limits ( ! notes ^: frequ5cies are #dj1 #hj1 #afj1 #cbj1 #fdj1 #abhj1 #befj1 & #eabj4 ,^! musical notes are di/+ui%$1 z e "o kn[s1 by c]ta9 lett]s or signs on a clef4 ,?us ! note call$ ! middle ,c ( a piano has a frequ5cy ( #bdh1 & is d5ot$ by ! sign ,illu/ration ,! octave is divid$ into c]ta9 musical int]vals by notes1 ! frequ5cies ( :i* h a c]ta9 ratio to t ( ! fundam5tal note4 ,?is ratio is det]m9$ by :at is call$ ! scale1 or gamut4 ,?us1 9 ! major diatonic natural scale1 if we d5ote ! fundam5tal note by ,c1 call$ d or ut 9 s++1 & its frequ5cy by n1 !n ! o!r notes 9 ! natural scale are d5ot$ by ! lett]s1 & h frequ5cies z bel[4 d re mi fa sol la si d ,c ,d ,e ,f ,g ,a ,b ,c#a n n n n n n n #bn ,h5ce if ! note ,c has #bdh vibrations p] second1 !n ! note ,d w h #i #bdh #h #bgi vibrations p] second4 ,on look+ at ! above scale ( ! eight notes =m+ an octave1 x w be se5 t !re are ?ree k9ds ( ratios ( frequ5cies ( ! v>i\s notes4 7#a7 ,! ratio ( ,c to ,d1 or ,f to ,g1 or ,a to ,b1 :i* is t ( #h to #i4 7#b7 ,! ratio ( ,d to ,e1 & ,g to ,a1 :i* is t ( #i to #aj4 7#c7 ,! ratio ( ,e to ,f1 or ,b to ,c#a1 :i* is t ( #ae to #af4 ,! fir/ two ( ^! int]vals or ratios are bo? call$ a tone1 & ! ?ird is call$ a semitone4 ,! two tones1 h[ev]1 are n exactly ! same1 b _! ratio to "o ano!r is t ( to or ( #hj to #ha4 ,?is int]val is call$ a comma1 & c be di/+ui%$ by a good musical e>4 ,sev]al ( ^! int]vals or ratios ( frequ5cies h receiv$ names4 ,?us ! int]val ,c to ,e1 #d3e1 is call$ a major ?ird1 & ! int]val ,e to ,g1 #e3f1 is call$ a m9or ?ird2 ! int]val ,c to ,g1 #b3c1 is call$ a fif?1 & t ( ,c to ,c#a1 #a3b1 is call$ an octave4 ,= ! purposes ( music x has be5 f\nd necess>y to introduce o!r notes betwe5 ! sev5 notes ( ! octave4 ,if a note is introduc$ :i* has a frequ5cy great] ?an any "o ( ! sev5 9 ! ratio ( #be to #bd1 t is call$ a %>p5$ note2 ?us ! note ( :i* ! frequ5cy is n w\ld be call$ ,g %>p1 & writt5 ,g4 ,9 ! same way1 if ! frequ5cy ( any note is l[]$ 9 ! ratio ( #bd to #be1 x is said to be flatt5$4 ,!n ! note ^: frequ5cy is n w\ld be call$ ,g flat1 & writt5 ,g4 ,x is obvi\s t if we 7 to introduce flats & %>ps to all ! eight notes we %\ld h tw5ty-f\r notes 9 ! octave1 & ! v>i\s int]vals w\ld become too num]\s & confus+ = memory or p]=mance4 ,h5ce 9 key$ in/rum5ts ! difficulty has be5 ov]come by employ+ a scale ( equal temp]am5t1 made z foll[s3 ,! int]val ( an octave is divid$ into twelve p>ts by introduc+ elev5 notes1 ! ratio ( ! frequ5cy ( ea* note to its neighb\rs on ei!r side be+ ! same1 & equal to ! ratio #a to #ajeidf4 ,! scale ?us =m$ is call$ ! *romatic scale1 & by ?is means a numb] ( ! flats & %>ps become id5tical2 ?us1 = in/ance1 ,c & ,d become ! same note4 ,! octave has !re=e twelve notes1 :i* are ! sev5 :ite keys1 & ! five black ones ( ! octave ( ! keybo>d ( a piano or organ4 ,e "o n entirely de/itute ( a musical e> is aw>e t c]ta9 ( ^! musical int]vals1 su* z ! fif?1 ! octave1 or ! major ?ird1 produce an agreeable impression on ! e> :5 ! notes =m+ !m are s\nd$ toge!r4 ,on ! o!r h&1 "s int]vals1 su* z ! sev5?1 are n pleasant4 ,! =m] we call concords1 & ! latt] discords4 ,! "q !n arises--,:at is ! reason = ?is diff]5ce 9 ! effect ( ! air-vibrations on ! e>8 ,?is leads u to consid] ! nature ( simple & complex air vibrations or waves4 ,let u consid]1 9 ! fir/ place1 ! effect ( s5d+ out into ! air two sets ( air waves ( slightly diff]5t wave l5g?s4 ,^! waves bo? travel at ! same rate1 h5ce we %all n affect ! comb9$ effects ( ! waves ^u ! air if we consid] bo? sets ( waves to /& /ill4 ,= ! sake ( simplicity1 we w consid] t ! wave-l5g? ( "o tra9 is #bj in*es1 & t ( ! o!r is #ba4 ,moreov]1 let ! two wave-tra9s be s plac$ relatively to "o ano!r t !y bo? />t f "o po9t 9 ! same phase ( movem5t2 t is1 let _! z]o po9ts1 or _! humps or holl[s1 co9cide4 ,!n if we draw two wavy l9es 7see ,fig4 #ef7 to repres5t ^! two tra9s1 x w be evid5t t1 s9ce ! wave-l5g? ( "o is #a in* long] ?an t ( ! o!r--t is1 a di/ance equal to tw5ty wave-l5g?s--"o wave-tra9 w h ga9$ a :ole wave-l5g? ^u ! o!r1 & 9 a di/ance equal to t5 wave-l5g?s1 "o wave tra9 w h ga9$ half a wave-l5g? ^u ! o!r4 ,if we !re=e imag9e ! two wave-tra9s sup]impos$1 we %all f9d1 on look+ along ! l9e ( propagation1 an alt]nate d\bl+ or de/ruction ( wave-effect at regul> int]vals4 ,9 o!r words1 ! effect ( sup]impos+ two tra9s ( waves ( slightly diff]5t wave-l5g?s is to produce a resultant wave-tra9 9 :i* ! wave-amplitude increases up to a c]ta9 po9t1 & !n dies away aga9 ne>ly to no?+1 z %[n 9 ! l[e/ ( ! ?ree wave-l9es 9 ,fig4 #ef4 ,illu/ration3 ,,fig4 #ef4--,! =mation ( beats by two wave-tra9s4 ,we mu/1 !n1 det]m9e h[ f> ap>t ^! po9ts ( maximum wave-amplitude or po9ts ( no wave effect lie4 ,if ! wave-l5g? ( "o tra9 is1 z /at$1 #bj in*es1 !n a l5g? ( t5 wave-l5g?s is #bjj in*es1 & ?is mu/ be1 !re=e1 ! di/ance f a place ( maximum comb9$ wave-effect to a place ( z]o wave-effect4 ,accord+ly1 ! di/ance betwe5 two places :]e ! two wave tra9s help "o ano!r mu/ be #djj in*es1 & ?is mu/ also be ! di/ance betwe5 two adjac5t places ( wave-de/ruction4 ,if1 !re=e1 we look along ! wavy l9e repres5t+ ! resultant wave1 e #djj in*es we %all f9d a maximum wave-amplitude1 & e #djj in*es a place :]e ! waves h de/roy$ ea* o!r4 ,we may call ?is di/ance a wave-tra9 l5g?1 & x is obvi\sly equal to ! product ( ! con/itu5t wave-l5g?s divid$ by ! diff]5ce ( ! two con/itu5t wave-l5g?s4 ,x foll[s f ?is t if we suppose ! two wave-tra9s to move =w>d ) equal spe$1 ! numb] ( maximum po9ts or z]o po9ts :i* w pass any place 9 ! unit ( "t w be equal to ! diff]5ce betwe5 ! frequ5cies ( ! con/itu5ts4 ,let u n[ r$uce ?is to an exp]im5t4 ,"h are two organ-pipes exactly tun$ to unison1 & :5 bo? are s\nd$ toge!r we h two id5tical wave-tra9s s5t out into ! air4 ,we c1 h[ev]1 slightly l5g!n "o ( ! pipes1 & s put !m out ( tune4 ,:5 ?is is done y c no long] he> ! smoo? s\nd1 b a sort ( wax+ & wan+ 9 ! s\nd1 & ?is alt]nate increase & dim9ution 9 l\dness is call$ a beat4 ,we c easily take c\nt ( ! numb] ( beats p] second1 & by ! reason+ giv5 above we see t ! numb] ( beats p] second mu/ be equal to ! diff]5ce betwe5 ! frequ5cies ( ! two sets ( waves4 ,?us if "o organ-pipe is giv+ #ajj vibrations p] second to ! air1 & ! o!r #ajb1 we he> two beats p] second4 ,n[1 up to a c]ta9 po9t we c c\nt ^! beats1 b :5 !y come quick] ?an ab\t #aj p] second1 we cease to be able to he> !m sep>ately4 ,:5 !y come at ! rate ( ab\t #cj p] second !y communicate to ! comb9$ s\nd a peculi> rasp+ & unpleasant effect :i* we call a discord4 ,if !y come mu* m quickly ?an #gj p] second we cease to be consci\s ( _! pres5ce by any discordant effect 9 ! s\nd4 ,! !ory 0 fir/ put =w>d by ! fam\s physici/1 ,von ,helmholtz1 t ! reason c]ta9 musical int]vals are n agreeable to ! tra9$ e> is because ! diff]5ce betwe5 ! frequ5cies ( ! con/itu5t fundam5tal tones or ! h>monics pres5t 9 !m give rise to beats1 approximately ( #cj to #dj p] second4 ,9 ord] to simplify our explanations we w deal ) two cases only1 viz4 t ( ! octave int]val & t ( ! sev5?4 ,! fir/ is a p]fect concord1 & ! second1 at lea/ on /r+$ in/rum5ts1 is a discord4 ,x has already be5 expla9$ t :5 a /r+ vibrates x does s n only z a :ole1 b also 9 sections1 giv+ out a fundam5tal note ) sup]pos$ h>monics4 ,suppose we consid] ! octave ( notes ly+ betwe5 ! frequ5cies #bfd & #ebh1 :i* correspond to ! notes ,c & ,c#a =m+ ! middle octave on a piano4 ,! frequ5cies & diff]5ces ( ! eight tones 9 ?is octave are z foll[s3-- ,,frequ5cies ,,( ,,! ,,notes ,,( ,,! ,,middle ,,octave ,,( ,a ,,piano4 ,notes4 ,frequ5cy4 ,diff]5ce4 ,c #bfd #cc ,d #big #cc ,e #ccj #bb ,f #ceb #dd ,g #cif #dd ,a #ddj #ee ,b #die #cc ,c#a #ebh ,x w ?us be se5 t ! diff]5ces betwe5 ! frequ5cies ( adjac5t notes are su* z to make beats betwe5 !m :i* h a numb] p] second s ne> to ! limits ( #cj to #dj t adjac5t notes s\nd$ toge!r are discords4 ,suppose1 h[ev]1 we s\nd ! sev5?1 viz4 ,c & ,b1 toge!r4 ,! frequ5cies are #bfd & #die1 & ! diff]5ce is #bca4 ,s9ce1 !n1 ! diff]5ce betwe5 ! frequ5cies lies f> beyond ! limit ( #cj to #dj p] second1 h[ comes x t 9 ?is case we h a discord8 ,to answ] ?is "q we mu/ consid] ! h>monics pres5t ) ! fundam5tals4 ,write d[n ea* frequ5cy multipli$ respectively by ! numb]s #a1 #b1 #c1 #d1 etc4-- ,c4 ,b4 ,fundam5tal #bfd #die ,fir/ h>monic #ebh #iij ,second 0 #gib #adge ,?ird 0 #ajef #aihj ,f\r? 0 #acbj #bdge ,fif? 0 #aehd #bigj ,on look+ at ^! numb]s we see t al?\gh ! diff]5ce betwe5 ! frequ5cies ( ! two fundam5tals is too great to produce ! disagreeable numb] ( beats1 yet ! diff]5ce betwe5 ! frequ5cies ( ! fundam5tal ( note ,b 7#die7 & ! fir/ h>monic ( note ,c 7#ebh7 is exactly #cc1 :i* is1 !re=e1 ! requir$ numb]4 ,accord+ly1 ! discordant "* ( ! sev5? int]val play$ on a piano is n due to ! beats betwe5 ! prim>y tones1 b to beats aris+ betwe5 ! fir/ h>monic ( "o & ! fundam5tal ( ! o!r4 ,x w be a useful ex]cise to ! read] to select any o!r int]val1 & write d[n ! prim>y frequ5cies & ! ov]tone frequ5cies1 or h>monics1 & !n det]m9e :e!r betwe5 any pairs disagreeable beats c occur4 ,! pres5ce ( h>monics or ov]tones is1 !re=e1 a s\rce ( discord 9 "s cases1 b nev]!less ^! ov]tones communicate a c]ta9 "* to ! s\nd4 ,helmholtz's *ief conclusions z reg>ds ! cause ( concord & discord 9 musical tones 7 z foll[s3-- 7#a7 ,musical s\nds :i* are pure1 t is1 h no h>monics mix$ up ) !m1 are s(t & agreeable1 b )\t brilliancy4 ,( ?is k9d are ! tones emitt$ by tun+-=ks g5tly /ruck or op5 organ-pipes n bl[n viol5tly4 7#b7 ,! pres5ce ( h>monics up to ! six? communicates =ce & brilliancy & "* to ! tone4 ,( ?is k9d are ! notes ( ! piano & organ-pipes m /rongly bl[n4 7#c7 ,if only ! unev5 h>monics1 viz4 ! fir/1 ?ird1 fif?1 etc41 are pres5t1 ! s\nd acquires a c]ta9 nasal "*4 7#d7 ,if ! high] h>monics are /rong1 !n ! s\nd acquires great p5etrat+ =ce1 z 9 ! case ( brass in/rum5ts1 trumpet1 trombone1 cl>ionet1 etc4 7#e7 ,! causes ( discord are beats hav+ a frequ5cy ( #cj to #dj or s1 tak+ place betwe5 ! two prim>y tones or ! h>monics ( ei!r note4 ,! pleasure d]iv$ f ! s\nd ( a musical in/rum5t is dep5d5t1 to a l>ge ext5t1 on ! exi/5ce ( ! desirable h>monics 9 ea* tone1 or on ! exclusion ( undesirable ones4 ,9 ! next place1 let u consid] a little ! means at our disposal = creat+ & en=c+ ! class ( air-waves :i* give rise to ! s5sations ( musical tones4 ,broadly speak+1 !re are ?ree *ief =ms ( musical air-wave-mak+ appliance1 viz4 ^? :i* dep5d on ! vibrations ( columns ( air1 on /r+s1 & on plates respectively4 ,"o ( ! olde/ & simple/ =ms ( musical in/rum5t is t repres5t$ by ! pan-pipes1 /ill us$ z an or*e/ral accompanim5t 9 ! case ( ! ev]-popul> p]ipatetic !atrical display call$ ,pun* & ,judy4 ,if we take a metal or wood5 pipe clos$ at ! bottom1 & bl[ g5tly across ! op5 end1 we obta9 a musical note4 ,! air 9 ! pipe is set 9 vibration1 & ! tone we obta9 dep5ds on ! l5g? ( ! column ( air1 :i* is ! same z ! l5g? ( ! pipe4 ,! mann] 9 :i* ?is air-vibration is />t$ is z foll[s3 ,on bl[+ across ! op5 end ( ! pipe clos$ at ! bottom a p>tial vacuum is made 9 x4 ,t ?is is s1 c be se5 9 any sc5t spray-produc]1 9 :i* two glass tubes are fix$ at "r angles to ea* o!r4 ,"o tube dips into ! sc5t1 & ?r\gh ! o!r a puff ( air is s5t across ! op5 m\? ( ! fir/4 ,! liquid is suck$ up ! v]tical tube by reason ( ! p>tial vacuum made above x4 ,if we employ a pipe clos$ at ! bottom & bl[ across ! op5 end1 ! fir/ effect ( ! exhau/ion is t ! jet ( air is p>tly suck$ d[n into ! clos$ tube1 & ?us compresses ! air 9 x4 ,?is air !n reb\nds1 & aga9 a p>tial vacuum is made 9 ! tube4 ,s ! result is an alt]nate compression & expansion ( ! air 9 ! clos$ tube4 ,! column ( air is alt]nately /ret*$ & squeez$1 & a /ate ( /ation>y vibration is set up 9 ! air 9 ! tube2 j z 9 ! case ( a rope fix$ at "o end & j]k$ up & d[n at ! o!r end4 ,! natural "t-p]iod ( vibration ( ! column ( air 9 ! tube controls ! behavi\r ( ! jet ( air bl[n across its m\?1 ! en]gy ( ! jet ( air be+ drawn ^u to keep ! column ( air 9 ! tube 9 a /ate ( oscillation4 ,?us a flutt] is excit$ 9 ! air 9 ! tube1 :i* is ma9ta9$ z long z !re is a bla/ ( air across its m\?1 & ?is communicates to ! air outside a wave-motion4 ,we h1 !re=e1 a musical note produc$1 ! wave-l5g? ( :i* is f\r times ! l5g? ( ! clos$ tube across ! m\? ( :i* we are bl[+4 ,accord+ly1 a v simple musical in/rum5t su* z ! pan-pipes consi/s ( a r[ ( tubes clos$ at ! bottom1 ! tubes be+ ( diff]5t l5g?s4 ,a curr5t ( air f ! m\? is bl[n across ! tubes tak5 9 a c]ta9 ord]1 & we c obta9 a simple melody by t process ( selection4 ,illu/ration3 ,,fig4 #eg4--;,a clos$ organ-pipe4 ,an organ-pipe is only a m p]fect means = do+ ! same ?+4 ,organ-pipes may be ei!r op5 or clos$ pipes4 ,also !y h ei!r a re$ or a flute at "o end = ! purpose ( e/abli%+ air-vibrations :5 a curr5t ( air is bl[n into ! pipe4 ,! =m ( organ-pipe mo/ easy to und]/& is ! clos$ flute pipe4 ,?is consi/s ( a wood5 tube clos$ at ! upp] end1 & at ! l[] end hav+ a foot-tube & m\?piece z %[n 9 section 9 ,fig4 #eg4 ,:5 a g5tle curr5t ( air is bl[n 9 at ! foot-tube1 x imp+es on ! %>p edge or *amf] ( ! m\?piece1 & x acts j z :5 bl[n across ! op5 end ( a simple clos$ pipe4 ,t is to say1 x sets up a /ate ( alt]nate compression & expansion ( ! air 9 ! pipe4 ,at ! clos$ end1 p]iod-*anges 9 d5sity 9 ! air are e/abli%$1 b no great movem5t takes place4 ,at ! op5 end or m\? !re are no great *anges ( d5sity1 b ! air is alt]nately mov+ 9 & out at ! m\?piece4 ,! /eady bla/ ( air aga9/ ! *amf]1 !re=e1 sets up a /ate ( /eady oscillation ( ! air 9 ! pipe1 ! air be+ squeez$ up & ext5d$ alt]nately s t !re is fir/ a /ate ( compression1 & !n a /ate ( p>tial r>efaction 9 ! air at ! clos$ end ( ! pipe4 ,9 ?is case1 also1 ! wave-motion communicat$ to ! surr\nd+ air has a wave-l5g? equal to f\r times ! l5g? ( ! pipe4 ,if we op5 ! upp] end ( ! pipe1 x at once emits a note :i* has a wave-l5g? equal to d\ble ! l5g? ( ! pipe4 ,h5ce ! note emitt$ by an op5-end$ organ-pipe is an octave high] ?an t giv5 out by a clos$ organ-pipe ( ! same l5g?4 ,! action ( an op5 organ-pipe is n q s easy to compreh5d z t ( a clos$ pipe4 ,! difficulty is to see h[ /ation>y air waves c be set up 9 a pipe :i* is op5 at bo? ends4 ,! easie/ way to compreh5d ! matt] is z foll[s3 ,:5 ! bla/ ( air aga9/ ! lip ( ! pipe beg9s to p>tially exhau/ ! air 9 x1 ! r>efaction s begun does n comm5ce ev]y:]e 9 ! pipe at once4 ,x />ts f ! m\?piece end1 & is propagat$ along ! pipe at a rate equal to ! velocity ( s\nd4 ,! air at ! op5 ends ( ! pipe moves 9 to supply ?is r$uc$ pressure1 &1 9 s do+1 ov]%oots ! m>k1 & ! result is a region ( compression is =m$ 9 ! c5tral portions ( ! pipe 7see ,fig4 #eh74 ,! next in/ant ?is compress$ air exp&s aga91 & moves out at ! two op5 ends ( ! pipe4 ,we h ?us e/abli%$ 9 ! pipe an oscillatory /ate :i*1 at ! c5tral region ( ! pipe1 consi/s 9 an alt]nate compression & expansion or r>efaction ( ! air1 :il/ at ! op5 end & m\?piece end !re is an alt]nate ru%+ 9 & ru%+ out ( ! air4 ,h5ce 9 ! c5tre ( ! pipe we h little or no movem5t ( ! air1 b rapid alt]nations ( pressure1 or1 :i* is ! same ?+1 d5sity2 & at ! two ends little or no *ange 9 d5sity1 b rapid movem5t ( ! air 9 & out ( ! pipe4 ,illu/ration3 ,,fig4 #eh4--;,an op5 organ-pipe4 ,an analogy betwe5 ! vibration ( ! air 9 a clos$ & op5 organ-pipe might be f\nd 9 consid]+ ! vibration ( an ela/ic rod--fir/1 :5 clamp$ at "o end1 & secondly1 :5 clamp$ at ! two ends4 ,! deflection ( ! rod at any po9t may be consid]$ to repres5t *ange ( air-pressure1 & ! fix$ po9t or po9ts ! op5 end ( ! pipe at :i* !re c be no *ange ( d5sity1 because !re x is 9 close communication ) ! op5 air outside ! pipe4 ,x is at once evid5t t ! l5g? ( ! op5 organ-pipe1 :5 s\nd+ its fundam5tal tone1 is "o-half ( ! l5g? ( ! air wave x produces4 ,accord+ly1 f ! =mula1 wave-velocity frequ5cy wave-l5g?1 we see t1 s9ce ! velocity ( s\nd at ord9>y temp]ature is ab\t #aabj feet p] second1 an approximate rule = obta9+ ! frequ5cy ( ! vibrations giv5 out by an op5 organ-pipe is z foll[s3-- ,frequ5cy #aabj divid$ by twice ! l5g? ( pipe4 ,we say approximate1 because1 z a matt] ( fact1 = a reason r too complicat$ to expla9 "h1 ! wave-l5g? ( ! air-vibrations is equal to r m ?an d\ble ! l5g? ( ! pipe4 ,9 fact1 :at we may call ! effective l5g? ( ! pipe is equal to its real end-to-end l5g? increas$ by a fraction ( its diamet]1 :i* is v ne>ly f\r-fif?s4 ,illu/ration3 ,,fig4 #ei4 ,we c confirm by exp]im5ts ! /atem5ts made z to ! condition ( ! air 9 a s\nd+ organ-pipe4 ,"h is a pipe ) ?ree little holes bor$ 9 x at ! top1 middle1 & bottom 7see ,fig4 #ei74 ,ea* ( ^! is cov]$ ) a ?9 indi>ubb] membrane1 & ?is1 aga91 by a little box :i* has a gas-pipe lead+ to x & a gas-jet connect$ ) x4 ,if we lead gas into ! box & light ! jet1 we h a little flame1 z y see4 ,if1 !n1 ! indi>ubb] membrane is press$ 9 & out1 x w cause ! gas-flame to flick]4 ,su* an arrangem5t is call$ a manometric flame1 because x s]ves to detect or measure *anges ( pressure 9 ! pipe4 ,! flick] ( ! flame :5 ! organ-pipe is s\nd$ is1 h[ev]1 s rapid t we _c foll[ x unless we look at ! image 9 a cubical revolv+ mirror ( ! k9d already us$4 ,:5 s reg>d$1 if ! flame is /eady1 we see a broad b& ( light4 ,if we s\nd ! organ-pipe g5tly & look at ! b&s ( light correspond+ to ! ?ree flames1 we see t ! flames at ! top & bottom ( ! pipe are ne>ly /eady1 b t ! "o at ! middle ( ! pipe is flick]+ rapidly1 ! b& ( light be+ *ang$ to a saw-too?-l =m 7see ,fig4 #fj74 ,?is %[s u t rapid *anges ( pressure are tak+ place at ! c5tre ( ! pipe4 ,aga91 if we prep>e a little tamb\r9e 7by /ret*+ p>*m5t-pap] ov] a wood5 r+71 & l[] x by a /r+ into ! s\nd+ organ-pipe1 we %all f9d t gra9s ( s& scatt]$ ov] ?is tamb\r9e jump ab\t rapidly :5 ! membrane is held ne> ! top or ! bottom ( ! pipe1 b are quiesc5t :5 x is at ! middle4 ,illu/ration3 ,,fig4 #fj4 ,?is %[s u t !re is viol5t movem5t ( ! air at ! ends1 b n 9 ! c5tre1 ?us confirm+ ! d$uctions ( !ory4 ,x %\ld be not$ t if ! pipe is ov]-bl[n or s\nd$ too /rongly1 h>monics w make _! appe>ance1 & ! simple /ate ( affairs w no long] exi/4 ,! celebrat$ ma!matician1 ,daniel ,b]n\lli1 discov]$ t an organ-pipe c be made to yield a succession ( musical notes by prop]ly v>y+ ! pressure ( ! curr5t ( air bl[n into x4 ,if ! pipe is an op5 "o1 !n1 if we call ! frequ5cy ( ! prim>y note #a1 obta9$ :5 ! pipe is g5tly bl[n1 if we bl[ m /rongly1 ! pipe yields notes :i* are ! h>monics ( ! fundam5tal "o1 t is to say1 h frequ5cies repres5t$ by #b1 #c1 #d1 #e1 etc41 z ! bla/ ( air increases 9 =ce4 ,?us1 if ! pipe is "o ab\t #b feet 9 l5g?1 x w yield a note ne> to ! middle ,c on a piano4 ,if m /rongly bl[n1 x gives a note1 ,c#a1 an octave high]1 hav+ d\ble ! frequ5cy4 ,if m /rongly bl[n /ill1 x yields a note :i* is ! fif?1 ,g#a1 above ! la/1 & has ?ree times ! frequ5cy ( ! prim>y tone2 & s on4 ,if ! pipe is clos$ at ! top1 !n ov]-bl[+ ! pipe makes x yield ! odd h>monics1 or ! tones :i* are relat$ 9 frequ5cy to ! prim>y tone 9 ! ratio ( #a1 #c1 #e1 etc4 ,h5ce1 if a /opp$ pipe gives a note1 ,c1 its fir/ ov]tone is ! fif? above ! octave1 or ,g#a4 ,x is usual1 9 adju/+ ! air-pressure ( an organ-bell[s1 to all[ su* a pressure z t "s ( ! ov]tones1 or h>monics1 %all exi/4 ,! pres5ce ( ^! h>monics 9 a note gives brilliancy to x1 :]eas an absolutely pure or simple musical tone1 ?\gh n disagreeable to ! e>1 is n fully satisfy+4 ,any "o ) a good e> c detect ^! h>monics or ov]tones 9 a s+le note s\nd$ on a piano or organ due to ! subdivision ( ! vibrat+ /r+ or air-column into sections sep>at$ by nodes4 ,x w be se5 t ! ac\/ic action ( ! organ-pipe dep5ds ess5tially ^u "s op]ation t5d+ at ! comm5cem5t to make an expansion ( ! air 9 ! pipe at "o end1 & subsequ5tly to cause an increase ( air-pressure 9 x4 ,?is c be effect$ n only by bl[+ into ! pipe1 b 9 ano!r way1 by introduc+ a hot body into a pipe op5 at bo? ends4 ,we c %[ "h z an illu/ration ( ?is an int]e/+ exp]im5t due to ,"l ,rayleigh4 ,a long ca/-iron wat]-pipe ab\t #d in*es 9 diamet] & #h feet long is susp5d$ f ! ceil+4 ,ab\t #a foot up ! tube f ! l[] end a piece ( iron-wire gauze is fix$ 7see ,fig4 #fa74 ,by means ( a gas-burn] introduc$ into ! tube1 we heat ! gauze r$ hot1 & on )draw+ ! lamp ! tube sudd5ly emits a deep organ-l note = a few mom5ts4 ,! heat$ metal creates an up-draught 9 ! tube at ! l[] end1 &1 z 9 ! case ( ! op5 organ-pipe1 causes also an 9-suction ( air at ! upp] end4 ,! column ( air is ?us set vibrat+ ) a po9t ( alt]nate cond5sation & r>efaction 9 ! c5tre1 & 9-draughts & out-ru%es ( air at ! ends4 ,inde$1 ?is ru% ( air into & out ( ! pipe at ! l[] end dur+ ! "t x is s\nd+ its note is s viol5t t if ! h&s are plac$ j bel[ ! bottom end ( ! tube !y w feel *ill$1 z if plac$ ne> an electric fan1 by ! bla/ ( air4 ,clos+ ! bottom end ( ! pipe ) a %eet ( metal at once /ops ! air-movem5t1 & ) x ! musical note4 ,illu/ration3 ,,fig4 #fa4 ,illu/ration3 ,,fig4 #fb4--,s++ flame4 ,9 ano!r =m ! exp]im5t has long be5 kn[n "u ! "n ( a s++ flame4 ,a small jet ( burn+ hydrog5 gas is introduc$ into a glass tube ab\t #c feet 9 l5g?4 ,! jet mu/ consi/ ( a long n>r[ brass tube1 & ! prop] position = ! jet mu/ be f\nd by trial 7see ,fig4 #fb74 ,:5 ?is is done1 h[ev]1 ! tube emits a cle> musical note1 due to ! tube act+ z an op5 organ-pipe4 ,if ! flame is exam9$ 9 a revolv+ mirror :5 ! tube is s++1 x w be f\nd to be 9 vibration 9 sympa?y ) ! movem5t ( air 9 ! tube4 ,! tube (t5 refuses to />t s++1 b may be made to d x by giv+ x a little tap4 ,! actions tak+ place 9 ! tube are some?+ z foll[s3 ,:5 ! flame is introduc$1 x heats & r>efies ! air ar\nd x4 ,?is causes an 9-ru% ( air bo? at ! top & bottom ( ! tube4 ,a /ate ( /eady oscillation is !n e/abli%$1 9 :i* ! air at ! c5tre und]goes p]iodical expansions & compressions1 & ! pressure ( ! air r\nd ! flame *anges 9 ! same mann]4 ,! flame is !re=e alt]nately exp&$ & contract$4 ,:5 x exp&s1 x heats ! air m4 ,:5 x is compress$1 x heats x less4 ,?is v>iation ( ! flame causes air to be suck$ 9 or expell$ f bo? op5 ends ( ! tube1 & e/abli%es ! /ate ( /eady vibration 9 accordance ) ! l5g? ( ! tube4 ,! flame & ! air-column act & react on ea* o!r1 & e/abli% a /ate ( /ation>y a]ial oscillation 9 accordance ) ! natural "t-p]iod ( ! column ( air4 ,! tube c be made to give out n only its fundam5tal note1 b a s]ies ( h>monics1 or ov]tones1 ) frequ5cies #b1 #c1 #d1 #e1 etc41 times ! fundam5tal note1 by v>y+ ! position ( ! flame1 :i* mu/ always be j "u ! place :]e a node1 or place ( alt]nate cond5sation & r>efaction1 occurs4 ,we may1 9 ! next place1 ) advantage briefly exam9e ! pr9ciples ( con/ruction ( "o musical in/rum5t1 & allude to "s rec5t improvem5ts4 ,"o ( ! mo/ int]e/+ ( all ! musical appliances devis$ by human +5uity is ! viol91 compris+ z x does 9 its con/ruction an art1 a sci5ce1 & a tradition4 ,9 pr9ciple ! viol9 is no?+ b a wood5 box1 along ! top ( :i* are /ret*$ f\r /r+s1 :i* are /ra9$ ov] a piece ( wood call$ a bridge4 ,^! /r+s h _! effective l5g? alt]$ 9 play+ by plac+ ! f+] ( ! p]=m] at "s place on !m1 & !y are set 9 vibration by draw+ ov] !m a well-ros9$ b[ made ( horsehair4 ,! vibrat+ /r+ communicates its vibrations to ! surface ( ! box or body by means ( ! bridge1 & ?is aga9 to ! air 9 ! int]ior4 ,! body ?us s]ves two purposes4 ,x acts z a resonat+-*amb]1 & also x af=ds a l>ge surface ( contact ) ! surr\nd+ air1 :]eby a great] mass ( air is set simultane\sly 9 wave-motion4 ,! f\r /r+s are normally tun$ 9 fif?s1 s t ! fundam5tal note ( ea* is an int]val ( a fif? above ! next4 ,! p]=m] v>ies ! note giv5 by ea* /r+ by %ort5+ its vibrat+ l5g? by press+ ! f+] ^u x4 ,! skill$ viol9i/ has also great control ov] ! tone1 & c det]m9e ! h>monics1 or ov]tones1 :i* %all accompany ! fundam5tal by alt]+ ! po9t on ! /r+ at :i* ! b[ is appli$1 & lightly t\*+ x at "s o!r po9t4 ,! great art 9 ! con/ruction ( ! viol9 re/s 9 ! manufacture ( ! wood5 body4 ,its =m1 mat]ials1 & m9ute details ( con/ruction h be5 ! subject ( c\ntless exp]im5ts 9 pa/ ages1 & until q rec5tly no ess5tial improvem5t 0 made 9 ! in/rum5t z complet$ by ! ma/]s ( viol9 con/ruction ?ree c5turies ago4 ,9 classical =m ! viol9 consi/s ( a wood5 box ( *>act]i/ic %ape1 compos$ ( a back1 belly1 & six ribs4 ,^! are %ap$ out ( ?9 wood1 ! belly be+ made ( p9e1 & maple us$ = ! re/4 ,a neck or h&le is affix$ to "o end1 & a tail-piece1 to :i* ! gut-/r+s are fa/5$1 to ! o!r4 ,! /r+s are /ra9$ ov] a ?9 piece ( wood :i* re/s on two feet on ! belly4 ,"o ( ^! feet re/s ov] a block ( wood 9 ! int]ior ( ! box call$ ! s\nd-po/1 & ?is =ms a rigid c5tre2 ! o!r foot /&s on ! resonant "p ( ! belly4 ,! belly is /r5g!n$ 9 addition by a b> ( wood1 :i* is glu$ to x j "u ! place :]e ! active foot ( ! bridge re/s4 ,! ribs or sides ( ! box are b5t inw>ds at ! c5tre to enable ! play+-b[ to get at ! /r+s m easily4 ,! selection ( ! wood & its v>ni%+ is ! mo/ important "p ( ! con/ruction4 ,! wood mu/ be ela/ic1 & its ela/icity has to be pres]v$ by ! use ( an appropriate h>d v>ni%1 or else x w n take up ! vibrations imp>t$ by ! /r+s4 ,! old mak]s us$ wood :i* 0 only j suffici5tly season$1 & appli$ _! v>ni% at once4 ,an ess5tial adjunct is a good b[1 :i* is ( m importance ?an g5]ally suppos$4 ,some?+ may be got out ( a poor viol9 by a good play]1 b no "o c play ) a bad b[4 ,! process ( elicit+ a musical tone f ! viol9 is z foll[s3 ,! play]1 hold+ ! in/rum5t 9 ! left h&1 & ) its tail end press$ aga9/ ! left %\ld]1 places a f+] ( ! left h& lightly on "s po9t on a /r+1 & sweeps ! b[ g5tly across ! /r+ s z to set x 9 vibration1 yield+ its fundam5tal note1 accompani$ by ! l[] h>monics4 ,! purity & /r5g? ( ! note dep5d ess5tially ^u ! skill ) :i* ?is t\* ( ! b[ is made1 creat+ & su/a9+ ! same k9d ( vibration on ! /r+ ?r\gh\t its sweep4 ,! /r+ !n presses int]mitt5tly on ! bridge1 & ?is aga9 turns1 s to speak1 r\nd "o foot z r\nd a pivot1 & presses int]mitt5tly on ! ela/ic wood5 belly4 ,! belly takes up ^! vibrations1 & ! air 9 ! int]ior is ?r[n into sympa!tic vibration by resonance4 ,! s\nd escapes by ! -holes 9 ! belly4 ,! extraord9>y ?+ ab\t ! viol9 is t ! %ape ( ! box p]mits x to take up vibrations ly+ betwe5 all ! range ( musical tones4 ,! air-cavity does n m]ely resonate to "o note1 b to hundr$s ( diff]5t rates ( vibration4 ,! peculi> *>m ( ! viol9 is ! quality ( ! s\nd :i* a skill$ play] c elicit f x4 ,t wond]ful plead+1 sympa!tic1 voice-l tone1 :i* conveys s mu* emotional mean+ to ! tra9$ musical e>1 is due to ! prop] admixture ( ! h>monics1 or ov]tones1 ) ! fundam5tal notes4 ,! /r+ vibrates n m]ely z a :ole1 b 9 sections4 ,h5ce ! place at :i* ! b[ t\*es mu/ always be an anti-node1 or v5tral po9t1 & ! smalle/ *ange 9 ?is position greatly affects ! quality ( ! tone4 ,q rec5tly an entirely new dep>ture has be5 made 9 viol9 con/ruction by ,mr4 ,augu/us ,/roh1 a well-kn[n inv5tor4 ,he has aboli%$ ! wood5 body & bridge1 & sub/itut$ = !m an alum9ium trumpet-%ap$ tube z ! resonant *amb]1 end+ 9 a circul> corrugat$ alum9ium disc1 on ! c5tre ( :i* re/s an alum9ium lev] pivot$ at "o po9t4 ,! /r+s are /ra9$ ov] ?is lev]1 & held on a light tube1 :i* does duty z a po9t ( atta*m5t ( all p>ts ( ! in/rum5t4 ,! /r+s are ! same1 & ! manipulation ( ! in/rum5t id5tical ) t ( ! ord9>y viol94 ,! vibrations ( ! /r+s are communicat$ by ! pivot$ lev] ov] :i* !y pass to ! corrugat$ alum9ium disc1 & by ?is to ! air ly+ 9 ! trumpet-tube4 ,?is tube po9ts /raight away f ! play]1 & directs ! air waves to ! audi5ce 9 front4 ,! tone ( ! new viol9 is decl>$ by connoisseurs to be rem>kably full1 mell[1 & resonant4 ,! notes h a ri*ness & p[] :i* satisfies ! e>1 & is g5]ally only to be f\nd 9 ! h&iwork ( ! classical con/ructors ( ! ord9>y =m ( viol94 ,"o great advantage 9 ! ,/roh viol9 is t e "o c be made p]fectly ( ! same excell5ce4 ,! alum9ium discs are /amp$ out by a /eel die1 & are !re=e all id5tical4 ,! elem5t ( *ance or p]sonal skill 9 mak+ has be5 elim9at$ by a sci5tific & me*anical con/ruction4 ,?us ! musician becomes possess$ ( an in/rum5t 9 :i* sci5tific con/ruction pr$om9ates ov] individual art or tradition 9 manufacture1 yet at ! same "t ! musical effects :i* skill 9 play+ c produce are n at all dim9i%$4 ,:il/ our att5tion has s f> be5 fix$ on ! ext]nal op]ations 9 ! air :i* con/itute a tra9 ( music-mak+ waves1 x seems only appropriate to make1 9 conclusion1 a brief ref]5ce to ! app>atus :i* we possess 9 our e>s = appreciat+ ^! subtle *anges 9 air-pressure ) c]ta9ty & pleasure4 ,! e> itself is a m>vell\s appliance = detect+ ! exi/5ce ( waves & ripples 9 ! air1 & x embodies 9 itself _m ( ! pr9ciples :i* h be5 expla9$ to-day4 ,illu/ration3 ,,fig4 #fc4--;,diagram ( ! human e>4 ,! organ ( he>+ is a sort ( h\se ) ?ree *amb]s 9 x1 or1 r1 two rooms & an entrance hall1 ) ! front door always op54 ,?is entrance passage ( ! e> is a %ort tube :i* communicates at "o end ) ! op5 air1 be+ !re provid$ ) a s\nd-deflect+ scre5 9 ! %ape ( an ext]nal ornam5tal %ell1 commonly call$ ! e>4 ,9 _m animals ?is ext]nal app5dage is capable ( be+ turn$ into diff]5t positions1 to assi/ 9 det]m9+ ! direction 9 :i* ! s\nd wave is com+4 ,! entrance tube ( ! e> is clos$ at ! bottom by a delicate membrane call$ ! tympanum1 or drum4 ,aga9/ ?is drum-head ! air waves imp+e1 & x is press$ 9 & out by ! *anges ( air-pressure4 ,?is drum sep>ates ! out] end f a *amb] call$ ! middle e>1 & ! middle e> communicates1 by a sort ( back /aircase1 or tube call$ ! ,eu/a*ian tube1 ) ! cavity at ! back ( ! m\? 7see ,fig4 #fc74 ,beh9d ! middle e>1 & buri$ 9 ! bony /ructure ( ! skull1 is a ?ird1 m secret *amb]1 call$ ! inn] e>4 ,?is is sep>at$ f ! middle e> by two little w9d[s1 :i* are also cov]$ ) delicate membranes4 ,9 ! middle e> !re is a *a9 ( ?ree small bones l9k$ ) "o ano!r1 :i* are connect$ at "o end ) ! tympanum1 or drum1 & at ! o!r end ) ! s-call$ oval w9d[ ( ! inn] e>4 ,helmholtz has %[n t ?is little *a9 ( bones =ms a sy/em ( lev]s1 by means ( :i* ! movem5ts ( ! tympanum are dim9i%$ 9 ext5t1 b increas$ 9 =ce 9 ! ratio ( #b to #c4 ,! int]nal e> is ! real seat ( audition1 & x comprises ! p>ts call$ ! labyr9?1 ! semicircul> canals1 & ! co*lea4 ,^! are cavities l9$ ) delicate membranes & fill$ ) fluid4 ,9 ! co*lea !re is an organ call$ ,corti's organ1 :i* is a v]itable h>p ( t5 ?\s& /r+s4 ,?is consi/s ( innum]able n]ve-fibres1 :i* are an ext5sion ( ! auditory n]ve4 ,! details ( ! organic /ructure are f> too complicat$ = description "h4 ,suffice x to say t air waves1 beat+ aga9/ ! tympanum1 propagate vibrations along ! *a9 ( bones into ! fluids 9 ! inn] e>1 & f9ally exp5d !mselves on ^! n]ve-fibres1 :i* are ! real organs ( s\nd-s5sation4 ,helmholtz put =w>d ! +5i\s hypo!sis t ea* fibre 9 ! organ ( ,corti 0 tun$1 s to speak1 to a diff]5t note1 & t a composite s\nd fall+ ^u ! e> 0 analyz$ or dis5tangl$ by ?is organ into its con/itu5ts4 ,al?\gh ?is !ory1 z ,helmholtz orig9ally /at$ x1 has n altoge!r be5 upheld by subsequ5t obs]vation1 x is c]ta9 t ! e> possesses ?is wond]ful p[] ( analysis4 ,x c be %[n by ma!matical reason+ ( an advanc$ k9d t any musical s\nd1 no matt] :at its quality1 c be resolv$ into ! sum ( a numb] ( select$ pure s\nds su* z ^? giv5 by a tun+-=k4 ,consid] n[ = "o mom5t ! physical /ate ( ! air 9 a conc]t-room 9 :i* a l>ge or*e/ra is p]=m+4 ,! air is trav]s$ by a *aos ( waves ( v>i\s wave-l5g?s4 ,! deep notes ( ! viol9cello1 organ1 & trumpets are produc+ waves #aj to #bj feet 9 wave-l5g?1 :i* may be be/ describ$ z bill[s 9 ! air4 ,! viol9-/r+s & middle notes ( ! piano1 h>p1 or flute are yield+ air waves f #f or #h feet to a few in*es long1 :il/ ! high] notes ( viol9s & flutes are air ripples "s #c or #d in*es 9 l5g?4 ,if we c\ld see ! p>ticles ( ! air 9 ! conc]t-room1 & fa/5 our att5tion ^u any "o ( !m1 we %\ld see x execut+ a mo/ complicat$ motion "u ! comb9$ action ( ^! air-wave-produc+ in/rum5ts4 ,we %\ld be fasc9at$ by ! amaz+ dance ( molecules to & fro & f side to side1 z ! m$ley ( waves ( compression or r>efaction embrac$ !m & drove !m hi!r & ?i!r 9 _! resi/less grasp4 ,! tympana ( our e>s are !re=e und]go+ motions ( a l complicat$ k9d1 & ?is complex movem5t is transmitt$ ?r\gh ! *a9 ( bones 9 ! middle e> to ! inn] e>1 or true organ ( s5sation4 ,b !re1 by "s wondr\s me*anism n at all yet fully und]/ood1 an analysis takes place ( ^! entangl$ motions4 ,! well-tra9$ e> sep>ates betwe5 ! effect due to ea* k9d ( musical in/rum5t1 & ev5 detects a want ( tun+ 9 any "o ( !m4 ,x resolves ea* s\nd into its h>monics1 appreciates _! relative int5sity1 is satisfi$ or dissatisfi$ ) ! admixture4 ,9 ! inn] *amb] ( ! e> physical movem5ts are 9 "s :olly inscrutable mann] translat$ into s5sations ( s\nd1 & ! confus$ aggregation ( waves & ripples 9 ! air1 beat+ aga9/ ! tympanic membrane !re1 takes effect 9 produc+ impulses :i* travel up ! auditory n]ve & exp5d _! en]gy f9ally 9 ! creation ( s5sations ( melody & tune1 :i* ar\se emotions1 revive memories1 & /ir sometimes ! deepe/ feel+s ( our m9ds4 ,,*apt] ,v4 ,,electric ,,oscillations ,,& ,,electric ,,waves4 ,9 ! previ\s *apt]s y\r att5tion has be5 direct$ to ! subject ( waves on wat] & waves 9 air1 & we %all n[ proce$ to discuss "s ( ! m difficult matt]s connect$ ) ! production ( waves 9 ! !r4 ,we %all f9d t ?is portion ( our subject makes m dem&s ^u our p[]s ( compreh5sion1 s9ce mu* t we h to consid] is n directly ! object ( s5se p]ception1 & ! inf]5ces :i* we h to make f obs]v$ facts are less simple & easy to foll[4 ,nev]!less1 ,i tru/ t if y h be5 able to grasp cle>ly ! nature ( a surface-wave on wat] & ( a compressional wave 9 air1 y w n readily all[ y\rselves to be disc\rag$ f enc\nt]+ a new class ( ideas1 b w be able to advance /ill fur!r1 & ga9 a m or less cle> conception ( ! nature ( an electric wave 9 ! !r4 ,9 ! fir/ place1 we mu/ consid] ! m$ium 9 :i* ^! waves are creat$4 ,we c see ) our eyes a wat]-surface1 & we are able to und]/& )\t mu* difficulty t ! surface c be ?r[n into humps & holl[s1 or become wr9kl$1 & also t ^! elevations & depressions c *ange _! position1 ?us creat+ a surface wave :i* moves =w>d4 ,! movem5t ( ! wat] wave is1 !re=e1 only ! result ( a local elevation ( ! surface :i* travels along or takes place progressively at diff]5t places on ! surface4 ,!n1 aga91 9 ! case ( an air wave1 al?\gh we _c see ! air1 we are able1 ) "s little assi/ance f exp]im5ts1 to pres5t to ourselves a cle> m5tal picture ( a progressive movem5t ?r\gh ! air ( a region ( compression1 t is to say1 a c]ta9 slice1 lay]1 or zone ( ! air is m compress$ ?an ! neighb\r+ portions1 & ?is region ( compression *anges its place progressively4 ,x has be5 c>efully expla9$ t ! production ( a wave ( any k9d implies1 !re=e1 two ?+s--fir/1 a m$ium or mat]ial 9 :i* ! wave exi/s2 &1 secondly1 "s k9d ( p]iodic *ange or movem5t :i* is exp]i5c$ by ! v>i\s portions ( ?is m$ium at diff]5t places successively4 ,if1 !re=e1 we are giv5 any m$ium1 say wat] or air1 & ask$ to expla9 ! production ( a wave 9 x1 we h fir/ to consid] :at k9d ( *anges c take place 9 x1 or on x1 :i* c appe> progressively at diff]5t p>ts4 ,9 ! case ( ! wat]-surface1 "s p>ts may be heap$ up high] ?an ! re/1 & ! heap+ up may occur at successive places 9 su* fa%ion t :5 x disappe>s at "o place x reappe>s at a contigu\s or neighb\r+ place4 ,9 ! case ( air1 "s portion may be compress$ m ?an ! re/1 & ! place ( compression may move =w>d1 s t z ! compression is releas$ 9 "o place x makes its appe>ance 9 an adjac5t "o4 ,9 ! fir/ case1 we h a wave ( elevation on wat]2 9 ! second case1 a wave ( compression 9 ! air4 ,9 ! next place1 let me c>ry y ) me "o /ep m4 ,"h is a glass bulb f :i* ! great] "p ( ! air has be5 remov$4 ,we say1 !re=e1 t !re is a vacuum 9 ! bulb4 ,x is impossible = u to remove absolutely e trace ( air f ! bulb1 & s produce :at w\ld be call$ a p]fect vacuum2 b we c imag9e x to be accompli%$1 & we c picture to ourselves ! glass bulb absolutely depriv$ ( e trace ( air or o!r mat]ial sub/ance4 ,! "q !n arises--,is ! bulb really empty1 or is !re /ill some?+ 9 its int]ior8 ,! same inquiry may be put 9 ano!r way4 ,! air we brea! =ms an atmosph]e :i* surr\nds our e>? z a g>m5t1 b x decreases rapidly 9 d5sity z we asc5d4 ,at a height ( ab\t #ej miles above ! e>? !re is reason to believe ! air is exce$+ly r>efi$ &1 except = ! pres5ce ( meteoric du/1 ! space betwe5 ! sun & ! e>?1 & betwe5 ! />s & ! e>?1 is 9 all probability a highly p]fect vacuum1 9 ! s5se t x is empty ( g5]ally diffus$ matt]4 ,! "q !n arises--,is int]/ell> space absolutely & completely empty8 ,we "k p]fectly well t rays ( light come to u f ! sun & />s ?r\gh ?is empty space1 & a fact ( capital importance is1 t ^! rays ( light1 swift-foot$ ?\gh !y are1 take "t to travel4 ,x 0 long ago suspect$ t ?is 0 ! case1 & ! celebrat$ ,galileo made ! fir/ exp]im5tal attempt to det]m9e ! velocity ( light4 ,no real k on ! subject 0 ga9$1 h[ev]1 until aft] he _h made 8 discov]y t ! planet ,jupit] is accompani$ by f\r moons 7a fif? moon has be5 discov]$ s9ce71 & t ^! rotate r\nd ! planet 9 def9ite p]iods ( "t1 con/itut+1 !re=e1 ! 8h&s0 ( a p]fect cele/ial clock4 ,! sunlight1 fall+ on ! great globe :i* =ms ! body ( ! planet ,jupit]1 ca/s beh9d x a conical %ad[2 & ! little moons1 9 _! rotation1 are plung$ into ?is %ad[ cone at int]vals1 & !n = a "t become invisible1 or eclips$4 ,z soon1 h[ev]1 z ^! eclipses ( ,jupit]'s moons began to be regul>ly obs]v$1 x 0 f\nd t ! int]vals ( "t betwe5 two eclipses ( any "o moon 7 n equal1 b exhibit$ a progressive v>iation 9 magnitude1 & 7 long] by ab\t #af m9utes & #bf seconds at "o "t ( ! ye> ?an at ! o!r4 ,! a/ronom] ,roem]1 9 ! ye> #afge1 correctly conclud$ t ?is diff]5ce mu/ be due to ! fact t rays ( light take "t to trav]se ! e>?'s orbit1 & n to any want ( regul>ity 9 ! op]ation ( ?is cele/ial timepiece4 ,h5ce1 al?\gh ! eclipses d happ5 at equal int]vals ( "t1 our in=mation ab\t !m is delay$ by ! "t tak5 = ! ray ( light to travel ov] ! v>iable di/ance betwe5 ,jupit] & our e>?4 ,^! obs]vations1 critically consid]$1 l$1 !re=e1 to ! conclusion t ! spe$ ( light rays is ab\t #ahf1ejj miles a second4 ,by means :i* x w\ld take too long to describe "h1 exp]im5tal measurem5ts ( ! velocity ( light h be5 made _m times s9ce by v>i\s inve/igators by me?ods :i* d n involve a/ronomical obs]vations1 & ! result has be5 to confirm ! above value1 & to give u a v exact k ( ! spe$ ) :i* rays ( light travel ?r\gh space4 ,x is z %[n 9 ! table bel[3-- ,,! ,,velocity ,,( ,,light4 ,miles p] second4 ,f obs]vations on ,jupit]'s satellites 7,roem]7 #ahf1ejj 0 exp]im5tal measurem5ts by ,f\cault 7#ahfb7 #ahe1agg 0 0 0 0 ,cornu 7#ahgd7 #ahe1dhg 0 0 0 0 0 7#ahgh7 #ahf1dac 0 0 0 0 ,mi*elson 7#ahgi7 #ahf1cfd 0 0 0 0 0 7#ahhb7 #ahf1cbh 0 0 0 0 ,newcomb 7#ahhb7 #ahf1ccc ,:5 any?+ takes "t to travel f "o place to ano!r1 x c only be "o ( two ?+s4 ,x mu/ ei!r be an actual object :i* is transf]r$ bodily f place to place1 l a lett] s5t by po/ or a bullet fir$ f a gun1 or else x mu/ be a wave-motion creat$ 9 a m$ium ( "s k9d :i* fills all space4 ,! illu/ri\s ,newton sugge/$ an hypo!sis or supposition z to ! nature ( light1 viz4 t x consi/s ( small corpuscles %ot out viol5tly f e lum9\s body4 ,x is a wond]ful te/imony to ,newton's exalt$ p[]s ( ?\ght1 t ! mo/ rec5t inve/igations %[ t hot & lum9\s bodies1 su* z ! sun & a lamp1 are 9 fact project+ small bodies call$ corpuscles into space1 b !re is abundant pro( t ^! are n ! cause ( light4 ,subsequ5tly to ! date ( ,newton's speculations on ! nature ( light1 ! alt]native hypo!sis 0 develop$1 viz4 t x consi/s 9 a wave-motion 9 a univ]sally diffus$ m$ium call$ ! !r4 ,a great gulf1 h[ev]1 sep>ates m]e conjecture & speculation f t accumulation ( rigid pro( :i* sci5tific inve/igation dem&s1 & h5ce1 al?\gh ?is conception ( an !r _h aris5 z an hypo!sis 9 ! m9ds ( ,huygh5s1 ,desc>tes1 & _m o!r philosoph]s1 x 0 n accept$ by ,newton1 & ! g5]al ass5t ( sci5tific inve/igators to ! hypo!sis ( a univ]sal !r 0 long def]r$4 ,! philosoph] to :om we owe ! crucial demon/ration ( ! validity (1 & inde$ necessity =1 ?is assumption 0 ,dr4 ,?omas ,"y1 ! fir/ ,pr(essor ( ,natural ,philosophy 9 ! ,royal ,in/itution ( ,london4 ,"y 0 a man ^: exalt$ intellectual p[]s 7 n prop]ly appreciat$ by ! _w until aft] 8 decease4 ,8 rese>*es 9 physical optics alone are1 h[ev]1 epo*-mak+ 9 "*4 ,he x 0 :o fir/ gave a pro( t "u "s circum/ances x is possible = two rays ( light to de/roy ea* o!r1 & ?us produce d>kness4 ,briefly describ$1 ! exp]im5t is z foll[s3 ,if a beam ( light ( "o col\r1 say r$1 proce$+ f a s+le s\rce ( light1 falls ^u a scre5 9 :i* are two small holes v ne> toge!r1 we %all obta9 f ^! holes two /reams ( light orig9at+1 z x 71 f closely contigu\s s\rces4 ,if we !n hold a :ite scre5 n f> f ^! holes1 & receive on x ! light proce$+ f !m1 we %all f9d t ! scre5 is m>k$ ) alt]nate b&s ( r$ light & black b&s4 ,if we cov] up "o ( ! small holes1 ! black b&s vani% & ! scre5 is uni=mly illum9at$4 ,"y po9t$ out t ?is effect 0 due to int]f]5ce1 & t ! diff]5ce ( ! di/ances f any black b& to ! two holes 0 an exact odd multiple ( a c]ta9 small di/ance call$ ! wave-l5g? ( ! light4 ,if light is a sub/ance1 no possible explanation c be giv5 :i* w enable u to acc\nt = ! comb9ation ( two rays ( light produc+ d>kness at _! meet+-po9t4 ,if1 on ! o!r h&1 rays ( light consi/ ( waves ( "s k9d 9 a m$ium1 !n1 z we h se5 9 ! case ( wat] ripples & air waves1 x is q possible = two wave-tra9s to annihilate ea* o!r's effect at a c]ta9 po9t1 if a holl[ ( "o wave-tra9 rea*es t place co9cid5tly ) a hump belong+ to ! o!r4 ,accord+ly1 ! exp]im5t ( produc+ int]f]5ce betwe5 two sets ( light rays s t !y de/roy ea* o!r is a /rong argum5t 9 fav\r ( ! view t light mu/ consi/ 9 "s k9d ( wave-motion exi/+ 9 a m$ium susceptible ( support+ x1 fill+ all space1 & exi/+ 9 all transp>5t bodies4 ,?is m$ium we call ! lum9if]\s !r4 ,! t]m 8!r10 or 8e!r10 has be5 9 use = _m c5turies to express ! idea ( some?+ m r>e1 t5u\s1 or ref9$ ?an ord9>y matt]4 ,! classical writ]s employ$ x to describe ! space above ! high] regions ( ! atmosph]e1 :i* 01 z !y2 suppos$1 occupi$ by a m$ium less palpable or mat]ial ?an ev5 air itself4 ,?us ,milton1 speak+ ( ! d[nfall ( ! enemy ( mank9d 78,p>adise ,lo/10 ,book ,i4 l9e #dd71 says-- 8444 ,him ! ,almighty ,p[] ,hurl$ headlong1 flam+1 f ! !real sky ,) hide\s ru9 & combu/ion d[n40 ,b al?\gh poets & philosoph]s _h made free use ( ! notion ( an !r1 or ev5 assum$ ! exi/5ce ( sev]al !rs1 ! conception did n become a s]i\s sci5tific hypo!sis until x 0 exp]im5tally %[n by ,"y t ! ph5om5a ( optics imp]atively dem& ! assumption ( su* a m$ium 9 space :i* is n ord9>y matt]1 b possesses qualities ( a special k9d1 enabl+ x to h creat$ 9 x waves :i* are propagat$ ) ! enorm\s velocity ( ne>ly "o ?\s& million feet a second4 ,! pro(s :i* h accumulat$ z to ! validity ( ?is hypo!sis to expla9 optical effects %[ t ?is m$ium or !r mu/ exi/1 n only 9 free space1 b also 9 ! int]ior ( e solid1 liquid1 or gase\s body1 al?\gh its prop]ties 9 ! int]ior ( transp>5t bodies are c]ta9ly v diff]5t f ^? :i* x possesses tak5 by itself4 ,?is !r fills e s-call$ vacuum1 & we _c pump x out f any vessel z we c ! air4 ,x occupies1 likewise1 all cele/ial space1 & suns & />s float1 s to speak1 9 an illimitable ocean ( !r4 ,we _c remove x f any enclos$ place1 because x passes q easily ?r\gh all mat]ial solid bodies1 & x is = ! same reason intangible1 & x is n possess$ ( weight4 ,h5ce we _c t\* x1 see x1 smell x1 ta/e x1 or 9 any way directly appreciate x by our s5ses1 except 9 s f> z t waves 9 x ( a c]ta9 k9d affect our eyes z light4 ,! fact t !re is su* a space-fill+ !r is1 !re=e1 only to be d$uc$ by reason+ f exp]im5ts & obs]vations1 b x is n directly ! object ( our s5se-p]ceptions 9 ! same way t wat] or air c be4 ,nev]!less1 !re is abundant pro( t x is n m]ely a conv5i5t sci5tific fiction1 b is z mu* an actuality z ord9>y gross1 tangible1 & pond]able sub/ances4 ,x is1 s to speak1 matt] ( a high] ord]1 & occupies a rank 9 ! hi]>*y ( creat$ ?+s :i* places x above ! mat]ials we c see & t\*4 ,! "q we h next to discuss is--,:at are ! fundam5tal prop]ties ( ?is !r8 & :at are ! t]ms 9 :i* we mu/ describe its qualities8 ,9 ord] to answ] ^! que/ions1 we mu/ direct att5tion to "s electrical effects1 s9ce x has be5 %[n t mo/ ( ! electrical ph5om5a1 l ^? ( optics1 po9t to ! necessity = ! assumption ( a simil> univ]sal m$ium1 diff]5t f ord9>y matt]4 ,abundant pro( has be5 ga!r$ 91 t ! electro-magnetic m$ium & ! lum9if]\s !r are "o & ! same4 ,we are met at ! v outset ( our electrical /udies by ! t]m electric curr5t4 ,mo/ ( u "k t ! op]ation ( electric telegraphs & telephones1 electric lamps & electric railways1 dep5d ^u ?is employm5t ( an ag5cy call$ an electric curr5t4 ,! "q !n arises--,:at is an electric curr5t8 & ! answ] to ?is "q is n easy to give 9 a few words4 ,we c1 h[ev]1 beg9 by expla9+ :at an electric curr5t c d1 & h[ its pres5ce c be recogniz$4 ,be=e me on ! table is a spiral ( copp] wire1 & 9 ?is wire1 by special means1 ,i c create :at we call an electric curr5t4 ,i %all ask y to notice t :5 ?is is done two effects are imm$iately produc$4 ,9 ! fir/ place1 ! wire becomes hot1 &1 secondly1 x becomes magnetic4 ,! fact t x is hot is evid5t1 because x is n[ ne>ly r$ hot1 & is visibly inc&esc5t 9 ! d>k4 ,if we dip ! wire 9 iron fil+s1 y w see t ^! cl+ to ! wire & are tak5 up by x1 j z :5 an ord9>y /eel magnet is sub/itut$ = ! wire4 ,! copp] wire1 :5 trav]s$ by ! curr5t1 also attracts a compass ne$le1 & we ?us demon/rate 9 ano!r way its magnetic quality4 ,:5ev]1 !re=e1 we f9d ^! two /ates ( heat & magnetism pres5t toge!r 9 & r\nd a wire1 we may take x z an indication t x =ms "p ( a circuit ?r\gh :i* an electric curr5t is fl[+4 ,an electric curr5t is a physical /ate or condition :i* c only exi/ 9 or all along a clos$ pa? :i* is call$ an electric circuit4 ,?is electric circuit may consi/ ( a metallic wire1 or1 z we g5]ally call x1 a conductor1 or1 z we %all see1 x may also 9 "p consi/ ( :at is usually call$ a non-conductor4 ,x is necess>y1 9 ! next place1 to po9t out t an electric curr5t has a directive quality4 ,x belongs to t category ( ?+s l =ces & movem5ts1 :i* h direction z well z magnitude4 ,x is n completely def9$ by ! answ] to ! "q--,h[ mu*8 ,we mu/ also ask--,9 :at direction8 ,! direction ( an electric curr5t is settl$ by hold+ a small compass ne$le ne> to ! conductor or wire 9 :i* ! curr5t exi/s4 ,! little magnet w set itself ) its nor? pole 9 "o direction or 9 ! opposite1 across ! wire4 ,t is to say1 ! axis ( ! compass ne$le places itself at "r angles to t ( ! wire4 ,! direction ( ! electric curr5t is decid$ 9 accordance ) ! foll[+ conv5tional rule3 ,imag9e y\rself plac$ ) y\r arms ext5d$ /raight out l a cross1 & t ! wire convey+ ! curr5t is plac$ be=e y\r face 9 a v]tical position4 ,imag9e1 also1 t ! position 9 :i* ! compass ne$le naturally sets :5 held betwe5 y & ! wire is su* t its ,nor? pole is on y\r "r-h& side4 ,!n ! curr5t w\ld be said to move upw>ds 9 ! wire4 ,a curr5t :i* is always 9 "o & ! same direction 9 a wire is call$ a cont9u\s1 direct1 or "o-way curr5t4 ,a curr5t :i* p]iodically *anges its direction s t x is fir/ 9 "o direction & !n 9 ! o!r is call$ an alt]nat+ or two-way curr5t4 ,i c n[ %[ y two exp]im5ts1 ! employm5t ( :i* w enable u always to decide :e!r a curr5t 9 a wire is a "o-way or a two-way curr5t4 ,9 ! fir/ exp]im5t y see a copp] wire /ret*$ betwe5 ! poles ( a p[]ful horse%oe magnet4 ,:5 a "o-way curr5t is s5t ?r\gh ! wire1 x is pull$ ei!r up or d[n1 l a fiddle or h>p /r+ be+ pluck$ by ! f+]4 ,if1 h[ev]1 we s5d a two-way curr5t ?r\gh ! wire1 x moves alt]nately up & d[n1 & vibrates j l a h>p-/r+ :5 pluck$ & left to itself4 ,! next exp]im5t gives u1 h[ev]1 a m conv5i5t me?od ( asc]ta9+ ! pres5ce 9 a wire ( an alt]nat+ or two-way electric curr5t4 ,if two wire circuits are laid p>allel to ea* o!r1 & we s5d ?r\gh "o ( ^! an electric curr5t1 !n1 9 accordance ) ,f>aday's mo/ notable discov]y1 we f9d t ! beg9n+ or ! end+ ( ! "o-way curr5t 9 ! fir/ wire gives rise at ! mom5t to a transitory curr5t 9 ! second wire4 ,if1 h[ev]1 we pass ?r\gh ! fir/ wire1 :i* we call ! prim>y circuit1 a two-way curr5t1 !n1 s9ce ?is is1 s to speak1 cont9ually beg9n+ & end+1 we h a simil> alt]nat+ or two-way electric curr5t produc$ 9 ! second>y circuit4 ,?is fact may be mo/ neatly & =cibly illu/rat$ by ! employm5t ( ! foll[+ pieces ( app>atus3 ,an insulat$ wire is w\nd _m times r\nd a great bundle ( iron wire1 ?us =m+ :at is call$ an electro-magnet4 ,?r\gh ?is wire is pass$ a /rong alt]nat+ electric curr5t :i* rev]ses its direction #afj times a second4 ,ov] ! top ( ! electro-magnet we hold ano!r coil ( insulat$ wire1 ! ends ( :i* are connect$ to a small electric gl[ lamp 7see ,fig4 #fd74 ,:5 held ne> to ! pole ( ! electro-magnet1 we f9d ! little lamp 9 ! second>y coil lights up brilliantly1 because !re is creat$ 9 t circuit a second>y or induc$ alt]nat+ electric curr5t by ! action ( ! o!r curr5t 9 ! prim>y or electro-magnet circuit4 ,?us we see t "o alt]nat+ electric curr5t c1 s to speak1 give bir? to ano!r 9 a second circuit held p>allel to ! fir/4 ,9 l mann] ?is second>y curr5t c give rise to a ?ird or t]ti>y curr5t1 & ! ?ird to a f\r?1 & s on indef9itely4 ,illu/ration3 ,,fig4 #fd4 ,we c always make use ( ?is te/ to asc]ta9 & prove ! exi/5ce ( an alt]nat+ curr5t 9 any electric circuit4 ,if we provide a coil ( insulat$ wire1 hav+ its ends connect$ to a small inc&esc5t lamp1 & hold ?is lamp coil or second>y circuit ne> to & p>allel ) any o!r circuit 9 :i* we suspect ! exi/5ce ( an alt]nat+ electric curr5t1 & if ! lamp 9 ! second>y circuit lights up1 !n we c say ) c]ta9ty t !re is an alt]nat+ or two-way electric curr5t 9 ! fir/ circuit4 ,hav+1 !n1 indicat$ briefly ! effects :i* are produc$ by an electric curr5t :5 x exi/s 9 a conduct+ circuit1 & ! way 9 :i* we c det]m9e its pres5ce & direction1 we mu/ pass on to discuss "s o!r facts connect$ ) its production4 ,x is a maxim 9 philosophy t e effect mu/ h a cause2 h5ce we mu/ assign a "n to ! cause ( ! effect we call electric curr5t4 ,?is cause we call electromotive =ce4 ,electromotive =ce may be creat$ 9 _m ways1 & "t w n p]mit u to ref] to ^! 9 detail1 b x mu/ be tak5 t electrical ma*9es1 batt]ies1 & dynamos are all ( !m appliances = creat+ electromotive =ce1 or1 z x is sometimes call$1 electric pressure1 j z v>i\s k9ds ( =ce-pumps are contrivances = creat+ pressure 9 fluids4 ,we f9d t electromotive =ce acts diff]5tly on v>i\s sub/ances :5 !y are subject$ to its op]ation4 ,9 "s sub/ances electromotive =ce produces a cont9u\s electric curr5t1 & 9 ^! cases ! mat]ial is call$ a conductor4 ,9 o!r cases electromotive =ce creates :at is call$ electric /ra91 or electric displacem5t1 & ^! sub/ances are g5]ally call$ non-conductors4 ,! diff]5ce betwe5 conductors & non-conductors c be illu/rat$ by a me*anical analogy4 ,consid]1 = in/ance1 a =ce-pump consi/+ ( a cyl9d] ) a tightly fitt$ pi/on2 suppose ! bottom ( ! pump-tube to be clos$ by a pipe hav+ 9 x a tap4 ,if we op5 ! tap & apply pressure to ! pi/on1 we c =ce out ( ! pipe a curr5t ( air :i* cont9ues to fl[ z long z ! pi/on is be+ press$ d[n4 ,9 ?is case ! pressure on ! pi/on corresponds to an electromotive =ce1 & ! curr5t ( air fl[+ out corresponds ) ! electric curr5t 9 ! electrical circuit4 ,suppos+1 h[ev]1 t we %ut ! tap & !n attempt to =ce d[n ! pi/on1 we f9d at once an ela/ic resi/ance to motion4 ,! pi/on c be press$ d[n a little way1 compress+ ! air & ?us creat+ a /ra92 b if ! pressure is remov$ ! pi/on flies up aga91 on acc\nt ( ! compressional ela/icity ( ! air4 ,9 ?is op]ation we h a me*anical illu/ration ( ! action ( electromotive =ce on a mat]ial su* z glass or air1 :i* is call$ a non-conductor1 or sometimes a dielectric4 ,9 ^! bodies electromotive =ce produces an electric /ra91 j z ! me*anical =ce produces 9 ! air enclos$ 9 ! cyl9d] a me*anical /ra94 ,:5 ! tap at ! bottom ( ! cyl9d] is clos$1 we c1 by apply+ pressure1 =ce d[n ! pi/on a little way1 b t movem5t _c be cont9u$1 because we are build+ up an oppos+ pressure due to ! ela/icity ( ! air4 ,x is possible to %[ y an electrical exp]im5t :i* has a close analogy ) ! above simple me*anical exp]im5t4 ,"h is a glass tube :i* has plat9um wires seal$ into ! two ends1 & ! tube is p>tly exhau/$ ( its air4 ,su* a tube is call$ a vacuum tube1 & :5 an electrical curr5t is pass$ ?r\gh ?is r>efi$ air1 x causes x to become lum9\s1 &1 z y see :5 ! room is d>k5$1 ! tube is fill$ ) a r$di% light4 ,a tube1 !re=e1 ( ?is k9d is v conv5i5t 9 "s exp]im5ts1 because we c1 9 effect1 see ! electric curr5t pass+ ?r\gh x4 ,if ,i connect "o end ( ?is tube ) ! e>?1 & ! o!r ) ! t]m9al ( an electrical ma*9e1 & if !n ! h&le ( ! electrical ma*9e is turn$1 ! tube w cont9ue to gl[ z long z ! electrical ma*9e is rotat$4 ,! electrical ma*9e mu/ be reg>d$ z a pump :i* is =c+ some?+ call$ electricity ?r\gh ! vacuum tube1 & z long z ! pressure is cont9u$ ! curr5t fl[s4 ,?is corresponds ) ! case 9 :i* ! tap at ! bottom ( ! =ce pump 0 op5 & a cont9u\s curr5t ( air c\ld be =c$ out ( x by press+ d[n ! pi/on4 ,suppos+1 h[ev]1 t ,i ins]t betwe5 ! vacuum tube & ! electrical ma*9e a plate ( glass1 :i* is cov]$ ov] ) t9foil on ! two sides su* an arrangem5t con/itutes :at is call$ a cond5s]1 or ,leyd5 pane4 ,we n[ repeat ! exp]im5t1 & beg9 to turn ! h&le ( ! electrical ma*9e4 ,y w notice t ! vacuum tube gl[s z be=e1 & is fill$ ) a r$di% light = a %ort "t1 b z we cont9ue to turn ! h&le ?is dies away1 & aft] a few mom5ts !re is no fur!r evid5ce ( an electric curr5t pass+ ?r\gh ! vacuum tube4 ,y w und]/&1 !re=e1 t an electric curr5t _c be caus$ to fl[ = an indef9ite "t 9 "o direction ?r\gh a glass plate1 al?\gh1 by ! application ( electromotive =ce1 x does evid5tly1 z y see1 pass ?r\gh x = a %ort "t4 ,?is is analog\s to ! op]ation ( ! =ce-pump :5 ! tap at ! bottom is clos$4 ,we !n f9d t we c move ! pi/on d[n a little way1 compress+ or /ra9+ ! enclos$ air1 b t its motion is soon /opp$ by an oppos+ resi/ance4 ,we !re=e say t 9 ! glass plate we h creat$ an electric /ra9 by ! action ( ! electromotive =ce1 j z we describe ! effect ( ! me*anical pressure on ! air by say+ t we h creat$ a compression 9 x4 ,b !re is an additional resemblance betwe5 ! electrically /ra9$ glass & ! me*anically compress$ air4 ,:5 any ela/ic object has be5 /ra9$1 & is sudd5ly releas$1 x rega9s its position ( equilibrium by a s]ies ( oscillations or vibrations4 ,?us1 = in/ance1 if we take a /rip ( /eel & fix "o end ( x 9 a vice1 & pull ! o!r end on "o side & !n release x1 ! /eel rega9s its position ( equilibrium only aft] hav+ execut$ a s]ies ( dim9i%+ sw+s to & fro4 ,9 ! same way1 if we place "s m]cury or wat] 9 a glass tube b5t 9 ! %ape ( ! lett] 1 & displace ! liquid by bl[+ into ! tube1 !n1 on releas+ ! pressure sudd5ly1 ! liquid w rega9 its position ( equilibrium by a s]ies ( oscillations :i* die gradually away4 ,y w n h any difficulty 9 see+ t ?is is really due to ! in]tia ( ! mat]ial1 :e!r x be /eel or m]cury or wat] :i* is displac$4 ,9 an exactly simil> mann]1 we f9d t :5 we h produc$ an electric /ra9 9 a %eet ( glass by ! application ( electromotive =ce1 & if we !n remove ! electromotive =ce & connect ! two t9foil or metal surfaces by means ( a piece ( wire1 ! electric /ra9 9 ! glass disappe>s ) a s]ies ( electric oscillations2 t is to say1 ! electric /ra9 9 ! glass does n disappe> or die away gradually1 b x is alt]nately rev]s$1 at ea* rev]sal ! /ra9 becom+ less & less 9 magnitude4 ,! result ( ?is oscillatory /ra9 9 ! glass is to produce 9 ! connect+ wire an alt]nat+ electric curr5t4 ,illu/ration3 ,,fig4 #fe4 ,a v famili> & simple piece ( electric app>atus is t kn[n z a ,leyd5 j> 7see ,fig4 #fe74 ,a ,leyd5 j> consi/s ( a glass vessel1 ! outside & inside surfaces ( :i* are respectively cov]$ ) t9foil4 ,if we apply to ^! two surfaces an electromotive =ce1 we produce :at is call$ an electric *>ge 9 ! j>1 :i* 9 reality consi/s 9 a /ate ( electric /ra9 9 ! walls ( ! vessel4 ,:5 ! j> is *>g$1 if we connect toge!r1 by means ( a ?ick wire1 ! outside & ! inside t9foil surfaces1 we h a bright sp>k produc$ at ! mom5t ( mak+ contact1 & we h a rapidly alt]nat+ electric curr5t produc$ 9 ! connect+ wire4 ,if ?is connect+ wire has a l[ resi/ance--9 o!r words1 is a v good conductor--!n ?is electric sp>k consi/s1 n 9 a dis*>ge ( electricity uni=mly 9 "o direction1 b ( a s]ies ( rapidly succe$+ sp>ks :i* are really dis*>ges ( electricity or electric curr5ts pass+ ?r\gh ! air alt]nately 9 opposite directions4 ,?is c be demon/rat$ by tak+ a photograph ( ! electric sp>k on a rapidly revolv+ photographic plate or /rip4 ,y are probably all famili> ) ! s5sitive photographic film :i* is employ$ 9 h& cam]as1 su* z ! kodak4 ,if a /rip ( ?is s5sitive film is b\nd r\nd ! edge ( a :eel1 & if ! :eel is set 9 v rapid rotation1 & if we ?r[ on ! film1 by means ( a l5s1 an image ( an oscillatory electric sp>k1 x w be cle> to y t1 if ! sp>k is cont9u\s1 x w produce ^u ! mov+ photographic film an image :i* w be ( ! nature ( a broad b&4 ,if1 h[ev]1 ! electric sp>k is int]mitt5t1 !n ?is photographic image w be cut up into a s]ies ( b>s or pat*es1 ea* "o ( :i* w correspond to a sep>ate image ( "o con/itu5t ( ! oscillatory sp>k4 ,photographs ( oscillatory electric sp>ks h 9 ?is way be5 tak5 by _m obs]v]s1 & h af=d$ a demon/ration t ! electric dis*>ge ( a ,leyd5 j>1 :5 tak5 ?r\gh a wire ( l[ resi/ance1 is n a cont9u\s movem5t ( electricity 9 "o direction1 b a rapidly alt]nat+ electric curr5t ?r\gh ! wire1 =m+ ! oscillatory sp>k1 & correspond+ ) an equally rapid alt]nat+ electric /ra9 9 ! glass1 bo? /ra9 & curr5t dy+ gradually away4 ,al?\gh ?is op]ation takes a long "t to describe1 yet1 nev]!less1 an oscillatory sp>k consi/+ ( #bj or #cj electric oscillations may all be ov] 9 ! or ev5 second4 ,9 ! photograph n[ ?r[n ^u ! scre5 7see ,fig4 #ff7 y see ! image ( an oscillatory electric sp>k1 ea* oscillation ( :i* la/$ second4 ,we c1 h[ev]1 give a /ill fur!r pro( t ! dis*>ge ( a ,leyd5 j> or electric cond5s] is1 "u "s circum/ances1 oscillatory1 9 ! foll[+ mann]3-- ,illu/ration3 ,,fig4 #ff4--;,a photograph ( an oscillatory electric sp>k 7,hemsale*74 ,y h already se5 t an alt]nat+ or two-way electric curr5t exi/+ 9 "o circuit c produce ano!r alt]nat+ or two-way electric curr5t 9 a neighb\r+ circuit4 ,be=e me1 on ! table1 is an arrangem5t by :i* a batt]y ( six ,leyd5 j>s1 ,l1 is cont9ually be+ *>g$ & dis*>g$ ?r\gh a ?ick wire :i* is w\nd a doz5 times r\nd a squ>e wood5 frame1 ,p 7see ,fig4 #fg74 ,9 proximity to ?is wood5 frame !re is ano!r wood5 frame1 ,s1 also hav+ on x a doz5 or two turns ( insulat$ wire2 ! circuit ( ?is la/ conductor is complet$ by a small inc&esc5t lamp1 ,g4 ,y w notice t :5 ! ,leyd5 j>s are *>g$ & dis*>g$ rapidly ?r\gh ! prim>y conductor1 ! little gl[-lamp ( ! second>y circuit lights up brilliantly1 &1 9 virtue ( :at has already be5 expla9$1 y w see t ?is exp]im5t is a pro( t ! dis*>ge ( ! ,leyd5 j>s ?r\gh ! prim>y circuit mu/ consi/ 9 an alt]nat+ or two-way curr5t2 9 o!r words1 x mu/ be oscillatory4 ,illu/ration3 ,,fig4 #fg4 ,a /ill fur!r pro( may be giv5 t ! dis*>ge ( a ,leyd5 j> or cond5s]1 :5 tak+ place ?r\gh a l[-resi/ance circuit1 is oscillatory 9 ! foll[+ mann]3-- ,we employ ! vacuum tube t we br\ght to y\r notice a few mom5ts ago4 ,:5 an electric curr5t is s5t always 9 ! same direction ?r\gh su* a tube1 x is well kn[n t ! two ends ( ! tube are n alike 9 appe>ance4 ,! tube1 z y h se51 is fill$ ) a lum9\s gl[2 b ?is gl[ is int]rupt$1 =m+ :at is call$ a d>k space ne> "o t]m9al ( ! tube1 ?is t]m9al be+ t :i* is t]m$ ! negative pole4 ,accord+ly1 ?is unsymmetrical appe>ance 9 ! light 9 ! tube is a pro( t ! electric curr5t is pass+ ?r\gh x always 9 "o direction4 ,we c1 h[ev]1 v>y ! exp]im5t1 & in/ead ( illum9at+ ! tube by means ( a direct-dis*>ge or induction coil1 :i* is always 9 "o direction1 we are able to illum9ate x by means ( a rapid s]ies ( dis*>ges f a ,leyd5 j>4 ,y w !n see t ! gl[-light 9 ! tube is symmetrical--! tube1 9 o!r words1 is alike at bo? ends2 & ?is %[s u t ! dis*>ge f ! tube "u ^! circum/ances mu/ be alt]nat+--t is1 fir/ 9 "o direction & !n 9 ! o!r4 ,:il/ ?is app>atus is 9 use1 we c %[ y ) x two o!r v pretty exp]im5ts dep5d5t ^u ! fact t ! dis*>ge ( a ,leyd5 j> ?r\gh a l[-resi/ance circuit is alt]nat+ or oscillatory4 ,a mom5t ago we employ$ ?is oscillatory dis*>ge 9 "o circuit to induce a second>y oscillatory dis*>ge 9 ano!r metallic circuit1 & ?is second>y oscillatory or alt]nat+ curr5t 0 made manife/ by its p[] to illum9ate a little inc&esc5t lamp4 ,if1 h[ev]1 we place a l>ge glass bulb1 ,p1 :i* has be5 p>tly exhau/$ ( its air1 9 ! int]ior ( ! prim>y dis*>ge coil1 y w see t ?is prim>y oscillatory dis*>ge ( ! ,leyd5 j> is able to create 9 ! glass bulb a brilliant lum9\s r+ ( light 7see ,fig4 #fh74 ,?is is call$ an electrodeless dis*>ge1 & x is due to ! fact t ! rapidly oscillatory curr5t exi/+ 9 ! wire wrapp$ r\nd ! bulb creates a simil> oscillatory dis*>ge 9 ! r>efi$ air 9 ! int]ior ( ! bulb1 ?is be+ a conductor1 & ?us r5d]s x lum9\s along a c]ta9 l9e4 ,! production ( ^! electrodeless dis*>ges 9 r>efi$ gases has be5 p>ticul>ly /udi$ by ,pr(essor ,j4 ,j4 ,?omson4 ,ano!r exp]im5t illu/rat+ :at is call$ ! inductive trans=mation ( electrical oscillations is 9 ! arrangem5t commonly call$ a ,tesla coil4 ,su* a coil is n[ be=e y4 ,x consi/s ( a long coil ( insulat$ wire :i* is plac$ 9 ! int]ior ( a tall glass vessel1 & on ! outside ( ?is glass vessel is w\nd ano!r insulat$ & mu* long] wire4 ,if ! alt]nat+ or oscillatory dis*>ge ( a ,leyd5 j> is all[$ to take place ?r\gh ! ?ick] wire 9 ! int]ior ( ! glass cyl9d]1 x g5]ates 9 ! out] or second>y wire a v p[]ful alt]nat+ or oscillatory electromotive =ce1 & we see t ?is is ! case by connect+ ! ends ( ?is second>y circuit to two insulat$ brass balls1 betwe5 :i* a torr5t ( sp>ks n[ passes4 ,we may v>y ! exp]im5t by connect+ ! ends ( ! second>y circuit ( ! ,tesla coil to two insulat$ conc5tric r+s ( ?91 b>e1 brass wire1 & !n1 :5 ! room is d>k5$1 we see ! space betwe5 ^! r+s fill$ ) a brilliant purple light1 :i* is due to ! dis*>ge tak+ place ?r\gh ! air "u ! action ( ! rapidly oscillatory electromotive =ce g5]at$ 9 ! second>y circuit4 ,illu/ration3 ,,fig4 #fh4--;,an electrodeless dis*>ge 9 an exhau/$ bulb4 ,i tru/ t ^! exp]im5ts w h produc$ a conviction 9 y\r m9ds t ! release ( ! electric /ra9 9 ! glass dielectric ( a ,leyd5 j> results 9 ! production ( electric oscillations or rapidly alt]nat+ electric curr5ts 9 ! metallic circuit connect+ ! two surfaces1 j z ! sudd5 release ( a compress$ spr+ results 9 a s]ies ( me*anical oscillations4 ,we may "h rem>k t any arrangem5t ( two metallic plates ) a %eet ( insulator or non-conductor betwe5 !m is call$ a cond5s]4 ,?us1 a cond5s] c be built up by coat+ a %eet+ ( glass on its two sides ) t9foil1 or 9 place ( glass we may use mica1 p>aff9 pap]1 or any o!r good non-conductor4 ,we may ev5 use air at ord9>y pressures2 & ?us1 if two metal plates are plac$ ne> to "o ano!r 9 air1 ! plates be+ bo? insulat$--t is1 support$ on non-conductors1--?is arrangem5t con/itutes :at is call$ an air cond5s]4 ,an air cond5s]1 !re=e1 is virtually only a k9d ( ,leyd5 j> 9 :i* ! glass is replac$ by air1 & ! t9foil by two /\t metal plates4 ,illu/ration3 ,,fig4 #fi4--;,h]tz oscillator4 ,i mu/ n[ proce$ to describe & %[ y a p>ticul> k9d ( air cond5s] :i* 0 inv5t$ by ! late ,pr(essor ,h]tz1 &1 9 consequ5ce1 is call$ a ,h]tz oscillator 7see ,fig4 #fi74 ,x consi/s ( two squ>e or r\nd metal plates :i* are c>ri$ on glass or ebonite legs1 & ^! plates h %ort1 /\t wires atta*$ to !m1 end+ 9 brass knobs4 ,if ^! plates are plac$ 9 l9e ) "o ano!r1 !y con/itute an air cond5s] ( a v peculi> k9d1 ! two brass plates correspond ) ! t9foil surfaces ( a ,leyd5 j>1 & ! air all r\nd !m corresponds ) ! glass ( ! j>4 ,suppos+ ! plates are s arrang$ t ! brass knobs are ab\t in* ap>t1 or r less1 if !n we connect ^! two brass plates to ! second>y t]m9als ( an induction coil or electrical ma*9e capable ( giv+ long sp>ks 9 air1 we %all f9d1 :5 ! electrical ma*9e or induction coil is set 9 action1 t a v bright crackl+ sp>k passes betwe5 ^! little knobs1 & ) prop] exp]i5ce x is easy to adju/ ! di/ance f ! knobs s t ?is sp>k is an oscillatory sp>k4 ,"u ^! circum/ances1 :at is tak+ place is z foll[s3 ,9 ! fir/ place1 an electromotive =ce is act+ betwe5 ! two plates1 & creat+ an electric /ra9 9 ! air all r\nd !m along c]ta9 l9es1 & also betwe5 ! two knobs4 ,! air1 & all o!r gases l x1 possess ?is peculi> prop]ty1 t :il/ at ord9>y pressures !y are ne>ly p]fect non-conductors1 yet1 nev]!less1 if !y are subject$ to m ?an a c]ta9 electric pressure1 !y pass in/antly into a condition 9 :i* !y become v good conductors4 ,accord+ly1 if we progressively increase ! electromotive =ce act+ betwe5 ! plates1 up to a c]ta9 po9t ! :ole arrangem5t acts l a ,leyd5 j>2 b !re comes a mom5t :5 ! air betwe5 ! knobs breaks d[n & passes f a non-conductive to a conductive condition4 ,! two plates !n resemble at t mom5t ! surfaces ( a *>g$ ,leyd5 j> :i* are connect$ toge!r by a good conductor1 &1 z we h already se51 "u ^? circum/ances ! dis*>ge is oscillatory1 & ! electric /ra9 9 ! non-conductor1 or dielectric1 viz4 ! air ar\nd ! plates1 dies away by a s]ies ( rapidly alt]nat+ electric /ra9s 9 opposite directions4 ,n[1 at ?is po9t ,i mu/ recall to y\r recollection t1 9 speak+ ab\t ! production ( air waves1 ,i po9t$ out t "o condition ess5tial to ! production ( an air wave 0 t !re mu/ be a v sudd5 application or release ( ! air-pressure1 su* z is caus$ by an explosion or escape ( compress$ air4 ,we _c produce an air wave by mov+ any object su* z a fan sl[ly to & fro ?r\gh ! air4 ,9 ord] to produce an air wave we mu/ /rike ! air a v sudd5 bl[1 or1 :i* comes to ! same ?+1 we mu/ apply & remove a v sudd5 pressure to ! air2 & "u ^! circum/ances we />t into exi/5ce an air wave1 :i* travels away f ! vibrat+ or rapidly mov+ body1 & cont9ues its j\rney out into surr\nd+ space4 ,i want to %[ y t1 9 ! case ( ! ,h]tz oscillator1 ^! v sudd5 rev]sals ( electric /ra9 9 ! air or space r\nd ab\t x1 :i* take place at ! mom5t :5 ! oscillatory sp>k passes betwe5 ! knobs1 creates 9 a simil> mann] :at is call$ an electric wave1 :i* travels out into ! space ar\nd4 ,! po9t y mu/ appreciate is1 t j z an air wave conveys away to di/ant places a rapidly alt]nat+ compression made 9 ! air by a vibrat+ body at a p>ticul> place1 s an electric wave conveys away to di/ant places an alt]nat+ electric /ra91 :i* is orig9at$ at "s po9t 9 ! m$ium by ! oscillatory dis*>ge ( "s =m ( cond5s]4 ,be=e1 h[ev]1 we c demon/rate ?is fact1 we mu/ h "s means = detect+ ! influ5ce ( :at we call an electric wave4 ,y w rememb] t1 9 ! case ( exp]im5ts ) air waves1 ,i us$ a s5sitive flame 9 ord] to make evid5t to y ! pres5ce ( waves 9 ! air :i* y c\ld n see1 s "h ,i mu/ use an appropriate detector = electric waves1 ! op]ation ( :i* w r5d] evid5t to u ! exi/5ce 9 ! space r\nd our electric oscillator ( ! electric waves we _c see4 ,"t w n p]mit me to discuss all ! diff]5t =ms ( electric-wave detector :i* h be5 inv5t$4 ,= our pres5t purposes we mu/ limit ourselves to ! description ( "o plan1 :i* dep5ds on ! rem>kable fact t f9ely p[d]$ dry metal or metallic fil+s are non-conductors ( ! electric curr5t until !y are subject$ to an electromotive =ce exce$+ a c]ta9 value1 :5 ! metallic fil+s at once pass into a conductive condition4 ,if y recall ! rem>ks made j n[ 9 connection ) ! special electrical prop]ties ( air & o!r gases1 y w notice t !re is a rem>kable simil>ity betwe5 ! electrical behavi\r ( air at ord9>y pressures to electromotive =ce1 & t ( a loose mass ( metallic fil+s4 ,bo? ! air & ! metallic fil+s are non-conductors z long z ! electromotive =ce act+ on !m does n exce$ a c]ta9 value1 b if x exce$s ?is critical value1 !y pass at once into a conductive condition4 ,! fact t pieces ( metal 9 loose contact ) "o ano!r behave 9 a simil> mann] 0 discov]$ m ?an tw5ty ye>s ago by ! late ,pr(essor ,d4 ,e4 ,hughes1 :o1 z y may p]haps "k1 0 ! inv5tor ( a pr9t+ telegraph1 ! microphone1 & _m o!r mo/ important electrical in/rum5ts4 ,pr(essor ,hughes 0 a great g5ius1 & 9 _m respects 9 advance ( 8 age4 ,he x 0 :o und\bt$ly discov]$ t an electric sp>k has ! p[] ( affect+ at a di/ance ! electric conductivity ( a metallic junction consi/+ ( two metals 9 loose contact4 ,! peculi> behavi\r ( metallic fil+s "u electromotive =ce1 & "u ! influ5ce ( electric sp>ks at a di/ance1 0 subsequ5tly r$iscov]$ by ,pr(essor ,branly2 & ! effect ( an electric oscillatory sp>k 9 *ang+ ! conductivity ( a light metal contact 0 also r$iscov]$ by ,sir ,oliv] ,lodge1 & ! ph5om5a inve/igat$ by _m o!r obs]v]s4 ,i c %[ y ! exp]im5t on a l>ge scale 9 ! foll[+ mann]3-- ,illu/ration3 ,,fig4 #gj4--;,a metal disc-coh]]4 ,i h "h a numb] ( alum9ium discs1 ! size ( sixp5ces1 /amp$ out ( ?9 metal1 & ^! are arrang$ 9 a sort ( semi-cyl9drical tr\gh betwe5 two t]m9al screws1 s t ! discs are v lightly press$ toge!r4 ,"u ^! circum/ances ! pile ( metal discs is n a conductor1 & x w n pass ! electric curr5t f a batt]y :i* is jo9$ up 9 s]ies ) an electric bell & ! pile ( discs 7see ,fig4 #gj74 ,suppos+1 h[ev]1 t ,i make an oscillatory sp>k 9 proximity to ?is pile ( metal discs1 z ,i c d by tak+ ! dis*>ge f a l>ge ,leyd5 j> ne> x2 ! pile ( discs at once becomes a conductor2 ! electric curr5t f ! batt]y c !n pass ?r\gh x1 & ! bell r+s4 ,su* an arrangem5t has be5 nam$ by ,sir ,oliv] ,lodge a coh]]1 because1 "u ! action ( ! oscillatory sp>k1 ! discs coh]e or /ick toge!r4 ,we c sep>ate ! discs by giv+ !m a %>p rap1 & !n ! op]ation c be aga9 repeat$4 ,a mu* m s5sitive arrangem5t c be made by tak+ a small box ( wood ?r\gh ! bottom ( :i* pass two nickel wires :i* are p>allel to "o ano!r1 b n 9 contact4 ,9 ?is box is plac$ a small quantity ( v f9ely p[d]$ metallic nickel or nickel fil+s1 & if ! quantity ( ^! fil+s is prop]ly adju/$1 x is possible to make an arrangem5t :i* possesses ! prop]ty t !re is no conductivity betwe5 ! two nickel wires "u ord9>y circum/ances1 b t !y become conductively connect$ to "o ano!r ! mom5t an oscillatory electric sp>k is made 9 ! neighb\rhood4 ,we %all speak ( ?is contrivance z an electric wave indicator1 & we %all employ x 9 subsequ5t exp]im5ts to enable u to detect ! pres5ce ( an electric wave4 ,we mu/ !n return = a mom5t to ! consid]ation ( ! production ( electrical oscillations 9 circuits ( v>i\s k9ds4 ,i tru/ x has be5 made pla9 to y t if two metallic surfaces1 sep>at$ by a non-conductor su* z air or glass1 are act$ ^u by an electromotive =ce1 ! non-conductor becomes electrically /ra9$4 ,ano!r way ( /at+ ?is is to say t a positive *>ge ( electricity exi/s on "o metal surface1 & a negative *>ge on ! o!r4 ,! only objection :i* c be rais$ to express+ ! facts 9 ?is mann] is t x fa/5s att5tion r ^u ! conductors ?an ^u ! insulator1 :i* is ! real /oreh\se ( ! en]gy4 ,if ^! two metal surfaces are !n connect$ toge!r by a conductor ( l[ resi/ance1 ! *>ges disappe> by a s]ies ( oscillations1 & ! result is an electric curr5t 9 ! conduct+ circuit connect+ ! plates1 :i* ru%es backw>ds & =w>ds 9 ! circuit1 b gradually dim9i%es 9 /r5g? until x completely dies away4 ,y may picture to y\rselves ! electrical effect z analog\s to ! foll[+ exp]im5t ) two air-vessels3 ,suppos+ we h two /rong /eel bottles1 into "o ( :i* we compress a quantity ( air1 & 9 ! o!r we make a vacuum by pump+ out ne>ly all ! air4 ,^! vessels w\ld correspond ) two conductors1 "o *>g$ ) positive electricity & ! o!r ) negative4 ,imag9e ^! vessels connect$ by a wide pipe 9 :i* is plac$ a tap or valve1 :i* c be op5$ sudd5ly s z to p]mit ! air to ru% ov] f ! full vessel to ! empty "o4 ,if ?is is done1 x is a matt] ( exp]i5ce t ! equality ( pressure betwe5 ! two vessels is n at once e/abli%$1 b 9 virtue ( ! in]tia quality ( ! air1 x only takes place aft] a s]ies ( oscillations ( air 9 ! pipe4 ,9 ru%+ ov] f ! full vessel to ! empty "o ! air1 s to speak1 ov]%oots ! m>k1 & ! /ate ( ! vessels z reg>ds air-pressure is exactly int]*ang$4 ,! air !n ru%es back aga91 & x is only aft] a s]ies ( to-&-fro movem5ts ( ! air 9 ! pipe t an exact equality ( pressure 9 ! two vessels is atta9$4 ,! electrical actions :i* take place 9 connection ) an electric dis*>ge betwe5 two conductors1 "o ( :i* is *>g$ positively & ! o!r negatively1 are exactly analog\s to ! above-describ$ exp]im5t ) two air-vessels1 "o ( :i* has air 9 x "u compression1 & ! o!r has _h ! air remov$ f x4 ,y w notice1 h[ev]1 t ! oscillations ( ! air 9 ! pipe 9 ! air-vessel exp]im5t dep5d ess5tially ^u ! fact t air is a sub/ance :i* has in]tia1 or mass1 & y w naturally ask :at is x :i* has in]tia1 or its equival5t1 9 ! electrical exp]im5t8 ,! answ] to ?is "q is z foll[s3 ,e electric circuit has a quality :i* is call$ inductance1 9 virtue ( :i* an electric curr5t _c be />t$ 9 x in/antly1 ev5 "u any electromotive =ce1 & conv]sely :5 ! curr5t is />t$ x _c be imm$iately br\ght to re/4 ,f ! simil>ity ( ?is quality ( ! circuit to ! in]tia ( ord9>y mat]ial sub/ances1 x has be5 sometimes call$ ! electric in]tia ( ! circuit4 ,! ^w 8in]tia0 really means inactivity1 or laz9ess1 b ! t]m z us$ 9 me*anics implies some?+ m ?an m]e inactivity4 ,x involves ! notion ( a p]si/5ce 9 motion :5 once ! body is set mov+4 ,:5 a mat]ial sub/ance is 9 motion x possesses en]gy1 & has ! p[] ( ov]com+ up to a c]ta9 po9t resi/ance to its motion4 ,?is en]gy-hold+ p[]1 or capacity = /or+ up en]gy ( motion1 :i* is *>act]i/ic ( all mat]ial sub/ances1 is a consequ5ce ( _! in]tia4 ,! fact is o!rwise express$ by /at+ t ! mass ( a mat]ial sub/ance is "o elem5t 9 ! production ( en]gy ( motion4 ,an electric curr5t 9 "o s5se resembles a mov+ sub/ance1 = x is an exhibition ( en]gy 9 association ) matt]4 ,! curr5t-en]gy is measur$ by ! product ( two factors3 "o is half ! squ>e ( ! curr5t-/r5g?1 & ! o!r is ! inductance ( ! circuit4 ,! analogy betwe5 ! two cases may be m exactly br\ght out by po9t+ out t ! en]gy ( motion ( a mov+ body is measur$ by ! product ( its mass & half ! squ>e ( its velocity4 ,h5ce x foll[s t ! p[] ( ov]com+ resi/ance1 or1 9 o!r words1 ( do+ useful "w or mis*ief1 :i* is possess$ by a heavy body 9 motion is proportional1 n simply to its spe$1 b to ! squ>e ( its spe$4 ,if a bullet1 mov+ ) a c]ta9 spe$1 c j pass ?r\gh "o plank #a in* ?ick1 !n1 :5 mov+ ) twice ! spe$1 x w pass ?r\gh f\r su* planks1 & if mov+ ) ?ree times ! spe$1 ?r\gh n9e planks ( equal ?ickness4 ,! en]gy ( an electric curr5t is simil>ly measur$ by ! product ( ! inductance ( ! circuit & half ! squ>e ( ! curr5t-/r5g?4 ,9 ! same or equal circuits two curr5ts1 ! /r5g?s ( :i* are 9 ! ratio ( #a to #b1 h en]gies 9 ! ratio ( #a to #d4 ,! great]1 !re=e1 ! inductance ( an electric circuit1 ! great] is ! t5d5cy ( an electric curr5t set fl[+ 9 x to run on aft] ! electromotive =ce is )drawn4 ,! inductance ( a circuit is increas$ by coil+ x into a coil ( _m turns1 & decreas$ by /ret*+ x out 9 a /raight l9e4 ,! important idea to grasp 9 connection ) ?is "p ( ! subject is t1 j z !re are two =ms ( me*anical en]gy1 viz4 en]gy ( me*anical /ra9 & en]gy ( motion1 s also !re are two =ms ( electrical en]gy1 viz4 en]gy ( electro-/atic /ra9 & electric-curr5t en]gy4 ,if1 = in/ance1 we b5d a b[ or ext5d a spr+1 ?is action involves ! exp5diture ( me*anical en]gy1 or "w1 & ! en]gy s sp5t is /or$ up z en]gy ( /ra91 or1 z x is call$1 di/orsional en]gy 9 ! di/ort$ b[ or spr+4 ,:51 h[ev]1 ! b[ communicates its en]gy to ! arr[ or ! spr+ to a ball1 & s sets ^! 9 motion1 we h 9 ! fly+ arr[ or ball a /ore ( en]gy ( motion4 ,if a slip ( /eel spr+ is fix$ at "o end1 & !n set 9 vibration1 we h a cont9ual trans=mation ( en]gy f ! motional to ! di/orsional =m4 ,at "o mom5t ! spr+ is mov+ viol5tly1 & at ! next x is b5t to its utmo/ ext5t2 & ^! /ates succe$ ea* o!r4 ,! /ore ( en]gy 9 ! vibrat+ spr+ is1 h[ev]1 gradually fritt]$ away1 p>tly because ! cont9ual b5d+ ( ! /eel heats x1 & ?is heat dissipates "s ( ! en]gy2 b also because ! spr+1 if vibrat+ quickly en\gh1 imp>ts its en]gy to ! surr\nd+ air1 & creates air waves1 :i* travel away1 & rapidly rob ! vibrat+ spr+ ( its /ock ( en]gy4 ,9 a precisely simil> mann] all electrical oscillation effects dep5d ^u ! fact t electric en]gy c exhibit itself 9 two =ms4 ,9 "o =m x is electro-/atic en]gy1 or en]gy ( electric /ra94 ,9 ?is =m we h x :5 we *>ge a ,leyd5 j>4 ,! glass is !n1 z expla9$1 9 a /ate ( electrical /ra91 & its condition is analog\s to t ( a /ret*$ spr+4 ,! same holds good :5 we h two conductors insulat$ f ea* o!r 9 air4 ,we h !n an electrical /ra9 9 ! air4 ,x is important1 h[ev]1 to notice t1 s9ce a p]fect vacuum c support electric /ra91 x foll[s t1 9 ! cases :]e air or glass con/itute ?is non-conductor1 or dielectric1 ( a cond5s]1 ! :ole ( ! en]gy _c be /or$ 9 ! mat]ial sub/ance1 ! glass or ! air4 ,! real /oreh\se ( ! en]gy is ! !r1 z modifi$ by ! pres5ce ( ! ord9>y matt] 9 ! same place4 ,:5 we dis*>ge ! ,leyd5 j> or cond5s]1 ! electro-/atic en]gy 9 ! dielectric disappe>s1 & we obta9 9 its place an electric curr5t 9 ! connect+ conductor2 & ?is1 z describ$1 is an exhibition ( en]gy 9 ano!r =m4 ,if ! resi/ance ( ! connect+ conductor is small1 !n we h electrical oscillations e/abli%$ :i* consi/ 9 an alt]nate trans=mation ( ! en]gy f an electro-/atic =m to ! electric-curr5t =m4 ,at ea* oscillation "s en]gy is fritt]$ away into heat 9 ! conductor1 & if ! conductor & cond5s] h a special =m1 en]gy may be rapidly remov$ f ! sy/em by ! electric waves :i* are =m$ 9 ! surr\nd+ !r or dielectric4 ,^! waves consi/ 9 ! propagation ?r\gh ! m$ium ( l9es ( electric /ra91 j z an air wave consi/s 9 ! propagation ?r\gh ! air ( regions ( air-compression1 or a wat] wave consi/s 9 ! propagation ( an elevation on ! surface4 ,return+ aga9 to ! discussion ( ! production ( electrical oscillations1 x is necess>y to consid] a little m 9 detail ! mann] 9 :i* we c create an electrical oscillation 9 :at we h call$ an op5 electric circuit4 ,let me beg9 ) an exp]im5t1 & x w !n be easi] = y to und]/& ! p>ticul> po9ts to be expla9$4 ,illu/ration3 ,,fig4 #ga4 ,be=e me are two long brass rods1 ea* ( !m ab\t #e feet 9 l5g?1 & ! ends ( ^! rods are provid$ ) poli%$ brass balls 7see ,fig4 #ga74 ,! rods are plac$ 9 "o l9e & support$ on pieces ( ebonite1 & are s fix$ t ! two balls are sep>at$ f "o ano!r by a space ( ab\t in*4 ,! two rods con/itute1 !re=e1 two insulat$ conductors4 ,^! rods are connect$ by coils ( wire ) ! t]m9als ( an in/rum5t call$ an induction coil1 :i* ,i %all n /op to describe1 b :i* y may reg>d z a k9d ( electrical ma*9e = produc+ electromotive =ce4 ,if we set ! induction coil 9 action1 x creates betwe5 its t]m9als an int]mitt5t b v p[]ful electromotive =ce1 :i* gradually increases up to a c]ta9 value1 at :i* x breaks d[n ! conductivity ( ! air-gap betwe5 ! two balls4 ,let u ?9k c>efully :at happ5s z ! electromotive =ce ( ! induction coil is increas+4 ,"o ( ! rods is 9 effect be+ electrifi$ ) positive1 & ! o!r ) negative1 electricity1 & ^! *>ges are increas+ 9 magnitude4 ,! two rods con/itute1 z x 71 ! two coat$ surfaces ( a k9d ( ,leyd5 j>1 or cond5s]1 ( :i* ! surr\nd+ air is ! non-conductor4 ,accord+ly1 by all t has be5 previ\sly expla9$1 y w easily und]/& t !re is an electric /ra9 9 ! air :i* exi/s along c]ta9 l9es1 call$ l9es ( electro-/atic /ra91 & ?is /ate 9 ! air is exactly simil> to ! condition 9 :i* ! glass ( a ,leyd5 j> f9ds itself :5 ! j> is *>g$4 ,if we 7 to del9eate ! direction ( ?is electric /ra9 by l9es drawn ?r\gh ! space ar\nd ! rods1 we %\ld h to draw !m some:at 9 ! fa%ion repres5t$ by ! dott$ l9es 9 ,fig4 #ga4 ,z ! electrical /ate ( ! rods gradually increases 9 int5sity1 a po9t is rea*$ at :i* ! air betwe5 ! balls c no long] ma9ta9 ?is /ra91 & x breaks d[n & passes into a conductive condition4 ,! /ate ( affairs r\nd ! rods is !n simil> to t ( a ,leyd5 j> be+ dis*>g$4 ,an electric curr5t is produc$ across ! air-gap1 mov+ f "o rod to ! o!r1 & ! int5sely heat$ air 9 betwe5 ! balls is visible to u z an electric sp>k4 ,?is sp>k1 if photograph$1 w\ld be f\nd to be an oscillatory sp>k4 ,! electric curr5t 9 ! rods _c cont9ue indef9itely3 x gradually falls (f 9 /r5g?1 b z x fl[s x creates 9 ! space ar\nd ! rods an electric /ra9 :i* is 9 ! opposite direction to t :i* produc$ x1 al?\gh tak+ place along ! same l9es4 ,aft] a v %ort "t1 !re=e1 ! electrical conditions :i* exi/$ at ! mom5t be=e ! air broke d[n are exactly reproduc$1 only ! direction ( ! /ra9 is rev]s$4 ,9 o!r words1 ! rod :i* 0 positively electrifi$ is n[ negatively1 & vice v]s4 ,!n ?is /ate ( /ra9 aga9 beg9s to disappe>1 produc+ 9 ! rod an electric curr5t1 aga9 9 ! rev]se direction2 & s ! en]gy1 :i* 0 orig9ally communicat$ to ! space r\nd ! rods 9 ! =m ( an electric /ra91 cont9ually *anges its =m1 exi/+ at "o mom5t z en]gy ( ! electric curr5t pass+ across ! sp>k gap1 & ! next mom5t z en]gy ( electric /ra94 ,we may ask :y ?is /ate ( ?+s does n cont9ue indef9itely1 & ! answ] to t "q is tw(old4 ,fir/ because ! rods possess a prop]ty call$ electrical resi/ance1 & ?is acts t[>ds ! electric curr5t j z friction acts t[>ds ! motion ( mat]ial sub/ances2 9 o!r words1 x fritt]s away ! en]gy into heat4 ,s at ea* rev]sal ( ! electric curr5t 9 ! rod a c]ta9 quantity ( ! orig9al /ore ( en]gy has disappe>$1 due to ! resi/ance4 ,!re is1 h[ev]1 a fur!r & m important s\rce ( dissipation ( en]gy1 & ?is is due to ! fact t an electrical oscillation ( ?is k9d tak+ place 9 a f9ite /raight circuit1 or1 z x is call$1 an op5 electric circuit1 creates 9 ! space ar\nd an electric wave4 ,! rapid rev]sal ( ! electric /ra9 9 ! air results 9 ! production ( an electric wave1 j z 9 ! case ( an explosion made 9 air1 ! rapid compression ( ! air results 9 ! production ( an air wave4 ,x is n easy = ^? :o come to ! subject = ! fir/ "t to fully grasp ! notion ( :at is impli$ by ! t]m 8an electric wave40 ,9 ! fir/ lecture1 y w p]haps rememb]1 ,i po9t$ out t ! production ( a wave 9 a m$ium ( any k9d c take place if ! m$ium possesses two prop]ties4 ,9 ! fir/ place1 x mu/ ela/ically resi/ "s *ange or di/ortion1 &1 9 ! second place1 :5 t di/ortion is made x mu/ t5d to disappe> if ! m$ium is left to itself1 & 9 s do+ ! displacem5t ( ! m$ium mu/ ov]%oot ! m>k & be reproduc$ 9 ! opposite direction1 ow+ to "s in]tia-l quality or p[] ( p]si/5ce 9 ! m$ium4 ,x w\ld lead u into matt]s beyond ! scope ( elem5t>y lectures if we 7 to attempt to summ>ize all ! evid5ce :i* exi/s t5d+ to %[ t ! ph5om5a ( electricity & magnetism mu/ dep5d ^u actions tak+ place 9 "s m$ium call$ ! electro-magnetic m$ium4 ,all ! great inve/igators at ! beg9n+ ( ! la/ c5tury1 :5 electrical & magnetic ph5om5a 7 beg9n+ to be explor$1 came to ?is conclusion1 & 9 ! writ+s ( ,joseph ,h5ry1 ( ,ampre1 & ( ,f>aday we f9d ref]5ces aga9 & aga9 to _! conviction t ! ph5om5a ( electricity imply ! exi/5ce ( a m$ium exactly 9 ! same way z d ! ph5om5a ( optics4 ,x is only1 h[ev]1 9 rec5t ye>s t we h _h evid5ce be=e u1 "s ( :i* w be review$ 9 ! next lecture1 :i* af=ds conv9c+ pro( t ! lum9if]\s !r & ! electro-magnetic m$ium mu/ be ! same4 ,! consid]ation ( ! simple/ electrical effects is suffici5t to %[ t1 if ?is m$ium exi/s1 x possesses at lea/ two prop]ties1 "o ( :i* is t x (f]s an ela/ic resi/ance to ! production ( electric /ra9 9 x by means ( electromotive =ce4 ,a "q :i* is sure to arise 9 ! m9ds ( ^? :o consid] ?is subject c>efully is1 ,:at is ! nature ( an electric /ra98 ,& ! only answ] :i* we c give at ! pres5t mom5t is t we mu/ be cont5t to leave ! "q unansw]$4 ,we d n "k en\gh yet ab\t ! me*anical /ructure ( ! electro-magnetic m$ium1 or !r1 to be able to pron\nce 9 detail on ! nature ( ! *ange we call an electric /ra94 ,x may be a motion ( "s k9d1 x may be a compression or a twi/1 or x may be some?+ totally diff]5t & at pres5t un?9kable by u1 b1 :atev] x is1 x is "s k9d ( *ange :i* is produc$ "u ! action ( electromotive =ce1 & :i* disappe>s :5 ! electromotive =ce is remov$4 ,cl]k-,maxwell1 to :om we owe "s ( our mo/ sugge/ive conceptions ( mod]n electricity1 co9$ ! phrase electric displacem5t to describe ! *ange :i* we are "h call+ an electric /ra94 ,"o ess5tial elem5t 9 ,maxwell's !ory ( electricity is t an electric /ra9 or displacem5t1 :il/ x is be+ made or :il/ x is disappe>+1 is 9 effect an electric curr5t1 & x is = t reason sometimes spok5 ( z a displacem5t curr5t4 ,we h se5 t e electric circuit possesses a quality analog\s to in]tia1 t is to say1 :5 a curr5t is produc$ 9 x x t5ds to p]si/1 & x _c be creat$ at its full value in/antly by any electromotive =ce4 ,j z we _c1 at ! pres5t mom5t1 pron\nce 9 detail on ! real nature ( electric /ra91 s we _c say :e!r t quality :i* we call inductance ( a circuit is dep5d5t ^u a true in]tia ( ! electro-magnetic m$ium or on "s entirely diff]5t quality m fundam5tal4 ,x may be rem>k$1 9 pass+1 t !re is a /rong t5d5cy 9 ! human m9d to seek = & be satisfi$ ) :at we call$ me*anical explanations4 ,?is probably arises f ! fact t ! only ?+s :i* we c picture to ourselves 9 our m9ds v cle>ly are movem5ts or *anges 9 relative positions4 ,if we c 9 imag9ation r$uce any physical op]ation to "s k9d ( movem5t or displacem5t tak+ place 9 "s k9d ( mat]ial1 we seem to arrive at a k9d ( t]m9us ( ?\ght :i* is m or less satisfactory4 ,we inv>iably aim at be+ able to visualize an op]ation conc]n+ :i* we are ?9k+1 & x requires "s m5tal self-control to be able to cont5t ourselves ) a g5]al expression :i* does n l5d itself readily to visualization4 ,!re are pl5ty ( indications1 h[ev]1 t ?is m5tal me?od ( proc$ure1 & ?is endeav\r to r$uce all physical op]ations to simple me*anics & to movem5ts ( "s k9d1 may 9 ! end be f\nd to be unju/ifiable2 & ! "t may arrive :5 we may be m satisfi$ to expla9 me*anical op]ations 9 t]ms ( electrical phraseology r ?an aim at dissect+ electrical effects into me*anical op]ations4 ,?us1 = in/ance1 in/ead ( speak+ ( electric in]tia1 x may be really m ju/ifiable to speak ( ! inductance ( ord9>y matt]4 ,! f9al t]ms 9 :i* we endeav\r to (f] ourselves an explanation ( physical ev5ts are 9 all probability v mu* a matt] ( conv5i5ce & cu/om4 ,we may1 h[ev]1 = pres5t purposes re/ cont5t by ?9k+ ( ! electro-magnetic m$ium z 9 "s s5se l a heavy ela/ic sub/ance :i* is capable ( und]go+ "s k9d ( /ra9 or di/ortion1 ! said /ra9 reliev+ itself z soon z ! di/ort+ =ce is )drawn2 b1 9 addition1 we mu/ ?9k ( ! m$ium z possess+ a quality analog\s to in]tia1 s t z di/ortion vani%es x ov]%oots ! m>k1 & ! m$ium only rega9s its /ate ( equilibrium at ! p>ticul> po9t consid]$1 by a s]ies ( oscillations or alt]nate di/ortions1 gradually decreas+ 9 am\nt4 ,any m$ium :i* possesses ^! two qualities has1 9 virtue ( explanations already giv51 ! prop]ty ( hav+ waves creat$ 9 x1 & :at we mean by an electric wave is a /ate ( electric /ra9 :i* is propagat$ ?r\gh ! !r ) a velocity equal to t ( light1 j z an air wave consi/s ( a /ate ( compression :i* is propagat$ ?r\gh ! air ) a velocity ( #aajj feet a second4 ,illu/ration3 ,,fig4 #gb4--;,electric-radiation detector 7,flem+74 ,to sum up1 we may !n say t :5ev] rapid electrical oscillations are creat$ 9 op5 circuit1 su* z ! two rods above describ$1 ! arrangem5t con/itutes a device = creat+ an impulse or effect 9 ! surr\nd+ space call$ an electric wave 9 ! !r or electro-magnetic m$ium2 j z an organ-pipe or piano-/r+ or o!r musical in/rum5t con/itutes a device = creat+ waves 9 ! air by means ( me*anical oscillations4 ,! exi/5ce ( ^! electric waves1 & _! transf]5ce to di/ant places1 c be r5d]$ evid5t by _! action z already describ$ ^u f9ely p[d]$ metals4 ,an app>atus :i* %[s ?is effect v well is n[ arrang$ be=e y4 ,at "o end ( ! table ,i h a pair ( rods connect$ to an induction coil1 con/itut+ a ,h]tz radiator1 ! action ( :i* has j be5 describ$4 ,at ! o!r end ( ! table are two simil> long rods1 b _! inn] ends are connect$ to two small plates ( silv]1 :i* =m ! sides ( a v n>r[ box1 & betwe5 ^! plates is plac$ a v small quantity ( metallic p[d]4 ,! con/ruction ( ?is little box is z foll[s3 ,a ?9 slip ( ivory has a little gap cut out ( x 7see ,fig4 #gb71 & on ! two sides ( ?is slip ( ivory are b\nd two silv] plates b5t 9 ! %ape ( ! lett] ,l1 =m+1 !re=e1 a v n>r[ box ) silv] sides4 ,! two silv] plates are connect$ to ! two long rods4 ,z already expla9$1 ! metallic fil+s or f9ely p[d]$ metal are n 9 _! ord9>y condition an electric conductor4 ,accord+ly1 if we connect to "o ( ! silv] plates "o t]m9al ( a batt]y jo9$ 9 s]ies ) an electric bell1 ! o!r end ( ! bell be+ connect$ to ! second silv] plate1 ?is batt]y _c s5d a curr5t ?r\gh ! bell1 because ! circuit is int]rupt$ by ! non-conductive metallic p[d] 9 ! little box4 ,suppos+1 !n1 t we cause a sp>k to pass betwe5 ! balls ( ! radiator1 & />t an electric wave4 ,:5 ?is electric wave rea*es ! long rods connect$ to ! receiv+ arrangem5t1 x sets up 9 ^! rods a sudd5 electromotive =ce1 & ?is electromotive =ce1 z already expla9$1 if ( suffici5t magnitude1 causes ! loose mass ( metallic fil+s to pass f a non-conductive to a conductive condition4 ,at t mom5t1 !re=e1 ! batt]y is able to s5d an electric curr5t ?r\gh ! bell1 & to cause x to r+4 ,we c1 h[ev]1 /op ! r++ by giv+ ! little box conta9+ ! metallic fil+s a tap1 :i* sep>ates !m f "o ano!r & int]rupts ! electric conductivity4 ,! function ( ! two rods connect$ ) ! receiv] is n q ! same z ! function ( ! two rods connect$ to ! radiator4 ,9 ord] to create a vigor\s electric wave1 we mu/ h a radiator :i* possesses :at is call$ consid]able electric capacity1 & also consid]able inductance1 & we c only d ?is 9 g5]al by us+ long rods4 ,on ! o!r h&1 at ! receiv+ end ! efficacy ( ! rods is due to ! fact t !y1 s to speak1 add toge!r ! electric /ra9 tak+ place ov] a consid]able di/ance2 9 o!r words1 ! electromotive =ce :i* is set up 9 ! receiv+ circuit is dep5d5t on ! l5g? ( ! rods4 ,! long]1 !re=e1 ^! rods1 ! great] is ! di/ance at :i* we c obta9 ! effect :i* is %[n to y ) a giv5 sp>k-l5g?4 ,"o po9t x is important to notice1 & t is1 t ! rods ( ! receiv] mu/ be p>allel to ! rods ( ! radiator if we are to obta9 any effect at a di/ance4 ,if we turn ! rods ( ! radiator r\nd s t !y are at "r angles to ^? ( ! receiv]1 y see t no sp>ks produc$ at ! radiator balls cause ! bell 9 connection ) ! receiv] to r+4 ,! reason = ?is is because ! electric /ra91 :i* is propagat$ out into ! space1 exi/s 9 a direction p>allel to ! radiator rods all along a l9e drawn p]p5dicul> to ! rods ?r\gh ! sp>k-gap4 ,! receiv] rods w n h electromotive =ce produc$ 9 !m by ?is travell+ l9e ( electric /ra9 unless !y are p>allel to its direction4 ,x is to be hop$ t ! above explanations h af=d$ indications ( :at is meant by an electric wave4 ,on ! o!r h&1 !re may be _m :o f9d x exce$+ly difficult to d]ive cle> ideas :5 ! subject is pres5t$ to !m clo!d 9 su* g5]al t]ms z we h be5 oblig$ to use4 ,x may assi/ matt]s1 !re=e1 if1 be=e conclud+ ?is *apt]1 a ^w or two is said on ! subject ( rec5t inve/igation into ! inn] me*anism ( an electric curr5t & an electric /ra94 ,x is impossible to d ?is1 h[ev]1 )\t mak+ m5tion1 9 ! briefe/ possible way1 ( mod]n rese>*es into ! con/itution ( matt]4 ,if y c imag9e y\rselves furni%$ ) a little cry/al ( ord9>y table salt1 *emically call$ *loride ( sodium1 & ! means ( cutt+ x up "u an imm5sely p[]ful microscope1 y might g on divid+ x up into small] & small] pieces4 ,if ?is process c\ld be cont9u$ suffici5tly f>1 we %\ld ultimately obta9 a v small fragm5t ( salt1 :i*1 if /ill fur!r divid$1 w\ld yield two portions ( matt] n alike & n salt4 ,?is smalle/ possible portion ( salt is call$ a molecule ( sodium *loride4 ,*emical facts tea* u t ?is molecule is made up ( two /ill small] portions ( matt]1 :i* are call$ respectively atoms ( *lor9e & sodium4 ,we h good reason to believe t all solids1 liquids1 & gases are compos$ ( molecules1 & ^! are built up ( atoms1 few or _m4 ,9 ! case ( "s sub/ances1 su* z salt1 ! molecule is v simple & compos$ ( two atoms4 ,9 o!r sub/ances1 su* z album5 or :ite ( egg1 ! molecules are v complicat$ & compos$ ( hundr$s ( atoms4 ,! ^w atom means some?+ :i* 8_c be cut10 & until comp>atively rec5t "t ! op9ion 0 held t atoms ( matt] 7 ! smalle/ indivisible portions ( matt] :i* c\ld exi/4 ,m ?an tw5ty-five ye>s ago1 ,sir ,william ,crookes %[$1 by num]\s beautiful exp]im5ts1 t 9 a vacuum tube1 su* z y h se5 us$ to-day1 a torr5t ( small p>ticles is project$ f ! negative t]m9al :5 an electric curr5t is pass$ ?r\gh ! tube4 ,?is /ream ( p>ticles is call$ ! ca?ode /ream1 or ! ca?ode radiator4 ,)9 rec5t times1 ,sir ,joseph ,?omson has furni%$ a pro( t ?is ca?ode /ream consi/s ( p>ticles v mu* small] ?an *emical atoms1 ea* p>ticle be+ *>g$ ) negative electricity4 ,^! p>ticles are n[ call$ corpuscles1 or electrons4 ,x has be5 %[n t ^! electrons are con/itu5ts ( *emical atoms1 & :5 we remove an electron f an atom we leave ! rema9d] positively electrifi$4 ,an atom c1 !re=e1 by v>i\s means be divid$ into two portions ( unequal size4 ,fir/1 a v small "p :i* is *>g$ ) negative electricity1 &1 secondly1 a rema9+ l>g] portion *>g$ ) positive electricity4 ,^! two p>ts tak5 toge!r are call$ ions1 i4e4 w&]]s4 ,! negative ions1 or electrons1 or corpuscles1 tak5 toge!r con/itute :at we call negative electricity1 & up to ! pres5t no "o has be5 able to %[ t ! corpuscle c be unelectrifi$4 ,h5ce ! view has be5 express$ t :at we call electricity is a k9d ( matt]1 atomic 9 /ructure1 & t ^! negative ions or corpuscles collectively are1 9 fact1 ! atoms ( ! electric fluid4 ,^! corpuscles c move freely 9 ! int]ior ( "s solids1 mov+ betwe5 ! molecules ( ! solid j z little dogs c run ab\t 9 & among/ a cr[d ( p 9 a /reet4 ,9 ^! cases ! sub/ance is call$ a conductor ( electricity4 ,9 o!r sub/ances ! movem5t ( ! corpuscles is m re/rict$1 & ^! con/itute ! v>i\s k9ds ( s-call$ non-conductors4 ,! corpuscle1 be+ a small *>ge ( negative electricity1 creates 9 all surr\nd+ space a /ate call$ electric =ce4 ,x is impossible to exp\nd ?is action m 9 detail )\t ! use ( ma!matical reason+ ( a difficult "*4 ,suffice x to say t ?is electric =ce mu/ be a p>ticul> condition ( /ra9 or motion 9 ! !r4 ,if ! corpuscle is 9 rapid motion1 x creates 9 addition ano!r k9d ( /ra9 or motion call$ magnetic =ce4 ,! electric =ce & ! magnetic =ce are relat$ to ea* o!r 9 free space 9 su* a mann] t if we "k ! diff]5ce betwe5 ! values ( ! electric =ce at two v ne> po9ts 9 space1 we are able to tell ! rate at :i* ! magnetic =ce is *ang+ ) "t 9 a direction at "r angles to ! l9e jo9+ ^! ne> po9ts 9 space4 ,we _c specify 9 great] detail ! exact nature ( ^! /ates or conditions :i* con/itute magnetic =ce & electric =ce1 until we "k mu* m ?an we d at pres5t ab\t ! real nature ( ! !r4 ,! two fundam5tal qualities ( ! !r are1 h[ev]1 its capacity to su/a9 ^! /ates we call ! magnetic =ce & ! electric =ce4 ,! electrons ( :i* we h spok5 n only give rise to electric & magnetic =ce :5 9 movem5t1 b !y are !mselves set 9 motion by ^! =ces4 ,?us electric =ce at any po9t moves electrons plac$ at t spot1 & an electron 9 motion is affect$ & has its direction ( motion *ang$ :5 magnetic =ce acts on x4 ,leav+ fur!r rem>ks on ! relations ( atoms1 electricity1 & !r until ! end ( ! la/ lecture1 we may conclude ! pres5t "o by expla9+ ! mann] 9 :i* ! obs]v$ facts connect$ ) a ,h]tz oscillator are int]pret$ 9 t]ms ( ?is electron hypo!sis ( electricity4 ,take ! simple case ( two long insulat$ metal rods sep>at$ by a sp>k-gap4 ,! process ( *>g+ "o rod positively & ! o!r negatively consi/s 9 =c+ m corpuscles1 or negative ions or electrons1 into "o conductor & remov+ "s f ! o!r4 ,any s\rce ( electromotive =ce1 su* z a dynamo or induction coil1 is1 on ?is hypo!sis1 a sort ( electron-pump1 :i* pumps electrons f "o conductor & puts !m into ano!r4 ,"o conductor1 !re=e1 ga9s 9 electron-pressure1 & ! o!r loses4 ,! excess ( electrons 9 "o conductor endeav\r to escape1 & a /ra9 is produc$ on ! electrons or atoms 9 ! surr\nd+ dielectric or air1 :i* may be look$ ^u z ! ef=t ( ! electrons1 m or less te!r$ to ! atoms1 to escape4 ,! air 9 ! sp>k-gap is subject$ to ! mo/ int5se /ra91 & :5 ?is rea*es a c]ta9 int5sity "s ( ! electrons are torn away f _! atoms1 & ! air 9 ! gap !n becomes a conductor4 ,! excess ( electrons 9 "o conductor ru% ?r\gh ! *annel ?us prep>$1 & ?is con/itutes an electric curr5t4 ,! fir/ ru% c>ries ov] too _m electrons to equilibrate ! electron-pressure1 & h5ce ! fir/ torr5t ( migrat+ electrons 9 "o direction is foll[$ by a back-ru% 9 ! opposite "o1 ?is aga9 9 turn by ano!r 9 ! orig9al direction1 & s ! equality 9 ! numb] ( electrons 9 ea* conductor is only e/abli%$ aft] a gradually dim9i%+ s]ies ( to-&-fro ru%es ( electrons across ! air-gap4 ,?is action con/itutes a tra9 ( electrical oscillations4 ,at ! same "t t ^! op]ations are go+ on 9 & betwe5 ! conductors1 ! electrons atta*$ to ! atoms ( ! air or o!r dielectric all ar\nd are be+ viol5tly oscillat$4 ,^! oscillations may n proce$ to su* an ext5t z to deta* electrons f _! atoms1 b !y are suffici5t to create rapidly rev]s$ electric & magnetic =ces4 ,x appe>s t ! v rapid movem5t to & fro ( an electron causes a wave 9 ! !r1 j z ! rapid movem5t ( ! h& ?r\gh wat] causes a wave 9 wat]1 or ! vibration ( ! prong ( a tun+-=k creates a wave 9 ! air4 ,! electron has "s grip on ! !r1 su* t ! sudd5 />t+ or /opp+ ( ! electron makes a di/urbance :i* we may popul>ly describe z a spla% 9 ! !r4 ,h5ce1 if a l>ge numb] ( electrons are sudd5ly />t$ into motion 9 ! same direction1 ! effect on ! !r is some?+ l ca/+ a multitude ( /ones on ! surface ( /ill wat]1 or ! simultane\s action ( a numb] ( small explosions 9 ! air4 ,any?+1 !re=e1 :i*1 s to speak1 lets ! electrons g gradually1 or s(t5s ! fir/ ru%1 is inimical to ! production ( a vigor\s electric wave4 ,on ! o!r h&1 any?+ :i* causes ! fir/ ru% ( electrons f "o conductor to ano!r across ! air-gap to be v sudd5 is advantage\s1 & results 9 a p[]ful wave4 ,exp]i5ce %[s t ! nature ( ! metal surfaces1 :e!r poli%$ or r\gh1 has a great influ5ce on ! wave-mak+ p[] ( ! radiator4 ,if ! sp>k-balls or surfaces are r\gh & n poli%$1 x seems to tone d[n ! viol5ce ( ! fir/ electron ru%1 & ! wave-mak+ p[] ( ! oscillator is n s great z if ! balls are poli%$4 ,at ?is po9t1 h[ev]1 x w be be/ to )hold fur!r discussion on po9ts ( !ory until we h consid]$ ! facts to be br\ght be=e y 9 ! next lecture1 %[+ t ! electric radiation manufactur$ by means ( electric oscillations is only "o v>iety ( a va/ range ( !r waves1 "s =ms ( :i* are recognizable by u z light & radiant heat4 ,,*apt] ,,vi4 ,,waves ,,& ,,ripples ,,9 ,,! ,,!r4 ,hav+ 9 ! la/ *apt] expla9$ ! nature & mode ( production ( electric oscillations1 & %[n t :5 ^! take place 9 an op5 electric circuit or long /raight rod !y give rise to c]ta9 actions at a di/ance1 r5d]$ evid5t by ! *anges tak+ place 9 ! conductivity ( metallic p[d]s1 we h n[ to pres5t ! outl9es ( a pro( t ^! actions are really due to a wave-motion ( "s description set up 9 ! !r1 :i* 9 nature is ess5tially ! same z t :i* con/itutes ! ag5cy we call light4 ,we %all beg9 by /udy+ a few ( ! epo*-mak+ discov]ies we owe to ! celebrat$ ,he9ri* ,h]tz1 ann\nc$ 9 a s]ies ( fam\s rese>*es ) :i* he surpris$ & delight$ ! sci5tific _w 9 ! ye>s #ahhg & #ahhh4 ,^! inve/igations op5$ a new & rem>kable field ( exp]im5tal "w4 ,! precise =m ( app>atus us$ by ,h]tz 9 ^! rese>*es is1 h[ev]1 unsuit$ = lecture demon/ration1 & ,i %all use on ?is occasion "s arrangem5ts ( my own1 :i* are only conv5i5t modifications ( appliances previ\sly employ$ by o!r exp]im5tali/s4 ,! devices "h %[n are1 h[ev]1 v conv5i5t = public demon/rations4 ,?is app>atus consi/s ( two p>ts1 a "p = g5]at+ electric waves1 :i* we %all call ! radiator1 & a "p = detect+ !m1 :i* is call$ ! receiv]4 ,! radiator consi/s ( a z9c box1 ,a 7see ,fig4 #gc71 :i* is provid$ ) holl[ trunnions1 & c be fix$ to a suitable /& & turn$ 9 any direction4 ,! box has an op5 end to x1 & 9 its int]ior !re are two brass rods ab\t #d in*es long1 ea* t]m9at+ 9 brass balls1 ,s1 #a in* 9 diamet]4 ,^! rods are ?ru/ ?r\gh corks fix$ 9 ! end ( two ebonite tubes1 :i* pass ?r\gh ! holl[ trunnions ( ! box4 ,! rods h _! ends atta*$ to v closely w\nd spirals ( gutta-p]*a-cov]$ wire conta9$ 9 ! ebonite tubes4 ,^! spirals are call$ *ok+ coils4 ,:5 ! balls are arrang$ 9 ! int]ior ( ! box 9 _! prop] position1 !y are ab\t in* ap>t1 & ! rods to :i* !y are atta*$ are 9 l9e ) ea* o!r4 ,illu/ration3 ,,fig4 #gc4--;,electric wave radiator 7,a7 & receiv] 7,b74 ,! out] ends ( ! *ok+ coils are connect$ to an induction coil or electrical ma*9e1 say a small ,wim%ur/ ma*9e1 suitable = produc+ electric sp>ks ab\t #b or #c in*es 9 l5g?4 ,if !n sp>ks are tak5 betwe5 ! balls1 we h an arrangem5t :i* is1 9 fact1 a small ,h]tz oscillator or radiator4 ,x has be5 fully expla9$ 9 ! la/ *apt] t ! action ( ! induction coil or electrical ma*9e is fir/ to create a diff]5ce 9 ! electric condition ( ! balls1 su* t "o is positively electrifi$ & ! o!r negatively4 ,! balls & rods & ! surr\nd+ air1 z already expla9$1 !n =m a sort ( ,leyd5 j> or cond5s]1 & 9 virtue ( ! electromotive =ce ! air is electrically /ra9$ ar\nd ! balls4 ,:5 ?is /ra9 rea*es a p>ticul> value1 ! air betwe5 ! balls passes at once into a conductive condition1 & we h a dis*>ge :i* is oscillatory 9 nature produc$ betwe5 ! conductors4 ,we may consid] t ! electrical *>ges on ! two rods ru% backw>ds & =w>ds1 sett+ up on ! rods an oscillatory surface electric curr5t1 & t ?is is accompani$ by a v rapid rev]sal ( ! /ra9 9 ! surr\nd+ non-conductor or dielectric4 ,?is /ate ( affairs results 9 s5d+ out into space an effect call$ an electric wave4 ,illu/ration3 ,,fig4 #gd4--;,electric radiation detector 7,mill]74 ,turn+1 !n1 to ! receiv] ,b 7,fig4 #gc71 we notice t ?is consi/s ( a simil>ly %ap$ metal box1 hav+ 9 x a bo>d to :i* are fix$ two %ort nickel wires4 ,^! are cross$ )\t t\*+ 9 ! int]ior ( a small ebonite box 7see ,fig4 #gd74 ,! wires are j cov]$ inside ! box ) a v small quantity ( f9e nickel fil+s4 ,to ! end ( ! z9c receiv]-box is fix$ a long lead pipe1 9 ! int]ior ( :i* are two insulat$ wires1 c1 d4 ,^! wires are jo9$ to ! extremities ( ! nickel wires 9 ! receiv]-box & !n1 pass+ ?r\gh ! lead pipe1 !y ent] ano!r metal box :i* conta9s a batt]y & electric bell4 ,! p9* ( nickel fil+s 9 ! small ebonite box is n an electric conductor 9 its ord9>y condition1 & h5ce ! electric circuit1 includ+ ! batt]y & bell1 is n complete4 ,if1 h[ev]1 an electric oscillation is set up 9 ! nickel receiv]-wires1 ! mass ( metal p>ticles connect+ !m at once becomes a conductor1 because little metallic granules /ick or coh]e toge!r4 ,! batt]y is ?us able to s5d an electric curr5t ?r\gh ! circuit1 :i* includes ! coh]]1 & ! electric bell is caus$ to r+4 ,x may be m5tion$ t 9 ! actual app>atus employ$ ! arrangem5t is n q s simple4 ,! coh]] w\ld be p]man5tly injur$ if we 7 to attempt to s5d ?r\gh x an electric curr5t /rong en\gh to r+ an electric bell4 ,h5ce we associate ) ! coh]] a contrivance call$ a relay4 ,a s+le voltaic cell1 ,e 7a dry cell7 7see ,fig4 #ge71 is jo9$ up 9 s]ies ) ! coh]] ,c & ?is relay ,r4 ,! latt] is a sort ( swit* or circuit-clos] ( su* k9d t :5 a v feeble curr5t passes ?r\gh x x closes a second circuit ?r\gh :i* a mu* /rong] curr5t c pass4 ,! transition ( ! nickel fil+s f a non-conductive to a conductive condition is1 !re=e1 only ! means by :i* a v small curr5t ( electricity is all[$ to pass ?r\gh ! circuit ( an electro-magnet :i* =ms ! circuit ( ! relay4 ,?is action causes a piece ( iron to be attract$1 & ?is aga9 9 turn closes ano!r circuit1 & s enables ! curr5t f a second batt]y1 ,f1 ( five or six cells to actuate ! electric bell ,g4 ,! arrangem5t ( ! two batt]ies1 ! relay coh]]1 & bell w be und]/ood by /udy+ ! diagram ( connections 9 ,fig4 #ge4 ,! really important condition 9 secur+ success 9 ! p]=mance ( ! exp]im5ts made ) ?is app>atus is t ! long wires :i* connect ! receiv]-box ) ! metal box conta9+ ! bell1 batt]y1 & relay %all be entirely enclos$ 9 a lead pipe )\t jo9t1 :i* is sold]$ at "o end into ! receiv]-box & at ! o!r into ! batt]y-box4 ,ano!r practical po9t is t ^! wires1 :]e !y ent] ! batt]y-box1 mu/ h includ$ 9 _! circuit two little coils ( insulat$ wire ( a good _m turns1 :i* are call$ 8*ok+ coils40 ,a ?ird elem5t ( success is t ! coh]] or s5sitive conductor %all be s5sitive en\gh1 b n too s5sitive4 ,?is condition c only be obta9$ by a process ( trial & failure4 ,be+ provid$ ) ^! two pieces ( app>atus1 we c n[ proce$ to exhibit a s]ies ( exp]im5ts ( great int]e/4 ,illu/ration3 ,,fig4 #ge4 ,9 ! fir/ place1 let ! radiator-box & receiv]-box be plac$ a few feet ap>t ) _! op5 m\?s fac+ ea* o!r1 l two guns arrang$ to fire d[n ea* o!r's ?roats4 ,!n1 if all is 9 ord] :5 we make an electric sp>k betwe5 ! two balls ( ! radiator1 ! electric bell 9 connection ) ! receiv] w beg9 to r+1 %[+ t ! coh]] 9 ! receiv]-box has be5 affect$ & made conductive by ! electric wave s5t out f ! radiator-box4 ,if a sm>t rap is !n giv5 to ! receiv]-box ! cl++ metallic fil+s 9 ! ebonite box w be sep>at$ aga9 &1 ! circuit be+ int]rupt$1 ! bell w /op r++4 ,?is be+ done1 ! radiator-box is !n turn$ a little on "o side by rotat+ x r\nd its holl[ trunnions l a gun until ! op5 m\?s ( ! two boxes no long] face ea* o!r4 ,x w !n be f\nd1 on repeat+ ! =m] exp]im5t1 t ! bell w n r+ :5 a sp>k is made betwe5 ! balls4 ,a little exp]im5t+ w %[ t ! action :i* affects ! coh]] is propagat$ out f ! radiator-box 9 /raight l9es l ! light f a lamp1 & t we are "h deal+ ) some?+ :i* has all ! "* ( radiation4 ,9 ! next place1 let ! receiv]- & radiator-boxes be aga9 arrang$ ) _! op5 m\?s fac+ ea* o!r4 ,we make a sp>k & aga9 secure ! responsive action ( ! bell4 ,we %all n[ proce$ to prove t ?is effect1 :i* is call$ electric radiation1 passes q freely ?r\gh c]ta9 sub/ances1 b is m or less completely /opp$ by o!rs4 ,= in/ance1 if we hold a %eet ( iron1 t9foil1 or ev5 pap] cov]$ ) silv] leaf betwe5 ! op5 m\?s ( ! radiator & receiv]1 we f9d t ! bell ( ! receiv] w n r+ ev5 :5 a rapid s]ies ( oscillatory sp>ks are made 9 ! radiator4 ,^! %eets ( metal1 ?ick or ?91 are q opaque to ! electric radiation proce$+ f ! sp>k-balls4 ,on ! o!r h&1 we f9d a %eet ( pap] or c>d1 a wood5 bo>d1 a %eet ( glass1 a slab ( wax or bitum51 sulphur1 m>ble1 or slate1 are all q p]vi\s or transp>5t1 & :5 held betwe5 ! radiator & receiv] d n h9d] at all p]ceptibly ! action ( ! =m] on ! latt]4 ,we conclude1 !re=e1 t "s bodies are opaque & "s transp>5t to ! electric radiation4 ,b ! classification does n agree ) ! classification z reg>ds opacity or transp>5cy = light4 ,wood1 m>ble1 & pit* are optically opaque1 b electrically transp>5t4 ,! g5]al law1 h[ev]1 :i* decides ! "q ( opacity or transp>5cy = electric radiation1 is z foll[s3 ,all good electrical conductors are opaque to electric radiation1 & all good insulators or non-conductors are transp>5t4 ,h5ce we see at once :y metal %eets are opaque1 & wood1 wax1 or glass transp>5t1 to ! electric radiation f ! sp>k-balls4 ,we may g "o /ep fur!r4 ,if we take "s %eets ( p]=at$ z9c or wire gauze1 or ev5 a l>ge packet ( p9s1 or pap] bag full ( iron fil+s1 we %all f9d t all ^! bodies are practically opaque to ! electric rays4 ,moreov]1 we c %[ t n only is ! above law true = solids1 b x holds good = liquids z well4 ,i h provid$ "h a numb] ( flat glass bottles :i* are fill$ ) v>i\s liquids1 salt wat]1 fre% wat]1 solution ( soda1 p>aff9 oil1 olive oil1 turp5t9e & me?ylat$ spirits4 ,if we te/ an empty glass bottle betwe5 ! radiator & receiv]1 we c assure ourselves t ! bottle itself is transp>5t to ! electric radiation4 ,if1 !n1 we take ! bottles conta9+ ! v>i\s liquids & te/ !m "o by "o betwe5 ! radiator & ! receiv]1 we f9d t ! bottles conta9+ ! p>aff9 oil1 ! olive oil1 & ! turp5t9e are transp>5t to ! electric radiation1 b t ! bottles conta9+ ! salt wat]1 ! fre% wat]1 ! solution ( soda1 & ! me?ylat$ spirits are all opaque4 ,! oils & liquids simil> to !m are all good non-conductors1 :]eas wat] & v>i\s aque\s solutions are fairly good conductors ( electricity1 & h5ce ^! liquids1 al?\gh !y are all ab\t equally transp>5t to light1 behave v diff]5tly to electric radiation4 ,z reg>ds ! electric ray1 a bottle full ( pure wat] is z opaque to ! electric radiation we are "h us+ z x w\ld be to light if x 7 fill$ ) black ink4 ,exp]im5t %[s t e object conta9+ wat]1 or :i* is wet1 is exce$+ly opaque to ! electric radiation we are employ+4 ,?us1 = in/ance1 if ,i take a dry du/] fold$ 9 f\r1 & hold x 9 ! pa? ( ! electric ray1 y see t x is q transp>5t1 & t ! bell atta*$ to ! receiv] r+s z easily z if !re 7 no du/] !re at all4 ,if1 h[ev]1 we dip ! du/] 9 wat]1 & !n hold x betwe5 ! radiator & receiv]1 we f9d t ! wet du/] is p]fectly opaque4 ,! human body consi/s l>gely ( wat] :i* exi/s 9 ! tissues1 & h5ce x is n surpris+ to f9d t ! h& or any "p ( ! body plac$ betwe5 ! radiator & receiv] int]cepts ! electric ray4 ,y see1 if ,i hold my h& 9 front ( ! radiator1 t no?+ is able to escape f x1 :5 sp>ks are made betwe5 ! balls1 :i* c affect ! receiv]4 ,9 ! same way x c be %[n by exp]im5t t ! human head is p]fectly opaque--9 fact1 mu* m opaque ?an an equally ?ick block ( wood2 & ?is opacity to ! electric ray is due 9 a v]itable s5se to ! wat] 9 ! bra94 ,all dry animal tissues1 su* z lea!r1 bone1 gelat9e1 & fle%1 if dry1 are v transp>5t to electric radiation ( ! k9d we are n[ us+1 b if ^! objects are made ?or\ghly wet1 !n !y become int5sely opaque4 ,illu/ration3 ,,fig4 #gf4--,! reflection ( an electric ray4 ,we c1 !n1 proce$ to %[ t ?is electric radiation c be reflect$1 j l light or s\nd1 by metal or o!r conduct+ surfaces1 & t ! law ( reflection ( ! electric ray is ! same z ! law ( reflection = rays ( light or s\nd4 ,if we place ! radiator ,a ) its m\? upw>ds1 /ill pres]v+ ! receiv] ,b 9 a horizontal position1 x is possible to adju/ ! two v ne> to "o ano!r1 b yet s t ! radiation f ! radiator does n affect ! receiv]4 ,if ,i n[ hold a metal plate1 ,p1 at an angle ( #de above ! m\? ( ! radiator1 y w notice t ! bell at once r+s1 ?us %[+ t ! electric radiation has be5 reflect$ into ! receiv]-box 7see ,fig4 #gf74 ,also we f9d t a v small deviation f ! angle ( #de is suffici5t to prev5t ! effect4 ,c>eful exp]im5ts 9 ! laboratory %[ t ! electric ray is reflect$ accord+ to ! optical law1 viz4 t ! angle ( reflection is equal to ! angle ( incid5ce4 ,we f9d t any good conduct+ surface w1 9 ?is mann]1 affect ! electric radiation4 ,?us ,i c reflect x f a %eet ( t9foil or ev5 f my h&1 & ! fact t ,i c1 s to speak1 take hold ( ?is electric radiation1 & deflect x 9 diff]5t directions by ! palm ( my h&1 produces 9 ! m9d a v /rong conviction t we are deal+ ) some?+ ( a v real nature 9 exp]im5t+ ) ?is electric radiation4 ,x w be 9 y\r remembrance t1 9 ! *apt] 9 :i* we 7 deal+ ) waves 9 ! air1 ,i %[$ y a v int]e/+ exp]im5t illu/rat+ ! refraction ( rays ( s\nd by means ( a c>bonic acid prism1 & ,i h n[ to br+ be=e y an exactly analog\s exp]im5t p]=m$ ) electric radiation4 ,"h1 = in/ance1 is a prism made ( p>aff9 wax1 a sub/ance :i* y h already se5 is transp>5t to ! electric ray4 ,if we arrange ! radiator- & receiv]-boxes at an angle to "o ano!r1 x is possible s to adju/ !m t ! electric radiation project$ f ! radiator-box ,a j escapes ! receiv]-box ,b1 & does n !re=e cause ! bell to r+ 7see ,fig4 #gg74 ,:5 ?is adju/m5t has be5 made we introduce ! p>aff9 prism ,p into ! pa? ( ! electric ray1 & if ! adju/m5ts are prop]ly made1 we f9d t ! electric ray is b5t r\nd or refract$1 & t x !n ent]s ! receiv]-box & causes ! bell to r+4 ,?is exp]im5t 0 fir/ p]=m$ by ,h]tz ) a v l>ge pit* prism1 b 8 app>atus 0 too cumb]some = lecture purposes1 & ! small] & m compact arrangem5t y see be=e y is !re=e pref]able = pres5t purposes4 ,illu/ration3 ,,fig4 #gg4--,! refraction ( an electric ray4 ,i h x 9 my p[] to %[ y a /ill m rem>kable exp]im5t 9 electric refraction4 ,x is f\nd t dry ice is v transp>5t to ^! electric rays1 b if ! ice is wett$ on ! surface1 !n1 z y h already le>nt1 ! film ( moi/ure is opaque4 ,we h _h con/ruct$ = ! purposes ( ?is lecture a prism ( ice by freez+ wat] 9 a prop]ly %ap$ z9c box4 ,?is prism is n[ be+ arrang$ betwe5 ! radiator & ! receiv]1 & its surfaces mu/ next be dri$ c>efully ) du/]s & :ite blott+ pap] to remove e trace ( moi/ure4 ,:5 ?is is done we f9d we c repeat ) ! ice prism ! same exp]im5t p]=m$ j n[ ) ! p>aff9 prism1 & we c refract ! electric ray4 ,if y w recall to y\r memory ! /atem5ts :i* 7 made 9 connection ) ! refraction ( rays ( s\nd & waves ( wat]1 y w rememb] t x 0 po9t$ out t ! refraction ( a ray ( s\nd & ! b5d+ ( a tra9 ( wat] waves 0 due to ! passage ( ! waves 9 ! air or 9 ! wat] f a region :]e !y 7 mov+ quickly to a region 9 :i* !y 7 compell$ to move m sl[ly2 & x 0 fur!rmore %[n t ?is b5d+ mu/ take place :5ev] a pla9 wave ( any k9d passes 9 an oblique direction f "o region to ano!r region :]e x und]goes an alt]ation 9 velocity4 ,9 o!r words1 x 0 %[n t ! b5d+ or refraction ( ! direction ( motion ( a wave1 :e!r 9 air or wat]1 is a pro( t !re is a diff]5ce 9 its velocity 9 ! two places b\nd$ by ! surface at :i* ! refraction takes place4 ,if ?is b5d+ takes place 9 su* fa%ion t ! ray is b5t t[>ds ! p]p5dicul> l9e drawn to ! b\nd+ surface1 :i* is ! same ?+ z say+ if ! l9e ( ! wave is b5t s z to make a less angle ) ! b\nd+ surface aft] x has pass$ f "o region to ! o!r1 !n x %[s t ! wave-motion travels m sl[ly aft] x has pass$ ! b\nd+ surface ?an be=e4 ,if we n[ return to ! consid]ation ( ! electric exp]im5t ) ! prism ( p>aff9 or ice1 we %all f9d t ?is1 prop]ly int]pret$1 gives u a pro( t ! electric radiation travels m sl[ly 9 p>aff9 wax or ice ?an x does 9 air1 & ! ratio betwe5 its velocity 9 air or 9 empty space & its velocity 9 any non-conductor is call$ ! electric index ( refraction = t non-conductor4 ,?is index c be det]m9$ by mak+ two measurem5ts4 ,fir/1 t ( ! refract+ angle ( ! prism2 & secondly1 t ( ! deviation ( ! ray4#bf ,i h made ^! two exp]im5ts = ! prisms ( p>aff9 & ice 9 my laboratory1 & ,i f9d ! electric refractive index ( p>aff9 to be #afd1 & ! electric refractive index ( ice to be #ahc4 ,9 connection ) ! refraction ( rays ( s\nd1 x 0 po9t$ out t a curv$ surface has ! p[] to div]ge or conv]ge rays ( s\nd1 & y w rememb] t we employ$ a s\nd-l5s = conv]g+ ! rays ( s\nd div]g+ f a :i/le1 j z an ord9>y burn+-glass1 or d\ble convex l5s1 c be employ$ to br+ ! rays ( sunlight to a focus4 ,we %all n[ attempt a simil> exp]im5t ) ! electric ray4 ,a block ( p>aff9 is fa%ion$ into ! %ape ( a semi-cyl9d]1 flat on "o side & convex on ! o!r1 & ?is plano-convex p>aff9 l5s has a convex surface hav+ a radius ( #f in*es4 ,if ,i place ! radiator ,a & receiv] ,b ab\t #d feet ap>t1 !n by mak+ a few little adju/m5ts x is possible to s arrange matt]s t ! radiation :i* proce$s f ! radiator is n p[]ful en\gh at a di/ance ( #d feet to s5sibly affect ! coh]] & make ! bell r+ 7see ,fig4 #gh74 ,if1 h[ev]1 ,i adju/ ! p>aff9 l5s ,l halfway betwe51 ,i %all conv]ge ?is electric radiation to a focus j ab\t ! place :]e ! coh]] is situat$1 & ! consequ5ce is t on mak+ sp>ks betwe5 ! balls ( ! radiator1 we f9d t ! bell atta*$ to ! receiv] at once r+s4 ,illu/ration3 ,,fig4 #gh4--;,conv]g+ a beam ( electric radiation4 ,we h1 !re=e1 "h br\ght to a focus1 by means ( a p>aff9 l5s1 ! electrical radiation j 9 ! same mann] t an ord9>y burn+-glass focuses ! rays ( light & heat ( ! sun1 & enables u to light ) x "s pap] or a cig>4 ,we h1 !re=e1 indubitable pro( 9 all ^! exp]im5ts t we h some?+ proce$+ f ! radiator :i* is capable ( be+ reflect$ or refract$ j l ! rays ( s\nd or ripples on ! surface ( wat]2 &1 moreov]1 we f9d t ?is electric radiation passes ?r\gh "s sub/ances b n ?r\gh o!rs4 ,!re is1 !re=e1 a /rong presumption t we are "h deal+ ) some?+ :i* is simil> 9 nature to light1 al?\gh x _c affect ! eye4 ,9 ord] t we may complete ! pro( we mu/ %[ t ?is radiation is susceptible ( int]f]5ce4 ,?is pro( may be p>tly obta9$ f ! consid]ation ( ! foll[+ facts connect$ ) ! opacity or transp>5cy ( wire grat+ to ! electric radiation3-- ,i h "h a wood5 frame across :i* are /ra9$ "s wires ab\t a qu>t] ( an in* ap>t 7see ,fig4 #gi74 ,if we hold ?is frame or grid 9 front ( ! radiator s t ! direction ( ^! wires is at "r angles to ! direction ( ! radiator rods :i* c>ry ! balls1 we f9d t ! grid is q transp>5t to ! electric radiation1 b if we turn ! grid r\nd s t ! wires ( ! grid are p>allel to ! radiator rods1 we f9d at once t ! grid becomes p]fectly opaque4 ,! same exp]im5t c be prettily %[n by means ( a pap] ( p9s4 ,"h are "s l>ge c>pet p9s arrang$ 9 r[s 9 pap]1 & if ,i hold ?is pap] ( p9s 9 betwe5 ! radiator & receiv] ) ! p9s p>allel to ! radiator1 x is p]fectly opaque to ! electric ray1 b if ,i turn x s t ! p9s are at "r angles1 x is q transp>5t4 ,! same exp]im5t succe$s ) a pap] ( ord9>y p9s1 b n s well ) a pap] ( midget p9s4 ,illu/ration3 ,,fig4 #gi4 ,! explanation ( ?is action ( a grid is z foll[s3 ,y h already se5 t an alt]nat+ curr5t 9 "o electric circuit c produce ano!r alt]nat+ curr5t 9 a second>y circuit plac$ p>allel ) ! fir/4 ,x is n difficult to %[1 ei!r exp]im5tally or f !ory1 t :5 ! prim>y curr5t is an electrical oscillation--t is1 a v rapid alt]nat+ curr5t--! curr5t 9 ! second>y circuit is also an electrical oscillation ( ! same frequ5cy or rapidity1 b t ! curr5ts 9 ! two circuits1 prim>y & second>y1 are always mov+ 9 opposite directions at ! same mom5t4 ,accord+ly1 if we hold a grid 9 front ( ! radiator1 ! wires ( ! grid h :at are call$ induc$ oscillations set up 9 !m1 & ^! induc$ oscillations !mselves create electric radiation4 ,accord+ly1 x is cle> t if a grid ( ?is k9d is held ne> to a radiator ) ! wires ( ! grid p>allel to ! radiator rods1 we h two sets ( radiations produc$ :i*1 at any po9t on ! side ( ! grid fur!/ f ! radiator rods1 mu/ neutralize "o ano!r1 & !re=e de/roy ea* o!r's effect4 ,h5ce x is possible to cause ! electric radiations proce$+ f two electric circuits p>allel ) ea* o!r to de/roy "o ano!r at a di/ant po9t2 & we may1 !re=e1 make use ( ! same argum5ts z 9 ! case ( a simil> exp]im5t ) light to prove t ?is electric radiation mu/ be a wave-motion4 ,x w\ld occupy too mu* ( our "t1 & x w\ld involve ! discussion ( matt]s :i* are r beyond ! scope ( elem5t>y lectures1 if we 7 to ent] into a complete analysis ( all ! argum5ts prov+ t ?is electric radiation1 :i* proce$s f an electric oscillator1 is really a wave-motion4 ,i may1 h[ev]1 m5tion "o fact1 :i* has be5 ! outcome ( an enorm\s am\nt ( exp]im5tal rese>*1 & t is1 t ! velocity ( ?is electric radiation ?r\gh space is id5tical ) t ( light4 ,x has already be5 m5tion$ t a ray ( light flits ?r\gh space at ! rate ( #a1jjj1jjj1jjj feet1 or ne>ly #ahf1ejj miles a second4 ,by suitable & v +5i\s arrangem5ts1 physici/s h be5 able to measure ! velocity ( electric radiation1 & h f\nd 9 e case t its velocity ( propagation is precisely ! same z a ray ( light4 ,let u1 !n1 summ>ize briefly :at we h le>nt4 ,we f9d t :5 we set up an electrical oscillation 9 an op5 circuit consi/+ ( two metallic rods plac$ 9 "o /raight l9e1 we h proce$+ f ?is circuit an electrical radiation :i* is capable ( be+ propagat$ ?r\gh space1 :i* moves 9 /raight l9es1 c be reflect$ & refract$1 c exhibit ! ph5om5a ( int]f]5ce1 & moreov] :i* is propagat$ ) exactly ! same velocity z light4 ,is x possible to resi/ ! conclusion t ?is effect :i* we call electric radiation1 & ! simil>ly behav+ physical ag5cy :i* we call light1 mu/ bo? be affections ( ! same m$ium8 ,x is h>dly necess>y to occupy "t ) exp]im5ts 9 %[+ t a ray ( light c be reflect$ & refract$ by mirrors & prisms1 & conv]g$ or div]g$ by transp>5t l5ses4 ,^! are simple optical facts1 & if y are n famili> ) !m x w be easy = y to make _! acqua9tance by /udy+ any simple book ^u optics2 b ,i %\ld l to draw y\r att5tion to ! fact t1 9 addition to rays ( light & electric radiation1 we are acqua9t$ ) ano!r k9d ( radiation1 :i* is also susceptible ( be+ refract$1 & t is commonly call$ d>k heat4 ,suppos+ t we take an iron ball & make x r$ hot 9 a furnace1 !n1 9 a p]fectly d>k room1 we see ! ball gl[+ brilliantly1 & we are consci\s by our s5sations t x is ?r[+ (f heat4 ,let u imag9e t ! ball is all[$ to cool d[n to a temp]ature ( ab\t #ejj ,c42 x w !n j cease to be visible 9 a p]fectly d>k room1 b yet if we hold our h& or a !rmomet] ne> to x1 we c detect its pres5ce by ! d>k radiant heat x s5ds out4 ,exp]im5ts %[ t ev5 :5 ! ball is brilliantly inc&esc5t1 ne>ly #ih or #ii p] c5t4 ( all ! radiation x s5ds out is d>k heat1 & only #a or #b p] c5t4 is radiation :i* c affect ! eye z light4 ,x is q easy to %[ t ?is d>k heat c be reflect$ j l light4 ,if ,i fix ?is r$-hot ball 9 ! focus ( a metallic mirror & lift up ball & mirror ne>ly to ! ceil+ & !n place ^u ! table ano!r convex1 poli%$1 metallic mirror1 ! top mirror w ga!r up & project d[nw>ds ! radiation f ! iron ball & ! bottom mirror w conv]ge t to a focus4 ,if !n we fix a r$-hot ball 9 ! focus ( ! upp] mirror & all[ x to cool until x is j n visible 9 ! d>k1 we %all f9d t we c /ill ignite a piece ( phosphorus or "s o!r inflammable sub/ance by hold+ x 9 ! focus ( ! bottom mirror1 ?us %[+ t ! d>k radiation f ! iron ball is susceptible ( reflection j z are rays ( light or electric rays4 ,9 fact1 if "t p]mitt$1 x w\ld be possible to %[ a :ole s]ies ( exp]im5ts ) d>k radiant heat :i* w\ld prove t ?is radiation possesses simil> prop]ties ( lum9\s or electric radiation 9 its behavi\r z reg>ds reflection1 refraction1 & int]f]5ce4 ,a va/ body ( pro( has be5 accumulat$ t all ^! =ms ( radiation are m]ely v>ieties ( "o & ! same ?+1 & t ! only ?+ 9 :i* !y really diff] f "o ano!r is 9 :at is call$ _! wave-l5g?4 ,at ?is po9t ,i w rem9d y once m ( t g5]al law :i* connects toge!r ! velocity ( propagation ( a wave-motion1 ! wave-l5g? & ! frequ5cy4 ,x is express$ 9 ! =mula3 wave-velocity 7,v7 equals frequ5cy 7n7 multipli$ by wave-l5g? 771 or 9 symbolical language-- ,v n ,accord+ly1 if ! velocity ( propagation c be det]m9$1 & if ! frequ5cy or p]iodicity ( ! wave-motion is kn[n1 !n ! wave-l5g? c be f\nd f ! above simple rule2 or conv]sely1 if ! velocity ( propagation & ! wave-l5g? are kn[n1 ! frequ5cy is det]m9$4 ,! wave-l5g? ( v>i\s k9ds ( mono*romatic 7"o-col\r7 light c be easily det]m9$ by means ( ,"y's exp]im5t on int]f]5ce4 ,if ! di/ance betwe5 ! two small holes f :i* ! two /reams ( light em]ge is measur$1 & if ! di/ance f !m to ! scre5 & also ! di/ance ( ! fir/ d>k b& f ! c5tral l9e is det]m9$1 x is !n v easy to calculate ! diff]5ce 9 ! di/ances f ! two holes to ! d>k b&4 ,?is diff]5ce1 h[ev]1 mu/1 z already expla9$1 be equal to "o-half wave-l5g? ( ! light employ$4 ,exp]im5ts made 9 v>i\s ways h %[n t ! wave-l5g? ( yell[ light is n f> f ! fifty ?\s&? "p ( an in*4 ,h5ce z ! velocity ( visible light is #ahf1ejj miles p] second1 or #ajjj million feet1 or #ab1jjj million in*es p] second1 :il/ ! wave-l5g? is some?+ l in*1 x is cle> t ! frequ5cy1 or numb] ( light waves :i* ent] ! eye p] second1 mu/ be reckon$ 9 millions ( millions4 ,9 fact1 x ranges f #djj to #gjj billions4 ,!re is a c]ta9 diff]5ce ( op9ion z to :at is meant by a billion4 ,we "h use ! ^w to signify a million times a million1 a million be+ a ?\s& times a ?\s&4 ,! foll[+ table %[s u ! frequ5cy or numb] ( waves p] second1 correspond+ to light rays produc+ col\r-s5sations ( v>i\s k9ds3-- ,,vibration ,,rates ,,( ,,!r ,,waves ,,affect+ ,,! ,,eye ,,z ,,light4 ,col\r s5sation4 ,vibrations p] second4 ,deep r$ #djj billions4 ,r$-orange #dcg 0 ,yell[-orange #deg 0 ,yell[ #eji 0 ,gre5 #egj 0 ,blue-gre5 #fag 0 ,blue-violet #fif 0 ,violet #gej 0 ,inve/igation has %[n t ! quality 9 a light ray :i* causes x to affect our eye ) a p>ticul> col\r-s5sation is its wave-l5g?1 :]eas ! quality :i* affects our eyes z brightness or brilliancy is due to ! amplitude ( ! waves4 ,x is some:at difficult to realize at fir/ t1 outside ( ourselves1 !re is no su* ?+ z col\r4 ,col\r is a s5sation produc$ :5 !r waves ( a c]ta9 wave-l5g? ent] ! eye & fall on ! ret9a4 ,if ! ret9a is /imulat$ #djj billions ( times p] second1 we exp]i5ce a s5sation ( r$ness1 & if x is /imulat$ #gjj billion times p] second1 we exp]i5ce a s5sation ( blu5ess2 b ext]nally1 !re is no su* ?+ z r$ & blue1 !re is only a diff]5ce 9 wave-frequ5cy4 ,x is a/oni%+ :5 we le>n = ! fir/ "t t #djj millions ( millions ( times p] second some?+ 9 ! back ( our eyes is mov$ or /imulat$ :5ev] we look at a lady's r$ dress1 a surgeon's r$ lamp1 or ! r$ petal ( a g]anium fl[]4 ,y w notice1 on ref]r+ to ! above table ( frequ5cies1 t ! range ( s5sibility ( ! human eye is v mu* small] ?an t ( ! e>4 ,our eyes are wond]ful in/rum5ts = detect+ wave-motion 9 ! !r1 & our e>s are appliances = detect+ wave-motion 9 ! air4 ,! e>1 h[ev]1 is1 z expla9$ 9 a previ\s *apt]1 s5sitive to air-vibration =m+ musical tones :i* lie betwe5 #cj & #cj1jjj p] second1 & ^! numb]s are 9 ! ratio ( #ajjj to #a1 & cov] a range ( ab\t t5 octaves4 ,! eye1 h[ev]1 is only s5sitive to !r-vibrations :i* lie 9 frequ5cy betwe5 #djj & #gjj billions p] second1 & ^! numb]s are 9 ! ratio ( ne>ly #b to #a1 or comprise only "o octave4 ,! "q1 ( c\rse1 imm$iately arises--,:at are ! prop]ties ( !r waves ! frequ5cy ( :i* lies outside ! above limits8 ,sci5tific inve/igation has made u acqua9t$ ) a va/ range or gamut ( !r-vibrations1 & we are able to summ>ize our pres5t k z foll[s3-- ,! physical effect we call light1 & t :i* we h up to ! pres5t mom5t m]ely call$ electric radiation1 are really id5tical 9 nature1 & bo? consi/ 9 waves propagat$ ?r\gh ! space-fill+ !r1 ! only diff]5ce betwe5 !m is 9 wave-l5g? & wave-amplitude4 ,9 betwe5 ^! two classes ( radiation comes a ?ird1 :i* is call$ ! d>k-heat radiation1 & beyond ! limits ( visible radiation we are acqua9t$ ) ano!r gr\p ( !r waves :i* _c affect ! eye z light1 b :i* f _! p[] to affect a photographic plate1 is call$ act9ic radiation4 ,h5ce1 briefly speak+1 f\r great gr\ps ( !r waves are kn[n to u1 call$ respectively-- #a4 ,act9ic1 or photographic rays4 #b4 ,lum9\s1 or light rays4 #c4 ,ultra-r$1 or d>k-heat rays4 #d4 ,electric1 or ,h]tz rays4 ,conv9c+ pro( has be5 af=d$ t ^! v>i\s rays are ess5tially ! same 9 nature1 & t !y consi/ 9 p]iodic di/urbances or waves propagat$ ?r\gh ! !r 9 e case ) ! velocity ( #ahf1ejj miles1 or #ajjj million feet1 or #cj1jjj million c5timetres p] second4 ,we may1 !re=e1 say t ^! classes ( !r waves diff] f ea* o!r only 9 ! same s5se 9 :i* a bass note 9 music diff]s f a treble "o2 t is1 ! diff]5ce is a diff]5ce 9 frequ5cy4 ,j1 !re=e1 z we h a gamut1 or scale ( musical tones1 or air-vibrations ( increas+ frequ5cy1 s we may arrange a gamut or scale ( !r waves progressively plac$ accord+ to _! vibration-rates4 ,our pres5t k conc]n+ !r waves c be/ be exhibit$ by arrang+ 9 a *>t a s]ies ( numb]s %[+ ! wave-l5g?s ( ! waves ) :i* we are s f> acqua9t$4 ,z a limit ( l5g? we %all take ! "o-?\s&? "p ( a millimetre4 ,mo/ p]sons "k t a millimetre is a ?\s&? "p ( a metre1 & is a %ort l5g? ne>ly equal to "o tw5ty-fif? ( an in*4 ,! ?\s&? "p ( a millimetre is call$ a micron1 & is d5ot$ by ! symbol #a4 ,?is la/ is !re=e an exce$+ly %ort l5g?1 ne>ly equal to "o tw5ty-five ?\s&? "p ( an in*4 ,foll[+1 also1 ! musical nom5clature1 we %all speak ( all ^? waves includ$ betwe5 two wave-l5g?s1 "o ( :i* is d\ble or half ! o!r1 z an octave4 ,?us all ! v>i\s waves ^: wave-l5g?s lie betwe5 #a & #b 9 l5g? are said to be an octave ( radiation4 ,z a prelim9>y to fur!r discussion let u consid]1 9 ! fir/ place1 ! simple facts ab\t ! radiation :i* affects our eyes z light4 ,! light :i* comes to u f ! sun is n a simple ?+4 ,x consi/s ( !r waves ( _m diff]5t wave-l5g?s m+l$ toge!r4 ,sir ,isaac ,newton fir/ reveal$ to u ! comp\nd nature ( :ite light by 8 celebrat$ exp]im5t ) a glass prism1 & 8 optical discov]ies 7 ! />t+-po9t = our in=mation on ?is subject4 ,if a beam ( sunlight is all[$ to fall on a glass prism1 ! rays ( light ( diff]5t wave-l5g?s :i* compose x are ea* b5t or refract$ to a diff]5t degree4 ,9 free space !r waves ( v>i\s wave-l5g?s all travel1 z f> z we "k1 at ! same rate4 ,?is equality 9 spe$ is1 h[ev]1 di/urb$ ! mom5t ! waves ent] a transp>5t mat]ial sub/ance su* z glass4 ,! velocity ( propagation is !n r$uc$ 9 all cases1 b x is g5]ally m r$uc$ = ! %ort] waves ?an = ! long] ones2 & z a consequ5ce ! rays ( %ort]-wave l5g?s are m b5t or refract$ ?an ! rays ( long] wave-l5g?4 ,we h1 !re=e1 a disp]sion ( ! compon5t rays1 or a sort+ out or analysis ( ! mixture ( rays ( v>i\s wave-l5g?s1 & if we receive ! light on a scre5 aft] pass+ ?r\gh ! prism we h a b& ( col\r$ light call$ a spectrum1 :i* consi/s ( a s]ies ( pat*es ( light ea* ( a diff]5t wave-l5g?4 ,! compon5t rays ( ! orig9al beam ( light are spread out fan-fa%ion by ! prism4 ,we may note1 9 pass+1 t x is n e transp>5t body :5 fa%ion$ into a prism :i* ?us analyzes ! light into a fan-%ap$ beam ) rays ( v>i\s wave-l5g?s arrang$ 9 ! ord] ( _! wave-l5g?s4 ,! sub/ances :i* behave z does glass or wat] :5 made into prisms are said to exhibit normal disp]sive p[]4 ,!re are1 h[ev]1 "s bodies1 su* z iod9e or an alcoholic solution ( fus*9e1 :i* exhibit anomal\s disp]sion & refract "s long] waves ( light m ?an "s %ort] ones4 ,! arrangem5ts = =m+ a normal spectrum are z foll[s3 ,we pass a beam ( light f ! electric lamp ?r\gh a l5s1 & place 9 front ( ?is l5s a metal plate ) a n>r[ v]tical slit-%ap$ op5+ 9 x4 ,at a prop] di/ance 9 front ( ! slit we place ano!r l5s1 & project ^u ! scre5 a %>p image ( ! slit 9 ! %ape ( a b> ( :ite light4 ,plac+ a holl[ glass prism fill$ ) bisulphide ( c>bon 9 front ( ! la/ l5s1 we f9d t ! v>i\s rays 9 ! :ite light are disp]s$1 & we produce on ! scre5 a b& ( ra9b[-col\r$ light1 call$ ! spectrum4 ,?is spectrum is 9 reality a s]ies ( diff]5tly col\r$ images ( ! slit plac$ side by side4 ,by mak+ use ( ! pr9ciple ( int]f]5ce z disclos$ by ,"y1 x is possible to make a measurem5t ( ! wave-l5g? ( ! rays ( light :i* produce ! s5sation ( v>i\s col\rs :5 !y fall ^u ! eye4 ,?us ! wave-l5g? ( ^? !r waves :i* produce ! s5sation ( deep r$ is #jge1 & t ( ! waves produc+ ! s5sation ( violet :5 !y fall ^u ! ret9a ( ! eye is #jdc4 ,! :ole ( ! visible spectrum is !re=e includ$ )9 a s+le octave ( !r radiation4 ,)9 ^! limits any *ange 9 ! wave-l5g?s makes itself felt 9 our eyes z a *ange ( col\r4 ,x is commonly said t !re are sev5 col\rs 9 ! spectrum--r$1 orange1 yell[1 gre51 blue1 indigo1 & violet4 ,z a matt] ( fact1 a highly tra9$ eye c discov] ab\t a ?\s& diff]5t t9ts 9 ! spectrum ( :ite light4 ,"t w n all[ u to ent] into any discussion ( :at is call$ col\r-vision & ! !ory ( s5sations ( col\r4 ,! fact ,i wi% to impress ^u y "h is t1 outside ( ourselves1 !re is no su* ?+ z col\r4 ,! rays ( light :i* produce ^! s5sations ( col\r :5 !y ent] ! eye diff] f "o ano!r only 9 wave-l5g? & wave-amplitude4 ,h5ce !re is a complete analogy betwe5 light ( diff]5t col\rs & s\nds ( diff]5t pit*es or tone4 ,r$ light diff]s f blue light only z a bass note 9 music diff]s f a treble note4 ,h5ce y mu/ di/+ui% v c>efully betwe5 a ray ( light 9 itself1 & ! s5sation x produces :5 x falls ^u ! ret9a ( ! eye4 ,our eyes are gift$ ) a m>vell\s p[] ( detect+ slight diff]5ces betwe5 ! wave-l5g? & ! amplitude ( ! rays :i* may /imulate two adjac5t portions ( ! ret9a ( our eyes4 ,t range ( s5sibility is1 h[ev]1 v limit$4 ,suppos+ we all[ a ray hav+ a wave-l5g? great] ?an #jge or less ?an #jdc to ent] ! human eye4 ,x produces no s5sation ( light at all4 ,accord+ly1 if we =m a spectrum ) sunlight1 we f9d a tol]ably %>p limit to ! visible spectrum4 ,suppos+1 h[ev]1 we all[ ! spectrum to fall ^u a s5sitive photographic plate1 we f9d t ! plate w be *emically act$ ^u f> beyond ! limits ( ! visible violet end ( ! spectrum4 ,h5ce we le>n t beyond ! violet !re is radiation ( a k9d :i* is invisible to ! eye1 yet c affect a photographic plate4 ,?is is call$ ! ultra-violet1 or act9ic radiation4 ,s*umann1 9 #ahic1 measur$ waves 9 act9ic radiation ( a wave-l5g? z %ort z #ja1 or "o two hundr$ & fifty ?\s&? "p ( an in*1 & h5ce we may say t we are acqua9t$ ) at lea/ two octaves ( invisible ultra-violet or act9ic radiation1 or !r waves h wave-l5g?s ly+ betwe5 ! limits #ja & #jd4 ,9 a simil> mann] v delicate heat-detect+ in/rum5ts or !rmomet]s call$ bolomet]s1 or !rmopiles1 %[ u t beyond ! visible-r$ end ( ! normal spectrum !re is radiation call$ ! ultra-r$ radiation1 or d>k-heat1 :i* _c affect ! eye4 ,! wave-l5g? ( d>k-heat radiation has be5 measur$ up to a limit ( #fg by ,pr(essor ,rub5s & ,pr(essor ,ni*ols 9 #ahig & #ahih4 ,accord+ly1 we c ass]t t beyond ! r$ end ( ! spectrum we are acqua9t$ ) six octaves or m ( ultra-r$ radiation1 viz4 t ly+ 9 wave-l5g? betwe5 #jge & #fg4 ,we may repres5t ! above facts 9 ano!r way z foll[s3 ,9 mo/ pianos ! keybo>d ext5ds ov] a range ( sev5 or eight octaves4 ,imag9e a piano hav+ a keybo>d ) n9e octaves1 & t ea* key 0 labell$ to correspond ) a light wave ( a p>ticul> l5g?4 ,at ! extreme treble end let ! fir/ key be labell$ #ja1 & at ! extreme base end let ! la/ key be labell$ #eab4 ,!n ! v>i\s octaves w be compris$ betwe5 ! keys m>k$ #ja1 #jb1 #jd1 #jh1 #af1 #cb1 #fd1 #abh1 #bef1 & #eab 7see ,fig4 #gg74 ,suppose t ea* key :5 /ruck caus$ "s k9d ( electric radiator to emit an !r wave ^: wave-l5g? reckon$ 9 microns or ?\s&?s ( a millimetre1 is indicat$ by ! numb] on ! key4 ,( all ?is great gamut ( !r waves only ! notes ( "o octave1 viz4 ! ?ird f ! treble end1 ! wave-l5g?s ( :i* lie betwe5 #jd & #jh1 affect ! ret9a ( ! human eye z light4 ,^? waves 9 ! two octaves high] up1 t is1 ( wave-l5g? less ?an #jd1 are able p[]fully to affect a photographic plate1 & s1 inde$1 d "s ( ! waves 9 ! visible octave4 ,we may1 9 fact1 say t all ! !r waves ) :i* we are acqua9t$1 ! wave-l5g? ( :i* is less ?an ab\t #je1 are able to make an impression ^u a photographic plate4 ,^! rays1 :atev] _! wave-l5g?s1 are call$ ! act9ic rays4 ,on ! o!r h&1 all ! !r waves ) wave-l5g? great] ?an ab\t #jh1 & = six octaves fur!r d[n1 c only be recogniz$ by _! ability to heat a delicate !rmopile or o!r heat-measur+ in/rum5t4 ,!y _c affect ! eye1 & !y h little or no effect 9 decompos+ silv] salts & impress+ a s5sitive photographic surface4 ,illu/ration3 ,,gamut ,,( ,,!r ,,waves4 ,wave-l5g?s 9 microns4 ( a millimetre4 #ja ,%orte/ ultra-violet wave-l5g? measur$ by ,s*umann1 #ahic4 #jb ,two octaves ( ultra-violet waves4 #jd 4444444444444 #jdc violet light ,v ,i ,b ,g ,y ,o ,r "o octave ( light waves4 4444444444444 #jge r$ light #jh #af #cb #fd #abh ,sev5 octaves ( d>k-heat waves4 #bef #eab 4444444444444 ,longe/ d>k-heat wave-l5g? #fg1 measur$ #ajbd by ,ni*ols 9 #ahih4 #bjdh #djif #haib ,five octaves ( unkn[n radiation4 #afchd #cbgfh ,%orte/ ,h]tz wave made by ,lampa #d mm4 7#ahig74 4444444444444 #feecf #ac mm4 #bf #eb #ajd #bjh ,h]tz radiation1 #ab octaves ( mo/ frequ5tly #daf us$ ,h]tz waves4 #hcb #affd #ccbh #ffef #accab 4444444444444 ,long] waves /ill up to #ajjj feet or m 9 wave-l5g? are us$ 9 wireless telegraphy4 ,,fig4 #hj4 ,x %\ld be not$1 h[ev]1 t :il/ !re are m or less def9ite limits to ! wave-l5g?s ( ! eye-affect+ radiation1 & probably also to ! act9ic1 or photographic radiation 7radiation ( "s wave-l5g?s be+ bo? visible & act9ic71 rays ( e wave-l5g? are 9 "s degree !rmal1 or heat-produc+4 ,! t]m d>k-heat radiation is1 h[ev]1 g5]ally re/rict$ to radiation ( t wave-l5g? :i* is non-visible & non-act9ic4 ,?is mode ( pres5t+ ! facts w call y\r att5tion aga9 to ! n>r[ limits ( s5sibility ( ! human eye z comp>$ ) ^? ( ! e>4 ,! above-m5tion$ range ( wave-l5g?s does n1 h[ev]1 exhau/ our p[]s ( !r-wave production4 ,if we skip ov] six octaves ly+ bel[ ! limits ( ! longe/ d>k-heat wave ) :i* we are acqua9t$1 we %\ld arrive at a wave ^: wave-l5g? is ab\t #djjj1 or #d millimetres4 ,at ?is po9t we enc\nt] ! %orte/ !r waves :i* h yet be5 made by means ( electrical oscillations 9 ! fa%ion fir/ discov]$ by ,h]tz4 ,x is n possible to def9e exactly ! wave-l5g? limits ( radiation z yet made by means ( electrical oscillations4 ,lampa has exp]im5t$ ) !r waves made by ! ,h]tz me?od1 ! wave-l5g? ( :i* 0 n m ?an #d millimetres4 ,pr(essors ,lodge1 ,rhigi1 ,bose1 ,tr\ton1 ! au?or1 & _m o!rs1 h c>ri$ out quasi-optical exp]im5ts ) electrically made !r waves1 ! wave-l5g? ( :i* rang$ f a few millimetres to sev]al in*es4 ,h]tz's own "w 0 *iefly done ) !r waves f #a or #b feet to #cj or #dj feet 9 wave-l5g?4 ,m rec5tly1 !r waves ( #hjj to #ajjj feet 9 wave-l5g? h be5 employ$ 9 wireless telegraphy4 ,p]haps we %all n be wrong 9 say+ t we are acqua9t$ ) sixte5 or sev5te5 octaves ( !r-wave radiation :i* is made electrically1 & is usually call$ ! ,h]tz radiation4 ,betwe5 ! radiation ( greate/ wave-l5g? :i* proce$s f hot or inc&esc5t bodies su* z ! sun1 ! electric arc1 or a hot ball1 & t ( ! %orte/ wave-l5g? :i* has be5 creat$ by means ( electrical oscillations set up 9 "s =m ( ,h]tz oscillator1 !re is a range ( six octaves ( !r waves :i*1 s f> z we "k1 h n yet be5 manufactur$ or detect$4 ,h]e9 lies an opportunity = mu* future sci5tific "w4 ,we h to discov] h[ to create & recognize ^! int]connect+ wave-l5g?s4 ,f ! fact t all ,h]tz waves travel ) ! same spe$ z light1 & f our ability to imitate1 z y h se51 ! well-kn[n optical ph5om5a ) ,h]tz radiation ( %ort wave-l5g?1 ! great induction has be5 made t all !r waves h ! same ess5tial nature1 & t invisible act9ic rays1 light rays1 d>k-heat rays1 & ,h]tz rays are all ( !m !r waves ( v>i\s wave-l5g?s & amplitudes4 ,?us we see1 z ,maxwell long ago pr$ict$1 t light 9 all probability is an electro-magnetic ph5om5on1 & !re=e all optical effects mu/ be capable ( receiv+ an electro-magnetic explanation4 ,! inclusion ?us made ( ! :ole sci5ce ( ,optics )9 ! doma9 ( ,electricity & ,magnetism is "o ( ! gr&e/ a*ievem5ts ( ,physical ,sci5ce4 ,x /&s second only to ,newton's great discov]y ( univ]sal gravitation1 :i* r$uc$ all ,physical ,a/ronomy to pure ,dynamics1 & %[$ t ! =ce conc]n$ 9 ! fall+ ( a /one is id5tical ) t :i* holds ! planets 9 _! orbits1 & controls ! motions ( galaxies ( suns4 ,at ! end ( ! la/ *apt] x 0 expla9$ t ^! ,h]tz radiations are creat$ 9 ! !r by ! sudd5ly />t+1 /opp+1 or rev]s+ ! motion ( cr[ds ( electrons1 :i* are1 z x 71 in/antly releas$ f a /ate ( pressure or t5sion1 & set mov+ inside a /raight insulat$ conductor1 :i* =ms an op5 electric circuit4 ,! radiations we call light & d>k heat are probably1 !re=e1 />t$ 9 a simil> mann] by vibrations ( ! electrons :i* =m p>ts (1 or :i* build up1 atoms4 ,!re are _m physical ph5om5a :i* seem to %[ t ! electrons :i* we c deta* f atoms 9 a high vacuum tube are capable ( vibrat+ freely 9 def9ite p]iods :5 9 connection ) _! atom4 ,if ! atoms are able to move freely1 & if ea* is practically indep5d5t1 z is ! case 9 a gas1 & if !y are !n caus$ to radiate by any means1 ! radiation emitt$ by ! vibration ( ^! electrons consi/s ( c]ta9 def9ite wave-l5g?s4 ,h5ce1 :5 we =m ! spectrum ( an inc&esc5t gas1 we f9d x to consi/ ( sev]al deta*$ bright l9es1 ea* correspond+ to "o p>ticul> wave-l5g?1 & we d n obta9 a uni=mly graduat$ b& ( col\r$ light4 ,if an atom is /ruck by collid+ ) ano!r1 & !n left to itself1 x appe>s z if ! electrons :i* compose x & =m "p ( x are set 9 vibration1 & ea* executes its oscillation 9 "s def9ite p]iod ( "t4 ,an atom has1 !re=e1 be5 comp>$ to a 8collection ( small tun+-=ks10 :i*1 if rudely /ruck1 w\ld result 9 ! emission ( a set ( air-wave tra9s1 ea* "o correspond+ 9 wave-l5g? to "o p>ticul> tun+-=k :i* emitt$ x4 ,h5ce1 if we c\ld adm9i/] a bl[ to su* a cong]ies ( tun+-=ks1 & !n analyze ! comp\nd s\nd1 we %\ld obta9 a s\nd spectrum consi/+ ( sep>at$ tones--9 o!r words1 a bright l9e spectrum ( ! complex s\nd4 ,suppos+1 h[ev]1 t we h a mass ( atoms mu* m closely 9 contact1 z 9 ! case ( a solid body1 ! cont9ual collisions betwe5 ! atoms & ! clos] contact betwe5 !m cause ! vibrations ( ! electrons to be 8=c$10 & n 8free40 ,h5ce ! electrons are compell$ to execute all v>ieties ( irregul> motion1 & ^! pr$om9ate ov] _! regul> free natural vibrations4 ,accord+ly1 ! waves emitt$ are ( a l>ge v>iety ( wave-l5g?1 & :5 ! radiation is analyz$ by a prism1 we obta9 a cont9u\s spectrum1 or b& ( _m-col\r$ light1 z ! result ( ! sep>ation ( ! rays ( diff]5t wave-l5g?s pres5t 9 x4 ,x is ?is fact :i* r5d]s our pres5t me?od ( creat+ artificial light s excessively uneconomical4 ,all our practical me?ods = mak+ light consi/ 9 heat+ a solid body 9 "o way or ano!r4 ,9 ! case ( ! electric light we heat electrically a c>bon rod or filam5t1 or else1 z 9 ! ,n]n/ lamp1 a rod compos$ ( magnesia & ! r>e e>?s4 ,9 ! case ( ! lime-light we heat a cyl9d] ( lime4 ,9 an ord9>y gas or c&le flame we heat small p>ticles ( c>bon1 & ! same is ! case ev5 9 ! sun itself4 ,b ?is process manufactures n only ! s+le octave ( radiation :i* c affect our eyes z light1 b a doz5 o!r octaves ( radiation to :i* !y are ins5sible4 ,h5ce x foll[s t ( ! :ole radiation f a gas flame1 only ab\t #c p] c5t4 is eye-affect+ light1 ! rema9d] is d>k heat4 ,9 ! case ( an inc&esc5t electric lamp1 ?is lum9\s effici5cy may am\nt to #e p] c5t41 & 9 ! electric arc to #aj or #ae p] c5t4 ,!re is1 h[ev]1 always a great dilution ( ! useful light by useless d>k heat4 ,! proportion ( ! light or eye-affect+ radiation to ! d>k heat 9 ! total radiation f any s\rce ( light increases ) ! temp]ature1 b x is n always m]ely a "q ( temp]ature4 ,?us ! electric arc is hott] ?an a c&le flame1 & ! sun is hott] ?an ! electric arc4 ,h5ce1 :il/ ! lum9\s rays only =m #c p>ts out ( #ajj1 or #c p] c5t4 ( ! radiation ( a c&le1 !y con/itute #aj to #ae p] c5t4 ( ^? ( ! electric arc1 & m ?an #cj p] c5t4 ( ^? ( ! sun4 ,on ! o!r h&1 ! gl[-worm & ! fire-fly seem to h possession ( a k & an art :i* is z yet d5i$ to man4 ,x has be5 %[n by ,pr(essor ,langley & ,mr4 ,v t ne>ly ! :ole ( ! radiation f ! natural tor* ( ! fire-fly is useful light1 & none ( x is useless d>k heat4 ,h5ce ^! photog5ic 7light-produc+7 insects h ! art1 :i* we h n1 ( creat+ cold light1 or unadult]at$ lum9\s radiation4 ,at ! pres5t mom5t 9 ord9>y inc&esc5t or gl[-lamp electric light+ we require to exp5d an am\nt ( p[]1 call$ "o horse-p[]1 to produce illum9ation equal to t ( #fjj c&les4 ,suppos+1 h[ev]1 t all our p[] c\ld be utiliz$ 9 g5]at+ m]ely ! rays useful = vision1 or :i* c impress our eyes1 we might be able to create by ! exp5diture ( "o horse-p[] m ?an tw5ty times z mu* illum9ation1 t is1 a light equal to #ab1jjj c&les4 ,^! figures %[ u :at rew>ds await ! inv5tor :o c discov] a means ( g5]at+ !r waves hav+ wave-l5g?s /rictly limit$ to ! range ly+ betwe5 ! limits #jd & #jg )\t1 at ! same "t1 be+ oblig$ to create radiation compris+ long] waves :i* are n useful = ! purpose ( r5d]+ objects visible to u4 ,= ! purposes ( artificial illum9ation we require only ! !r waves 9 ?is "o p>ticul> octave1 & no?+ else4 ,?is increase 9 ! effici5cy ( our s\rces ( artificial illum9ation is only likely to be br\ght ab\t :5 we ab&on ! process ( heat+ a solid sub/ance to make x give out light1 & adopt "s o!r means ( sett+ ! electrons 9 vibration4 ,x is almo/ impossible to discuss ! subject ( !r waves )\t "s ref]5ce to ! mo/ mod]n utilization ( !m 9 ! s-call$ wireless telegraphy4 ,)\t ent]+ ^u ! vex$ que/ions ( priority1 or on ! hi/orical developm5t ( ! art1 we %all simply conf9e our att5tion "h to a consid]ation ( ! me?ods employ$ by ,mr4 ,m>coni1 :o has accompli%$ su* wond]ful feats 9 ?is dep>tm5t ( inv5tion4 ,we h already se5 t :5 two insulat$ conductors are plac$ ) _! ends v ne> toge!r1 & are !n electrifi$1 "o positively & ! o!r negatively1 & !n all[$ to be sudd5ly connect$ by an electric sp>k1 !y con/itute an arrangem5t call$ an electrical oscillator4 ,if ! conductors take ! =m ( two long rods plac$ 9 "o l9e1 & if _! contigu\s ends are provid$ ) sp>k-balls sep>at$ by a small gap1 we h se5 t we h %[n t1 "u ! above-m5tion$ conditions1 electric curr5ts ( v high frequ5cy are set up 9 ^! rods4 ,= creat+ ^! oscillations1 an in/rum5t call$ an induction coil or sp>k-coil is g5]ally employ$4 ,y w und]/& ! arrangem5ts bett] if a brief description is giv5 fir/ ( ! sp>k-coil itself z us$ 9 wireless telegraphy4 ,illu/ration3 ,,fig4 #ha4--;,a #aj-;in* induction coil = wireless telegraphy 7,newton74 ,! appliance consi/s ( a l>ge bundle ( f9e iron wires1 :i* are w\nd ov] ) a long coil ( insulat$ wire4 ,?is =ms ! prim>y coil4 ,x is enclos$ entirely 9 a tube ( ebonite4 ,"o end ( ?is coil is a contact-break]1 :i* automatically int]rupts an electric curr5t fl[+ f a batt]y ?r\gh ! prim>y coil 7see ,fig4 #ha74 ,a h&-key is also plac$ 9 ! circuit to /op & />t ! prim>y curr5t z desir$4 ,ov] ! prim>y coil is a v long coil ( mu* f9] silk-cov]$ copp] wire1 call$ ! second>y coil4 ,! l5g? ( ?is coil is v consid]able1 & may am\nt to _m miles4 ,! second>y coil is divid$ into sections all c>efully insulat$ f ea* o!r4 ,ano!r important "p is ! cond5s]4 ,?is consi/s ( %eets ( t9foil laid betwe5 %eets ( wax$ pap]1 alt]nate t9foil %eets be+ connect$4 ,! arrangem5t =ms virtually a ,leyd5 j>1 & "o set ( t9foils is connect$ to "o side ( ! automatic break1 & ! o!r to ! adjac5t side4 ,:51 !re=e1 ! prim>y circuit is int]rupt$ by ! break1 ! cond5s] is at t mom5t ?r[n into s]ies ) ! prim>y coil4 ,! rapid int]ruption ( ! prim>y curr5t causes a second>y curr5t 9 ! f9e-wire coil4 ,! automatic contact-break] makes f t5 to fifty su* int]ruptions p] second4 ,at e 8break0 ( ! prim>y a v high electromotive =ce is g5]at$ 9 ! second>y circuit1 :i* may am\nt to _m hundr$s ( ?\s&s ( volts4 ,?is v high second>y electromotive =ce is able to cause an electric dis*>ge 9 ! =m ( a sp>k betwe5 brass balls connect$ to ! second>y circuit t]m9als4 ,coils are g5]ally rat$ by ! l5g? 79 in*es7 ( ! sp>k !y c produce betwe5 brass balls ab\t in* 9 diamet]4 ,! coil mo/ commonly us$ 9 wireless telegraphy is ?us te*nically t]m$ a 8#aj-;in* induction coil10 f ! l5g? ( ! sp>k ?is p>ticul> type ( coil c produce4 ,if ! insulat$ brass balls1 call$ ! sp>k-balls1 connect$ to ! second>y t]m9als1 are plac$ an in* or s ap>t1 & ! h&-key 9 ! prim>y circuit is clos$1 a batt]y connect$ to ! prim>y circuit w s5d a rapidly int]rupt$ curr5t ?r\gh ! prim>y coil1 & a torr5t ( sp>ks w pass betwe5 ! sp>k-balls4 ,! prim>y curr5t ( ! #aj-;in* coil is usually a curr5t ( #aj ampres1 suppli$ at a pressure ( #aj volts4 ,if ! h&-key is rais$ or press$1 x is possible to make long or %ort torr5ts ( second>y sp>ks4 ,suppose1 !n1 t we connect to ! second>y sp>k-balls two long insulat$ rods1 & place ! sp>k-balls ab\t in* ap>t4 ,on press+ ! h&-key1 we obta9 a peculi>ly bright crackl+ sp>k betwe5 ! balls1 :i* is an oscillatory sp>k1 & at ! same "t1 z already describ$1 electrical oscillations are set up 9 ! rods & electric waves giv5 (f4 ,we may repres5t to ourselves ^! electrical oscillations 9 ! rods z simil> to ! me*anical vibrations :i* w\ld be set up 9 a long ela/ic wood5 rod1 clamp$ at ! middle & set 9 vibration at ! ends4 ,or we may consid] !m simil> to ! fundam5tal vibrations ( an op5 organ-pipe1 ! middle ( ! pipe correspond+ ) ! middle ( ! rod4 ,9 comp>+ ! me*anical vibrations ( ! rod or ! ac\/ic vibration ( ! air 9 ! organ-pipe ) ! electrical oscillations 9 ! long rods1 we mu/ be> 9 m9d t ! displacem5t ( ! rod or ! air 9 ! organ-pipe at any po9t corresponds ) electrical pressure1 or pot5tial1 z x is call$1 at any po9t 9 ! long oscillator4 ,h5ce1 be>+ 9 m9d ! rem>ks 9 ! f\r? lecture1 x w be evid5t to y t j z ! l5g? ( ! air wave emitt$ by ! op5 organ-pipe is d\ble ! l5g? ( ! pipe1 s ! l5g? ( ! electric wave ?r[n (f f ! pair ( long rods is d\ble _! total l5g?4 ,in/ead ( us+ a pair ( rods = ! electrical oscillator1 x 0 f\nd by ,mr4 ,m>coni to be an improvem5t to employ only "o insulat$ rod1 held v]tically1 & to connect x to "o sp>k-ball ( ! coil1 & to connect ! opposite sp>k-ball to a metal plate buri$ 9 ! e>?4 ,!n1 :5 ! sp>k-balls are plac$ a little ap>t & ! h&-key press$1 we h a torr5t ( oscillatory sp>ks betwe5 ! 8e>!d ball0 & ! insulat$ rod ball4 ,?is sets up 9 ! rod electrical oscillations1 :i* run up & d[n ! rod4 ,x is easy to %[ t !re is a /rong electric curr5t pass+ into & out ( ! rod by connect+ x to ! sp>k-ball by means ( a piece ( f9e wire4 ,:5 ! sp>ks are tak51 we f9d ?is wire w become hot1 x may be r$ hot1 or sometimes x may be melt$4 ,by apply+ ! pr9ciples already expla9$1 x is n difficult to demon/rate t 9 ! case ( an oscillator consi/+ ( a s+le rod connect$ to "o sp>k-ball ! electric waves ?r[n (f are 9 wave-l5g? f\r times ! l5g? ( ! rod4 ,! electrical actions tak+ place1 !re=e1 are z foll[s3 ,at ea* int]ruption ( ! prim>y curr5t ( ! sp>k-coil !re is an electromotive =ce creat$ 9 ! second>y circuit1 :i* gradually *>ges up ! insulat$ rod until x atta9s a /ate 9 :i* x is said to be at a pot5tial or electrical pressure ( sev]al ?\s& volts4 ,! sp>k !n happ5s betwe5 ! balls1 & ! rod beg9s to dis*>ge4 ,?is process consi/s1 s to speak1 9 dra9+ ! electric *>ge out ( ! rod1 & x takes ! =m ( an electric curr5t 9 ! rod1 :i* has a z]o value at ! top insulat$ end1 & has its maximum value at ! sp>k-ball end4 ,also1 :5 ! oscillations take place1 we h v>iations ( electric pressure1 or pot5tial1 :i* are at a maximum at ! upp] or insulat$ end1 & h a z]o value at ! sp>k-ball end4 ,f ! rod we h a hemisph]ical electric wave radiat$4 ,9 ! language ( wireless telegraphi/s1 su* a simple insulat$ rod is call$ an insulat$ a]ial1 or an insulat$ ant5na4 ,a simple insulat$ a]ial has1 h[ev]1 a v small electrical capacity1 & x c /ore up s little electric en]gy t ! :ole ( x is radiat$ 9 ! fir/ oscillation4 ,h5ce1 /rictly speak+1 we h no tra9 ( electric waves radiat$1 b m]ely a solit>y wave or electric impulse4 ,! effect on ! !r ?us produc$ corresponds to ! effect on ! air caus$ by ! crack ( a :ip or an explosion1 & n to a musical note or tone z produc$ by an organ-pipe4 ,we c1 h[ev]1 make an arrangem5t :i* is sup]ior 9 electric wave-mak+ p[]1 z foll[s3-- ,illu/ration3 ,,fig4 #hb4--,transmitt] = wireless telegraphy4 ,! v]tical rod1 or ant5na1 ,a1 is n insulat$1 b is connect$ by its l[] end ) "o end ( a coil ( insulat$ wire1 ,s1 w\nd on a wood5 frame 7see ,fig4 #hb74 ,! o!r end ( ?is la/ coil is connect$ to a metal plate1 e1 buri$ 9 ! e>?4 ,ar\nd ! wood5 frame is w\nd a second insulat$ wire1 ,p1 "o end ( :i* is connect$ to "o sp>k-ball ( ! induction coil1 & ! o!r end to ! outside ( a ,leyd5 j>1 ,l1 or collection ( j>s4 ,?is d\ble coil on a frame is call$ an oscillation trans=m]4 ,! inside ( ?is cond5s] is connect$ to ! second sp>k-ball ( ! induction coil ,i4 ,:5 ^! sp>k-balls ,s are plac$ a %ort di/ance ap>t1 & ! coil set 9 action1 we h a torr5t ( oscillatory electric sp>ks betwe5 ^! balls1 & p[]ful oscillations set up 9 "o circuit ( ! oscillation-trans=m]4 ,^! oscillations induce o!r oscillations 9 ! second circuit ( ! oscillation-trans=m]1 viz4 9 ! "o connect$ to ! a]ial4 ,! oscillations produc$ 9 ! air-wire1 or a]ial1 are !re=e induc$1 or second>y oscillations4 ,! a]ial wire1 or ant5na1 has !re=e a mu* l>g] /ore ( electric en]gy to draw ^u1 viz4 t /or$ up 9 ! ,leyd5 j>s1 ?an if x 0 itself directly *>g$ by ! coil4 ,9 ord]1 h[ev]1 to obta9 ! be/ results c]ta9 adju/m5ts h to be made4 ,x has already be5 expla9$ t e op5 electrical circuit has a c]ta9 natural "t-p]iod = ! electrical oscillations :i* c be set up 9 x4 ,?is is te*nically call$ its tune4 ,if we adm9i/] a bl[ to a susp5d$ p5dulum we h se5 t1 if left to itself1 x vibrates 9 a def9ite p]iod ( "t1 call$ its natural p]iod4 ,9 ! same mann]1 if we h a cond5s] or ,leyd5 j> hav+ electrical capacity :i* is jo9$ 9 s]ies ) a coil ( wire hav+ electrical in]tia or inductance1 & apply to ! circuit s =m$ a sudd5 electromotive =ce or impulse1 & !n leave ! circuit to itself1 ! electric *>ge 9 x vibrates 9 a c]ta9 def9ite p]iod1 call$ its natural electrical p]iodic "t4 ,! a]ial1 or ant5na1 is simply a rod connect$ to ! e>?1 b x has a c]ta9 inductance1 & also a c]ta9 electrical capacity1 & h5ce any metal rod m]ely /uck at "o end 9 ! e>? has a p]fectly def9ite p]iodic "t = ! electrical oscillations :i* c be produc$ 9 x4 ,we may comp>e ! rod 9 ?is respect ) a piece ( /eel spr+ held at "o end 9 a vice4 ,if we pull ! spr+ on "o side1 & let x vibrate1 x does s 9 accordance ) its natural "t-p]iod = me*anical vibrations4 ,! s\nd waves giv5 out by x h a wave-l5g? equal to f\r times ! l5g? ( ! spr+4 ,9 ! same mann] ! fundam5tal wave-l5g? ( ! electric waves emitt$ by an 8e>!d a]ial10 or rod /uck 9 ! e>?1 :5 an electric impulse is appli$ to its l[] end1 & electrical oscillations are set up 9 x1 h a wave-l5g? equal to f\r times t ( ! rod4 ,h5ce to obta9 ! be/ result ! circuit1 includ+ ! a]ial ,a1 mu/ be 8tun$0 electrically to ! circuit includ+ ! ,leyd5 j> ,l4#bg ,a consid]ation ( ^! arrangem5ts w %[ y t if ! h&-key 9 ! prim>y circuit ( ! induction coil is press$ = a long or %ort "t1 we h long or %ort torr5ts ( sp>ks produc$ betwe5 ! second>y balls1 & long or %ort tra9s ( electric waves emitt$ f ! a]ial1 or e>!d v]tical wire4 ,:5ev] we h any two diff]5t signals1 we c always make an alphabet ) !m by suitable comb9ations ( ! two4 ,9 ! well-kn[n ,morse alphabet1 ) :i* e telegraphi/ is z famili> z we all are ) ! pr9t$ alphabet1 ! sign = ea* ( ! lett]s ( ! alphabet is compos$ ( gr\ps ( long & %ort symbols1 call$ dots & da%es1 z foll[s3 ,ea* lett] is made by select+ "s arrangem5ts ( dots or da%es1 ^! be+ ! te*nical names = ! two signs4 ,! ,morse code1 z us$ all ov] ! _w1 is giv5 9 ! table bel[-- ,illu/ration3 ,,! ,,morse ,,alphabet4 ,a -- ------ ,b ------ -- -- -- ,c ------ -- ------ -- ,d ------ -- -- ,e -- ,f -- -- ------ -- ,g ------ ------ -- ,h -- -- -- -- ,i -- -- ,j -- ------ ------ ------ ,k ------ -- ------ ,l -- ------ -- -- ,m ------ ------ ,n ------ -- ,o ------ ------ ------ ,p -- ------ ------ -- ,q ------ ------ -- ------ ,r -- ------ -- ,s -- -- -- ,t ------ ,u -- -- ------ ,v -- -- -- ------ ,w -- ------ ------ ,x ------ -- -- ------ ,y ------ -- ------ ------ ,z ------ ------ -- -- ,illu/ration3 ,,! ,,morse ,,num]als4 #a -- ------ ------ ------ ------ #b -- -- ------ ------ ------ #c -- -- -- ------ ------ #d -- -- -- -- ------ #e -- -- -- -- -- #f ------ -- -- -- -- #g ------ ------ -- -- -- #h ------ ------ ------ -- -- #i ------ ------ ------ ------ -- #j ------ ------ ------ ------ ------ ,full ,/op -- ------ -- ------ -- ------ ,signal = call+ up -- -- -- ------ -- -- -- ------ ,! process ( s5d+ a wireless message consi/s 9 s manipulat+ ! key 9 ! prim>y circuit ( ! induction coils t a rapid /ream ( sp>ks passes betwe5 ! second>y balls = a %ort] or = a long] "t4 ,?is gives rise to a correspond+ s]ies ( electric waves1 radiat$ f ! a]ial4 ,! da% is equal 9 duration to ab\t ?ree dots1 & a space equal to ?ree dots is left betwe5 ea* lett]1 & "o equal to five dots betwe5 ea* ^w4 ,?us1 9 ,morse alphabet ! s5t5ce 8,h[ are y80 is writt5-- ,illu/ration3 -- -- -- -- ------ ------ ------ -- ------ ------ -- ------ -- ------ -- -- ,h ,o ,w ,a ,r ,e ------ -- ------ ------ ------ ------ ------ -- -- ------ ,y ,o ,u ,we h1 9 ! next place1 to expla9 h[ ! signals s5t out are record$4 ,illu/ration3 ,,fig4 #hc4--,m>coni receiv+ arrangem5t = wireless telegraphy4 ,at ! receiv+ /ation is erect$ a second insulat$ a]ial1 ant5na1 or long v]tical rod1 ,a 7see ,fig4 #hc71 & ! l[] end is connect$ to ! e>? ?r\gh a coil ( f9e insulat$ wire1 ,p1 :i* =ms "o circuit ( an oscillation-trans=m]4 ,! second>y circuit1 ,s1 ( ?is oscillation-trans=m]1 :i* is call$ a jigg]1 is cut 9 ! middle & has a small cond5s]1 ,c#a1 ins]t$1 consi/+ ( two %eets ( t9foil sep>at$ by wax$ pap] 7see ,fig4 #hc71 & to ! ends ( ?is circuit is connect$ ! coh]]1 or metallic fil+s tube1 ,t1 :i* acts z a s5sitive receiv]4 ,! ,m>coni s5sitive tube 7see ,fig4 #hd7 is made z foll[s4 ,a glass tube ab\t in* 9 diamet] & #b in*es long has two silv] plugs put 9 x1 & ^! are sold]$ to two plat9um wires :i* are seal$ into ! clos$ ends ( ! tube4 ,! ends ( ! plugs are cut 9 a slant+ fa%ion & made v smoo?4 ,^! ends v ne>ly t\* ea* o!r4 ,a v small quantity ( v f9e metallic p[d] consi/+ ( n9ete5 p>ts nickel & "o "p silv] is !n plac$ betwe5 ! plugs4 ,! quantity ( ?is p[d] is sc>cely m ?an c\ld be tak5 up on ! head ( a l>ge p94 ,! glass tube is !n exhau/$ ( its air & seal$4 ,! tube is atta*$ to a bone rod by means ( :i* x is held 9 a clip4 ,illu/ration3 ,,fig4 #hd4--,m>coni coh]]4 ,to ! two sides ( ! above-m5tion$ cond5s] are connect$ two wires :i* lead to a circuit includ+ a s+le voltaic cell1 ,v1 & a relay1 ,e4 ,! relay is connect$ to ano!r circuit :i* includes a batt]y1 ,b1 & a piece ( app>atus call$ a ,morse pr9t]1 ,m1 = m>k+ dots & da%es on a /rip ( pap]4 ,! work+ details ( ! above r complicat$ sy/em ( app>atus devis$ by ,mr4 ,m>coni w\ld require = its full elucidation a l>ge am\nt ( explanation ( a te*nical "*4 ,! g5]al read] may1 h[ev]1 =m a suffici5tly cle> idea ( its p]=mance z foll[s3-- ,:5 ! electrical waves f ! di/ant transmitt+ /ation rea* ! a]ial at ! receiv+ /ation1 !y set up 9 x sympa!tic electrical oscillations4 ,! mo/ fav\rable conditions are :5 ! two a]ials at ! di/ant /ations are exactly simil>4 ,^! electrical oscillations1 or rapid electric curr5ts1 set up an electromotive =ce 9 ! second>y circuit ( ! oscillation-trans=m]1 & ?is acts1 z already expla9$1 ^u ! metallic fil+s 9 ! coh]]-tube & causes x to become an electrical conductor4 ,! cell atta*$ to ! relay !n s5ds a curr5t ?r\gh ! conductive circuit s =m$ & op]ates ! relay4 ,?is la/ contrivance is m]ely a v delicate swit* or circuit-clos] :i* is set 9 action by a small curr5t s5t ?r\gh "o ( its circuits1 & x !n closes a second circuit & s enables ano!r mu* l>g] batt]y to s5d a curr5t ?r\gh ! ,morse pr9t]4 ,! pr9t] !n pr9ts a dot ^u a mov+ /rip ( pap] & records a signal4 ,"o o!r elem5t 9 ?is r complicat$ arrangem5t rema9s to be notic$1 & t is ! tapp]4 ,und]nea? ! coh]]-tube is a little hamm] work$ by an electro-magnet l an electric bell4 ,?is tapp] is set vibrat+ by ! same curr5t :i* passes ?r\gh ! ,morse pr9t]1 & h5ce almo/ z soon z ! latt] has begun to pr9t1 ! s5sitive tube receives a little tap :i* causes ! metallic fil+s to become aga9 a non-conductor1 & s arre/s ! :ole ( ! electric curr5cy4 ,if x 7 n = ?is tapp]1 ! arrival ( ! electric wave w\ld cause ! pr9t] to beg9 pr9t+ a l9e :i* w\ld cont9ue4 ,! dot is1 s to speak1 an arre/$ l9e4 ,if1 h[ev]1 tra9s ( electric waves cont9ue to arrive1 !n dots cont9ue to be pr9t$ 9 close ord]1 & =m a da% on ! pap] /rip4 ,x w ?us be se5 t ! :ole arrangem5ts con/itute an exce$+ly +5i\s device ( su* a nature t a s+le t\* on ! h&-key at "o /ation caus+ a sp>k or two to take place betwe5 ! sp>k-balls makes a dot appe> ^u a b& ( pap] at ! di/ant /ation2 :il/1 if ! h&-key is held d[n s t a /ream ( sp>ks takes place at ! transmitt+ /ation1 a da% is record$ at ! receiv+ /ation4 ,! means by :i* ?is di/ant effect is produc$ is ! tra9 ( electric waves mov+ ov] ! e>?'s surface sett+ out f "o a]ial & arriv+ at ! o!r4 ,illu/ration3 ,,fig4 #he4 ,! read] :o has difficulty 9 foll[+ ! above explanations may p]haps ga!r a suffici5tly cle> notion ( ! processes at "w by consid]+ a r$uc$1 or simplifi$1 arrangem5t4 ,imag9e two long insulat$ rods1 ,a1 ,a 7see ,fig4 #he71 l lightn+-conductors set up at di/ant places4 ,suppose ea* rod cut ne> ! bottom1 & let a pair ( sp>k-balls1 ,s1 be ins]t$ 9 "o gap & a coh]] or s5sitive tube1 ,c1 9 ! o!r4 ,at "o /ation let an electrical ma*9e h its positive & negative t]m9als connect$ to ! two sp>k-balls1 & at ! o!r let a batt]y & electric bell be connect$ to ! ends ( ! coh]]4 ,!n1 z long z ! coh]] rema9s 9 a non-conductive condition1 ! electric bell does n r+4 ,if1 h[ev]1 a sp>k is made betwe5 ! balls1 9 virtue ( all t has be5 expla9$1 ! read] w und]/& t ! coh]]-tube becomes at once conductive by ! action ( ! electric wave s5t out f ! transmitt]-rod4 ,! batt]y at ! receiv]-rod !n s5ds a curr5t ?r\gh ! coh]]1 & r+s ! bell4 ,all ! o!r complicat$ details ( ! receiv] are = mak+ ! process ( /opp+ ! bell & beg9n+ ov] aga9 self-act+1 & also = ! production ( two k9ds ( signals1 a long & a %ort1 by means ( :i* an alphabet is made4 ,9 ord] t we may h telegraphy 9 any prop] s5se ( ! ^w1 we mu/ be able to transmit any intellig5ce at pleasure1 & n m]ely "o s+le arbitr>y signal4 ,?is transmission ( intellig5ce involves ! comm& ( an alphabet1 & t 9 turn requires ! p[] ( production ( two k9ds ( signals4 ,x rema9s to notice a few ( ! special details :i* *>act]ize ,mr4 ,m>coni's sy/em ( wireless telegraphy4 ,9 e/abli%+ wireless communication betwe5 two places1 ! fir/ ?+ to be done is to equip !m bo? ) a]ials4 ,if "o /ation is on l&1 x is usual to erect a /rong ma/ ab\t #aej feet high1 & to ! top ( ?is is atta*$ a sprit4 ,f ?is sprit a /r&$ copp] wire is susp5d$ by means ( an insulator ( ebonite1 s t ! upp] end ( ! wire is insulat$4 ,! l[] end ( ! wire is l$ into a little hut or into "s room ne> ! foot ( ! ma/ 9 :i* is ! receiv+ & transmitt+ app>atus4 ,if ! app>atus is to be in/all$ on bo>d %ip1 !n a simil> insulat$ wire is susp5d$ f a y>d>m or f a sprit atta*$ to a ma/4 ,ea* /ation is provid$ ) ! transmitt+ app>atus & ! receiv+ app>atus1 & ! att5dant *anges ov] ! a]ial f "o connection to ! o!r s z to receive or s5d at pleasure4 ,9 ! case ( long-di/ance wireless telegraphy1 ! a]ial is n a s+le wire1 b a collection ( wires1 susp5d$ s z to space !m a little f ea* o!r4 ,?us 9 ! case ( ! fir/ exp]im5ts made by ,m4 ,m>coni across ! ,atlantic1 ! a]ial erect$ on ! coa/ ( ,cornwall consi/$ ( fifty /r&$ copp] wires ea* #aej feet 9 l5g? susp5d$ 9 a fan-%ap$ fa%ion f a long transv]se /ay upheld betwe5 two ma/s4 ,! wires 7 spac$ out at ! top & ga!r$ 9 toge!r at ! bottom4 ,! "q :i* almo/ imm$iately occurs to mo/ p to ask is h[ f> x is possible to prev5t ! electric waves emanat+ f "o /ation affect+ all receiv+ in/rum5ts alike )9 a c]ta9 radius4 ,! answ] to ?is is t consid]able progress has be5 made 9 effect+ :at is call$ 8tun+0 ! v>i\s /ations4 ,9 speak+ ( ac\/ic resonance x has be5 po9t$ out t a tra9 ( air waves c set up vibration 9 o!r bodies :i* h ! same natural p]iod ( vibration4 ,?us1 if we op5 a piano s z to expose ! /r+s1 & if a s+] ) a /rong voice s+s a l\d true note & !n /ops sudd5ly1 x w be f\nd t "o p>ticul> /r+ ( ! piano is vibrat+1 viz4 t :i* w\ld give out if /ruck ! note :i* 0 sung1 b all ! re/ ( ! /r+s are sil5t4 ,x has be5 po9t$ out t e op5 electric circuit has a natural electrical "t-p]iod ( vibration 9 :i* its electric *>ge oscillates if x is di/urb$ by a sudd5 electromotive =ce & !n left to itself4 ,if ! two a]ials at two /ations are exactly alike1 & if ! v>i\s circuits con/itut+ ! oscillation-trans=m]s 9 ! transmitt+ & receiv+ appliances are all adju/$ to h ! same electrical p]iod1 !n x is f\nd t ! /ations s tun$ are sympa!tic at di/ances va/ly great] ?an !y w\ld be if n s tun$4 ,h5ce x is possible to arrange wireless telegraph app>atus s t x is n affect$ by any electric waves arriv+ f a di/ance :i* h n a p>ticul> "t-p]iod4 ,mr4 ,m>coni has also prov$ t x is possible to receive on ! same a]ial1 at ! same "t1 two diff]5t messages on sep>ate receiv+ in/rum5ts f two di/ant b prop]ly tun$ transmitt+ /ations4 ,s9ce ! date ( ^! pione] inv5tions _m diff]5t =ms ( wave detector h be5 discov]$1 & wireless telegraphy has %[n itself to be ( ! greate/ utility 9 effect+ communication betwe5 %ip & %ip1 & %ip & %ore4 ,its value 9 enabl+ intellig5ce to be transmitt$ f light%ips or ligh?\ses to coa/ /ations _c be ov] e/imat$4 ,"o v rem>kable feature ( ! app>atus z arrang$ by ,mr4 ,m>coni is ! small space x occupies4 ,x is 9 ?is respect mo/ admirably adapt$ = use on bo>d %ip4 ,x only requires a long1 insulat$1 v]tical wire :i* c easily be susp5d$ f a ma/1 & ! :ole receiv+ & transmitt+ app>atus c be plac$ on bo>d %ip 9 a small cab94 ,employ+ ! s5sitive tube & ,m>coni receiv+ arrangem5ts1 messages c easily be s5t #aej miles ov] ! sea-surface by means ( an a]ial #aej feet high & a #aj-;in* induction coil4 ,x is a curi\s fact t bett] results are obta9$ ov] a wat]-surface ?an ov] l&4 ,two simil> /ations ) ! same appliances c communicate at two or ?ree times great] di/ance if !y are sep>at$ by sea ?an if !y are on l& & h no wat] betwe54 ,?is is connect$ ) ! fact t electric waves are n able to pass ?r\gh sea-wat]1 b c diffuse ?r\gh dry e>?4 ,! sea-surface acts some:at l an optical reflector or mirror1 & ! electric waves glide along its surface4 ,! rotundity ( ! e>? )9 c]ta9 limits h>dly makes any p]ceptible effect ^u ! ease ( communication4 ,! waves s5t out by ! transmitt] ( a long-di/ance wireless /ation are f #cjjj to #bj1jjj feet 9 l5g?1 & !re is1 !re=e1 a consid]able am\nt ( b5d+ or diffraction4 ,x is a famili> fact1 z already expla9$1 t a wave-motion1 :e!r on wat] or 9 air1 spreads r\nd an ob/acle to a c]ta9 ext5t4 ,?us an int]pos+ rock or wall does n =m a %>ply m>k$ s\nd-%ad[1 b !re is "s deflection ( ! air waves by ! edge ( ! ob/acle4 ,! am\nt ( b5d+ :i* takes place dep5ds on ! l5g? ( ! wave4 ,if we take two places on ! sea-surface #bjj miles ap>t1 ! surface ( ! sea at ! halfway di/ance is j #a miles above ! /raight l9e jo9+ ! places4 ,9 o!r words1 ! rotundity ( ! e>? int]poses a m\nta9 ( wat] #a miles high betwe5 ! places4 ,! electric waves us$ 9 wireless telegraphy h a wave-l5g? ( ab\t #fjj to #ajjj feet1 or say five or six to ! mile4 ,h5ce ! int]position ( an object1 ! height ( :i* is "o-=tie? ( ! di/ance1 is n suffici5t to make a complete electric %ad[4 ,if we 71 = in/ance1 bl[+ a trumpet creat+ air waves #e feet long1 ! int]position ( a cliff betwe5 two places a mile ap>t1 b s situat$ t ! cliff protrud$ to ! ext5t ( #dj y>ds across ! l9e jo9+ !m1 w\ld n cut (f all s\nd4 ,!re w\ld be diffraction or diffusion en\gh ( ! air waves to enable ! s\nd to be he>d r\nd ! corn]4 ,9 ! same mann] ! electric waves are1 s to speak1 propagat$ r\nd ! corn] ( ! e>?4 ,m rem>kable /ill1 !y h be5 detect$1 :5 suffici5tly p[]ful1 at a di/ance ( #fjjj miles f ! g5]at+ /ation1 & 9 ?is case !y mu/ h travell$ a qu>t] ( ! way r\nd ! e>?4 ,a good conception ( ! relative spe$s ( wat] waves1 air waves1 & !r waves c be ga9$ by consid]+ ! "t ea* ( ^! w\ld take to cross ! ,atlantic ,ocean1 travell+ 9 its own m$ium4 ,suppose we c\ld1 at ! same mom5t1 create a spla% 9 ! sea ne> ,engl& suffici5tly great to cause a wave :i* w\ld travel ov] ! surface ( ! ,atlantic at ! spe$ ( _m ocean waves1 say at #cj miles an h\r4 ,to cov] a di/ance ( #cjjj miles ?is wat] wave w\ld !n require #ajj h\rs4 ,imag9e t we c\ld1 at ! same mom5t1 make a s\nd l\d en\gh to be he>d across ! same ocean1 travell+ at ! rate ( #aajj feet a second1 or ab\t #gjj miles an h\r1 ! s\nd wave w\ld cross f ,engl& to ! coa/ ( ! ,unit$ ,/ates 9 ab\t f\r h\rs4 ,if1 h[ev]1 we 7 to make an !r wave x w\ld flit across ! same di/ance 9 ab\t ! sixtie? "p ( a second4 ,if y h be5 able to foll[ me 9 ^! descriptions1 y w see t ! progress ( sci5tific inve/igation has l$ u f simple beg9n+s to a wond]ful conclusion4 ,x is t all space is fill$ ) :at we may call an ocean ( !r1 :i* c be toss$ into waves & ripples j z ! air we brea! is trav]s$ 9 all directions by a]ial vibrations1 & ! re/less sea by waves & ripples on ! wat]-surface4 ,we _c feel or h&le ?is impond]able !r1 b we h indubitable pro( t we c create waves 9 x by sudd5ly apply+ or rev]s+ some?+ we call electric =ce1 j z we are able to produce air or wat] waves by ! v sudd5 application ( me*anical =ce or pressure4 ,^! !r waves1 :5 />t$1 n only travel ?r\gh ! ocean ( !r ) a/oni%+ spe$1 b !y are ! means by :i* enorm\s quantities ( en]gy are transf]r$ ?r\gh space4 ,f e squ>e y>d ( ! sun's surface en]gy is ca/ =? at a rate equal to t produc$ by ! combu/ion ( elev5 tons ( be/ ,wel% coal p] h\r1 & convey$ away into surr\nd+ space by !r ripples1 to w>m & light ! sun's family ( planets4 ,e plant t gr[s ^u ! e>?'s surface is n\ri%$ into maturity by ! en]gy deliv]$ to x 9 ?is way4 ,e animal t basks 9 ! sunlight is kept w>m by ! impact ( ^! !r waves ^u ! e>?4 ,all ! coal we possess buri$ 9 ! e>?'s cru/1 & 9 ?is age ( /eam =m+ ! life-blood ( ! _w1 has be5 manufactur$ orig9ally by !r ripples beat+ 9 _! millions1 9 long-pa/ ages1 ^u ! vegetation ( ! primeval _w4 ,b 9 ano!r way ! !r s]ves z a vehicle ( en]gy--9 ! =m ( an electric curr5t4 ,e electric lamp t is light$1 e electric tram-c> t glides along1 is draw+ its supply ( en]gy ?r\gh ! !r4 ,! wire or conductor1 z we call x1 s]ves to guide & direct ! pa? ( ! en]gy transf]r$2 b ! en]gy is n 9 b ar\nd ! wire4 ,we h lately le>nt to make :at we may be/ describe z bill[s 9 ! !r1 & ^! are ! long waves we employ 9 wireless telegraphy4 ,b 9 telegraphy1 :e!r ) wires or )\t1 we are m]ely manipulat+ ! !r z a m$ium ( communication1 j z 9 spee* or he>+ we use ! air4 ,we !re=e f9d our physical inve/igations lead u to ?ree great f9al inquiries1 :5 we ask--,:at is ! nature ( electricity1 !r1 & en]gy8 ,already1 x seems possible1 we may obta9 "s clue to an answ] to ! fir/ "q1 & f9d x 9 a /udy ( ! electrons1 or t9y corpuscles :i* build up atoms4 ,conc]n+ ! /ructure ( !r1 physical inve/igation1 :i* has reveal$ its exi/5ce1 may be able to analyze a little m deeply its op]ations4 ,b ! "q1 ,:at is ,en]gy8 seems to take u to ! v conf9es ( physical inquiry1 :]e problems conc]n+ ! /ructure ( ! mat]ial univ]se seem to m]ge into que/ions conc]n+ its orig9 & my/]y4 ,9 its ultimate ess5ce1 en]gy may be incompreh5sible by u1 except z an exhibition ( ! direct op]ation ( t :i* we call ,m9d & ,w4 ,9 ^! f9al inquiries into ! nature ( ?+s1 ! wise/ ( u c m]ely speculate1 & ! majority b dimly appreh5d4 ,we mu/ n1 h[ev]1 travel beyond ! limits ( ?\ght prop] = ^! elem5t>y lectures4 ,_! *ief object has be5 to %[ y t ! swiftly mov+ ocean waves1 :i* da% & roll unceas+ly aga9/ ! coa/-l9es ( our isl& home1 are only in/ances ( "o =m ( wave-motion1 ( :i* we f9d o!r v>ieties 9 o!r m$ia1 giv+ rise to all ! entranc+ effects ( s\nd & light4 ,9 ^! expositions we h be5 able to d no m ?an t\* ! fr+e ( a great subject4 ,_! object w h be5 fulfill$ if !y h /imulat$ 9 y a desire to "k m ab\t ^! int]e/+ ?+s4 ,e /> & fl[]1 e wave or bird t hov]s ov] x1 c tell u a m>vell\s /ory1 if only we h eyes to see1 & e>s to he>4 ,we may f9d 9 ! commone/ ( surr\nd+ ?+s a limitless opportunity = intellig5t /udy & delight4 ,:51 !re=e1 y next sail y\r boat ^u a pond1 or wat* ducks or swans swimm+1 or ?r[ /ones into a pool1 or visit ! seaside1 may ,i hope t "s ( ! matt]s "h discuss$ w recur to y\r m9ds1 & t y w f9d a fre% mean+ & new int]e/ 9 ^! ev]yday objects4 ,yon may ?us1 p]haps1 receive an impulse attract+ y to ! /udy ( "s *apt]s 9 ! 8,fairy ,tale ( ,sci5ce10 m wond]ful ?an any romance wov5 by ! imag9ations ( m51 & op5 to y\rselves a s\rce ( elevat+ pleasure1 :i* "t w nei!r dim9i% nor de/roy4 ,,app5dix4 ---- ,,note ,a 7see p4 #ba74 ,! di/9ction betwe5 ! individual wave-velocity & a wave-gr\p velocity1 to :i*1 z /at$ 9 ! text1 att5tion 0 fir/ call$ by ,sir ,g4 ,g4 ,/okes 9 an ,exam9ation "q set at ,cambridge 9 #ahgf1 is closely connect$ ) ! ph5om5a ( beats 9 music4 ,if two inf9itely long sets ( deep-sea waves1 hav+ slightly diff]5t wave-l5g?s1 & !re=e slightly diff]5t velocities1 are sup]impos$1 we obta9 a resultant wave-tra9 :i* exhibits a v>iation 9 wave-amplitude along its c\rse p]iodically4 ,if we 7 to look along ! tra91 we %\ld see ! wave-amplitude at int]vals wax+ to a maximum & !n wan+ aga9 to no?+4 ,^! po9ts ( maximum amplitude regul>ly arrang$ 9 space con/itute1 z x 71 waves on waves4 ,!y are spac$ at equal di/ances1 & sep>at$ by int]vals ( m or less waveless or smoo? wat]4 ,^! maximum po9ts move =w>d ) a uni=m velocity1 :i* we may call ! velocity ( ! wave-tra91 & ! di/ance betwe5 maximum & maximum surface-di/urbances may be call$ ! wave-tra9 l5g?4 ,let v & v be ! velocities1 & n & n ! frequ5cies1 ( ! two con/itu5t wave-motions4 ,let & be ! correspond+ wave-l5g?s4 ,let ,v be ! wave-tra9 velocity1 ,n ! wave-tra9 frequ5cy1 & ,l ! wave-tra9 l5g?4 ,!n ,n is ! numb] ( times p] second :i* a place ( maximum wave-amplitude passes a giv5 fix$ po9t4 ,!n we h ! foll[+ obvi\s relations3-- v n1 v n1 ,n n - n v_/ - v_/ ,also a little consid]ation w %[ t-- ,l_/ _/7 - 7 s9ce is ne>ly equal1 by assumption1 to 4 ,h5ce we h-- #a_/,l #a_/ - #a_/2 & also ,v ,,nl ,accord+ly-- ,v ,n_/7#a_/,l7 7v_/ - v_/7_/7#a_/ - #a_/7 ,let u write #b_/k in/ead ( 1 & #b_/k in/ead ( 2 !n we h-- ,v 7vk - vk7_/7k - k7 7i47 ,& s9ce k & k1 v & v are ne>ly equal1 we may write ! above expression z a diff]5tial coeffici5t2 ?us-- ,v d7vk7_/d7k7 7ii47 ,suppose1 !n1 t1 z 9 ! case ( deep-sea waves1 ! wave-velocity v>ies z ! squ>e root ( ! wave-l5g?4 ,!n if ,c is a con/ant1 :i* 9 ! case ( gravitation waves is equal to g_/#b1 :]e g is ! accel]ation due to gravity1 we h-- v#b ,c1 or v#b 7g_/#b7 ,b #b_/k1 h5ce-- vk #b;,c_/v ,h5ce if we diff]5tiate ) respect to v1 we h-- d7vk7_/dv -#b;,c_/v#b ,aga91 k #b_/ #b;,c_/v#b2 !re=e-- d7k7_/dv -#b7b;,c_/v#c7 ,h5ce1 divid+ ! expression = d7vk7_/dv by t = d7k7_/dv1 we h-- ,v d7vk7_/d7k7 v_/#b ,9 o!r words1 ! wave-tra9 velocity is equal to half ! wave-velocity4 ,?is is ! case ) deep-sea waves4 ,suppose1 h[ev]1 t1 z 9 ! case ( air waves1 ! wave-velocity is indep5d5t ( ! wave-l5g?4 ,!n if two tra9s ( waves ( slightly diff]5t wave-l5g? are sup]pos$1 we h k & k diff]5t 9 value b ne>ly equal1 & v & v equal4 ,h5ce ! equation 7i47 takes ! =m-- ,v v ,9 o!r words1 ! beats travel =w>d ) ! same spe$ z ! con/itu5t waves4 ,& 9 ?is case !re is no diff]5ce betwe5 ! velocity ( ! wave-tra9 & ! velocity ( ! individual wave4 ,! above pro( may be g5]aliz$ z foll[s3-- ,let ! wave-velocity v>y z ! n? root ( ! wave-l5g?1 or let vn ,c2 & let #b_/k z be=e4 ,!n-- vn #b;,c_/k1 & vk #b;,c_/vn-#a #b;,cv-7n-#a7 also k #b_/ #b;,c_/vn #b;,cv-n ,h5ce d7vk7_/d7k7 7n-#av-7n-#a7-a7_/7nv-n-#a7 77n-#a7_/n7v or ,v 77n-#a7_/n7v ,t is1 ! wave-tra9 velocity is equal to 7n-#a7_/n times ! wave-velocity4 ,9 ! case ( sea waves n #b1 & 9 ! case ( air waves n inf9ity4 ,if n 7 #c1 !n ,v 7#b_/c7v1 or ! gr\p-velocity w\ld be two-?irds ! wave-velocity4 ,,note ,b 7see p4 #bgc74 ,e electric circuit compris+ a coil ( wire & a cond5s] has a def9ite "t-p]iod 9 :i* an electric *>ge giv5 to x w oscillate if a /ate ( electric /ra9 9 x is sudd5ly releas$4 ,?us ! ,leyd5 j> ,l & associat$ coil ,p %[n 9 ,fig4 #hb1 p4 #bga1 con/itutes an electric circuit1 hav+ a c]ta9 capacity measur$ 9 units1 call$ a micr(>ad1 & a c]ta9 inductance1 or electric in]tia measur$ 9 c5timetres4 ,! capacity ( ! circuit is ! quality ( x 9 virtue ( :i* an electric /ra9 or displacem5t c be made by an electromotive =ce act+ on x4 ,! inductance is ! in]tia quality ( ! circuit1 9 virtue ( :i* an electric curr5t creat$ 9 x t5ds to p]si/4 ,9 ! case ( me*anical oscillations su* z ^? made by vibrat+ a p5dulum1 ! "t ( "o complete oscillation1 ,t1 is connect$ ) ! mom5t ( in]tia1 ,i1 & ! me*anical =ce br\ght into play by a small displacem5t z foll[s3 ,suppose we give ! p5dulum a small angul> displacem5t1 d5ot$ by 4 ,!n ?is displacem5t br+s into exi/5ce a re/or+ =ce or torque :i* br+s ! p5dulum back1 :5 releas$1 to its orig9al position ( re/4 ,9 ! case ( a simple p5dulum consi/+ ( a small ball atta*$ to a /r+1 ! re/or+ torque creat$ by displac+ ! p5dulum ?r\gh a small angle1 1 is equal to ! product mgl1 :]e m is ! mass ( ! bob1 g is ! accel]ation ( gravity1 & l is ! l5g? ( ! /r+4 ,! ratio ( displacem5t 77 to ! re/or+ torque mgl is #a_/mgl4 ,?is may be call$ ! displacem5t p] unit torque1 & may o!rwise be call$ ! pliability ( ! sy/em1 & d5ot$ g5]ally by ,p4 ,let ,i d5ote ! mom5t ( in]tia4 ,?is quantity1 9 ! case ( a simple p5dulum1 is ! product ( ! mass ( ! bob & ! squ>e ( ! l5g? ( ! /r+1 or ,i ml#b4 ,9 ! case ( a body ( any %ape :i* c vibrate r\nd any c5tre or axis1 ! mom5t ( in]tia r\nd ?is axis ( rotation is ! sum ( ! products ( ea* elem5t ( its mass & ! squ>e ( _! respective di/ances f ?is axis4 ,! p]iodic "t ,t ( any small vibration ( ?is body is !n obta9$ by ! foll[+ rule3-- ,t #b77mom5t ( in]tia r\nd ! axis ( rotation7 7displacem5t p] unit ( torque1 or pliability77 or ,t #b7;,,ip74 ,9 ! case ( an electric circuit ! inductance corresponds to ! mom5t ( in]tia ( a body 9 me*anical vibration2 & ! capacity to its pliability z above def9$4 ,h5ce ! "t ( vibration1 or ! electrical "t-p]iod ( an electric circuit1 is giv5 by ! equation-- ,t #b7,,lc7 :]e ,l is ! inductance1 & ,c is ! capacity4 ,x c be %[n easily t ! frequ5cy n1 or numb] ( electrical vibrations p] second1 is giv5 by ! rule-- n #ejjjjjj_/777;capacity 9 micr(>ads7 7inductance 9 c5timetres777 ,= in/ance1 if we dis*>ge a ,leyd5 j> hav+ a capacity ( ( a micr(>ad ?r\gh a /\t piece ( copp] wire ab\t #d feet 9 l5g? & "o-six? ( an in* 9 diamet]1 hav+ an inductance ( ab\t #abjj c5timetres1 ! electrical oscillations ensu+ w\ld be at ! rate ( #b millions p] second4 ,any two electrical circuits :i* h ! same "t-p]iod are said to be 89 tune0 ) ea* o!r1 & ! process ( adju/+ ! inductance & capacity ( ! circuits to br+ ab\t ?is result is call$ electrical tun+4 ,9 ! case ( a v]tical a]ial wire z us$ 9 wireless telegraphy1 9 :i* ! oscillations are creat$ by ! inductive action ( an oscillation-trans=m] z %[n 9 ,fig4 #hb1 page #bga1 ! capacity ( ! ,leyd5 j> 9 ! cond5s] circuit mu/ be adju/$ s t ! "t-p]iod ( ! ne>ly clos$ or prim>y oscillation ,p agrees ) t ( ! op5 or second>y circuit ,s4 ,:5 ?is is ! case1 ! electrical oscillations set up 9 ! clos$ circuit h a f> great] effect 9 produc+ o!rs 9 ! op5 circuit ?an if ! two circuits 7 n 9 tune4 ,! l5g? ( ! wave giv5 (f f ! op5 circuit is approximately equal to f\r times ! l5g? ( ! a]ial wire1 includ+ ! l5g? ( ! coil =m+ ! second>y circuit ( ! oscillation-trans=m] 9 s]ies ) x4 ,,footnotes #a ,! wave-velocity 9 ! case ( waves on deep wat] v>ies z 7g_/#b71 :]e is ! wave-l5g?4 ,! rule 9 ! text is d$uc$ f ?is =mula4 #b ,if ,v is ! velocity ( ! wave 9 feet p] m9ute1 & ,v is ! velocity 9 miles p] h\r1 !n 7,v #ebhj7_/fj ,v4 ,b ,v 7#b71 & ,v n1 :]e is ! wave-l5g? 9 feet & n ! frequ5cy p] m9ute2 f :i* we h ,v #aih_/n1 or ! rule giv5 9 ! text4 #c ,! amplitude ( di/urbance ( a p>ticle ( wat] at a dep? equal to "o wave-l5g? is equal to #a_/b ( its amplitude at ! surface4 7,see ,lamb's 8,hydrodynamics10 p4 #ahi47 #d ,?is c easily be %[n to an audi5ce by project+ ! app>atus on a scre5 by ! aid ( an optical lant]n4 #e ,see 8,! ,spla% ( a ,drop10 by ,pr(essor ,a4 ,m4 ,wor?+ton1 ,f4,r4,s41 ,romance ( ,sci5ce ,s]ies1 publi%$ by ! ,society = ,promot+ ,*ri/ian ,k4 #f ,see ,osborne ,reynolds1 ,nature1 vol4 #af1 #ahgg1 p4 #cdc1 a pap] read be=e ! ,briti% ,association at ,plym\?2 see also ,app5dix1 ,note ,a4 #g ,a v int]e/+ article on 8,kumatology1 or ! ,sci5ce ( ,waves10 appe>$ 9 a numb] ( ,pe>son's ,magaz9e = ,july1 #aija4 ,9 ?is article1 by ,mr4 ,m>cus ,t9dal1 _m int]e/+ facts ab\t1 & pictures (1 sea waves are giv54 #h ,"l ,kelv9 7see lecture on 8,%ip ,waves10 ,popul> ,lectures1 vol4 iii4 p4 #dfh7 says ! wave-l5g? mu/ be at lea/ fifty times ! dep? ( ! canal4 #i ,see article 8,tides10 by ,g4 ,h4 ,d>w91 8,encyclopdia ,britannica10 #i? edit41 vol4 #bc1 p4 #cec4 #aj ,! progress ( ! ,sev]n 8bore0 has be5 photograph$ & reproduc$ by a k9ematograph by ,dr4 ,vaughan ,corni%4 ,= a s]ies ( pap]s be>+ on ?is sort ( wave1 by ,"l ,kelv91 see ! ,philosophical ,magaz9e = #ahhf & #ahhg4 #aa ,see ,"l ,kelv91 8,hydrok9etic ,solutions & ,obs]vations10 ,philosophical ,magaz9e1 ,novemb]1 #ahga4 #ab 8,on ! ,photography ( ,ripples10 by ,j4 ,h4 ,v9c5t1 ,philosophical ,magaz9e1 vol4 #dc1 #ahig1 p4 #daa1 & also vol4 #dh1 #ahii4 ,^! photographs ( ripples h be5 reproduc$ z lant]n slides by ,messrs4 ,newton & ,co41 ( ,fleet ,/reet1 ,london4 #ac ,"s smok]s c bl[ ^! smoke r+s f _! m\?1 & !y may sometimes be se5 :5 a gun is fir$ ) black old-fa%ion$ gunp[d]1 or f eng9e-funnels4 #ad ,= details & illu/rations ( ^! rese>*es1 ! read] is ref]r$ to pap]s by ,pr(essor ,h4 ,s4 ,hele-,%aw1 entitl$1 8,inve/igation ( ! ,nature ( ,surface-resi/ance ( ,wat]1 & ( ,/ream-l9e ,motion "u ,exp]im5tal ,conditions10 ,proce$+s ( ! ,in/itution ( ,naval ,ar*itects1 ,july1 #ahig1 & ,m>*1 #ahih4 ,a conv5i5t app>atus = exhibit+ ^! exp]im5ts 9 lectures has be5 design$ by ,pr(essor ,hele-,%aw1 & is manufactur$ by ! ,imp]ial ,eng9e]+ ,company1 ,pembroke ,place1 ,liv]pool4 #ae ,! ,fr5* ^w *elon means a /ep-ladd]-l arrangem5t2 b x is usually appli$ to an arrangem5t ( r[s ( objects :5 ea* r[ ext5ds a little beyond its neighb\r4 ,soldi]s are said to m>* 9 e*elon :5 ! ranks ( m5 are s ord]$4 #af ,see ,"l ,kelv9 on 8,%ip ,waves10 ,popul> ,lectures1 vol4 iii4 p4 #dhb4 #ag ,m accurately1 z ! #ahc p[] ( ! spe$4 #ah ,?is figure is tak5 by p]mission f an article by ,mr4 ,r4 ,w4 ,dana1 :i* appe>$ 9 ,nature = ,june #e1 #aijb1 ! diagram be+ borr[$ f a pap] by ,naval ,con/4 ,d4 ,w4 ,taylor1 ,u4,s41 read be=e ! 7,u4,s47 ,society ( ,naval ,ar*itects & ,m>9e ,eng9e]s 7#aijj74 #ai 8,practical ,applications ( ,model ,exp]im5ts to ,m]*ant ,%ip ,design10 by ,mr4 ,ar*ibald ,d5ny1 ,eng9e]+ ,conf]5ce1 ,in/itution ( ,civil ,eng9e]s1 ,may #be1 #ahig4 #bj ,reproduc$ "h by ! k9d p]mission ( ! editor ( ,h>mswor?'s ,magaz9e4 #ba ,see ,"l ,kelv9's ,popul> ,lectures1 vol4 iii41 8,navigation10 ,lecture on 8,%ip ,waves40 #bb ,see ,pr(essor ,w4 ,f4 ,b>rett1 ,nature1 #ahgg1 vol4 #af1 p4 #ab4 #bc ,?is foll[s f ! ord9>y =mula = ! focal l5g? f ( a biconvex l5s1 ea* surface hav+ a radius ( curvature equal to r4 ,= !n x c be %[n t f 7r_/#b7 7#a_/7 - #a77 :]e is ! index ( refracture ( ! l5s mat]ial4 ,z %[n lat] on1 ! ac\/ic index ( refraction ( c>bonic acid1 :5 t ( air is tak5 z unity1 is #abgc4 ,h5ce1 - #a #jbgc1 & #a_/7 - #a7 #c4 ,h5ce1 f #br771 or f is slightly less ?an twice ! radius ( curvature ( ! sph]ical segm5t =m+ ! s\nd-l5s4 #bd ,we c1 9 fact1 discov] ! ratio ( ! velocities f ! am\nt ( b5d+ ! ray exp]i5ces & ! angle ,,bac ( ! prism1 call$ its refract+ angle4 ,x c be %[n t if we d5ote ?is refract+ angle by ! lett] ,a1 & ! deflection or total b5d+ ( ! ray by ! lett] ,d1 !n ! ratio ( ! velocity ( ! wave 9 air to its velocity 9 c>bonic acid gas 7call$ ! ac\/ic refractive index71 be+ d5ot$ by ! ,greek lett] 2 we h-- s977,a ,d7_/#b7_/s97,a_/#b7 #be ,on ! occasion :5 ?is lecture 0 giv5 at ! ,royal ,in/itution1 a l>ge phonograph1 k9dly l5t by ! ,edison-,bell ,phonograph ,company1 ,ltd41 ( ,*>+ ,cross ,road1 ,london1 0 employ$ to reproduce a %ort address on ,natural ,hi/ory to ! "y p pres5t :i* _h be5 spok5 to ! in/rum5t t5 days previ\sly by ,"l ,avebury1 at ! reque/ ( ! au?or4 ,! address 0 he>d p]fectly by ! five or six hundr$ p]sons compris+ ! audi5ce4 #bf ,9 ! case ( ! p>aff9 prism ! refract+ angle 7i7 0 #fj1 & ! deviation ( ! ray 7d7 0 #ej4 ,h5ce1 by ! kn[n optical =mula = ! index ( refraction 7r71 we h-- r s977i d7_/#b7_/s97i_/#b7 s97#ee7_/s97#cj7 #afd ,= ! ice prism ! refract+ angle 0 #ej1 & ! deviation #ej2 accord+ly = ice we h-- r s977#ej #ej7_/b7_/s97#ej_/b7 s97#ej7_/s97#be7 #ahh ,see 8,cantor ,lectures10 ,society ( ,arts1 ,decemb] #ag1 #aijj4 ,j4 ,a ,flem+ on 8,electric ,oscillations & ,electric ,waves40 #bg ,see ,app5dix1 ,note ,b4 ,,index4 ,a ,act9ic rays1 #bed !r1 !1 #aia ----1 prop]ties (1 #aib ---- wave radiation1 range (1 #bfb ---- waves1 v>i\s k9ds (1 #bcd ,air1 movem5t (1 9 a conc]t-room1 #ahc ---- necess>y = production ( s\nd1 #ajc ---- p>ticles1 mode ( motion (1 9 case ( s\nd wave1 #aab ---- waves1 #ajc ---- ----1 int]f]5ce (1 #aci ---- ----1 l5g? (1 #aad ---- ----1 nature (1 #aad ---- ----1 spe$ (1 #aae ,alphabet us$ 9 telegraphy1 #bgd ,am]ica ,cup race1 pictures ( ya*ts ent]$ = !1 #id1 #ie ,am]ica ya*t1 !1 #ic ,amplitude1 #h ,anti-node1 #aei ,app>atus = detect+ electric waves1 #bcg ---- = exhibit+ motion ( air 9 case ( s\nd wave1 #aji ---- = inve/igat+ ! laws ( fall+ bodies1 #ce ,atlantic waves1 height (1 #h ---- ----1 l5g? (1 #i ,atomic !ory1 #bbf ,b ,beam ( s\nd focus$ by collodion l5s1 #aca ,beats1 ,helmholtz's !ory (1 #afe ----1 musical1 #afc ,bill[s1 #a ,bore1 #ch ,branly1 ,pr(essor1 electric wave detector1 #baa ,break+ wave1 #bi ,c ,canal-boat waves1 #ajj ,canal wave1 #cb ---- ---- velocity1 #cd ,capill>y ripples1 #dd ,*romatic scale1 #afb ,clef1 musical1 #afj ,clos$ organ-pipe1 #aga ,cl\d waves1 #cj ,coh]]1 ,lodge1 #bab ----1 ,m>coni1 #bgf ,column ( air set 9 vibration by tun+-=k1 #aeh ,conclusion1 #bhe ,concords & discords 9 music1 nature ( diff]5ce betwe51 #afb ----1 musical1 #afb ,conditions necess>y = production ( true wave 9 a m$ium1 #ae ,conductor1 electric1 #aig ,cons]vation ( en]gy1 law (1 #bc ,cons]vation ( matt]1 law (1 #bb ,conv]g5ce ( an electric ray by a p>aff9 l5s1 #bdc ,corni%1 ,dr4 ,vaughan1 #ca ,correspond+ spe$s1 ,fr\de's law (1 #ha ,cup ,races1 #ic ,curr5t1 electric1 #aic ,d ,d>k heat1 #bej ,deep-sea waves1 rule = det]m9+ spe$ (1 #aa ---- ----1 velocity (1 #aa ,def9ition ( a ripple1 #db ---- ( wave-frequ5cy1 #h ---- ( wave-l5g?1 #g ,dep? ( wat]1 effect (1 on spe$ ( canal wave1 #cd ,diff]5ce betwe5 electric conductors & non-conductors1 #aih ---- betwe5 velocity ( a wave & ( a wave-tra91 #bj ,discords 9 music1 #afb ,disp]sion ( !r waves1 #bef ,di/ances at :i* s\nd c be he>d1 #abj ,e ,e>1 p[] (1 to analyze s\nd1 #ahb1 #ahc ,e*elon waves made by a duck1 #gd ,eddies 9 liquids1 #fj ,eddy1 #fj ---- motion1 #fj ---- resi/ance1 #fh ,edison phonograph1 #adb ,ela/icity ( ! air1 #aaa ,electric circuit1 op51 #bag ---- conductor & non-conductor1 #aig ---- corpuscles1 #bbg ---- curr5t1 #aic ---- ----1 alt]nat+1 #aid ---- ----1 cont9u\s1 #aid ---- ---- en]gy1 #bae ---- ----1 nature (1 #aic ---- displacem5t1 #bba ---- en]gy1 me*anical analogue (1 #baf ---- =ce1 #bbh ,electric index ( refraction1 #bde ---- inductance1 #bad ---- in]tia1 #bad ---- oscillations1 #ahe ---- ----1 app>atus = produc+1 #bjc ---- ---- 9 op5 circuit1 #bag1 #bah ---- ---- produc$ by dis*>ge ( ,leyd5 j>1 #bjj ---- radiation1 #bch ---- ---- & light1 id5tity 9 nature (1 #bea ---- radiation-detector 7,flem+71 #bbd ---- ---- 7,mill]71 #bce ---- radiation1 velocity (1 #bdi ---- ray1 reflection (1 #bda ---- ----1 refraction (1 #bdc ---- /ra91 #aig ---- transp>5cy & opacity1 #bci1 #bdj ---- wave & air wave comp>$1 #bbc ---- ---- detector1 #baj ---- ----1 nature (1 #bcj ---- ----1 production (1 #bji ---- waves1 #ahe ,electrical or ,h]tz rays1 #bed ,electrodeless dis*>ge1 #bje ---- ----1 app>atus = produc+1 #bjf ,electro-magnet1 #aie ,electro-magnetic m$ium1 #bbj ---- !ory ( light1 #bfb ,electromotive =ce1 #aif ,electronic !ory ( electricity1 #bbi ,electrons1 #bbg ,en]gy1 #ba ----1 k9etic1 #be ---- ( electro-/atic /ra91 #bae ---- ( motion1 #be ---- ( mov+ wat]1 #cb ----1 pot5tial1 #be ----1 two =ms ( electric1 #bae ,e!r1 !1 #aia ,exp]im5tal tank1 uses (1 9 %ip-design1 #hf ---- tanks1 #he1 #hf ,exp]im5ts illu/rat+ surface t5sion1 #dj1 #da ,explosion ( guns he>d at great di/ances1 #abj ,f ,fall+ bodies1 laws (1 #ce ,fi%1 motion ( a1 #fg ,flame1 s5sitive1 #abg ,fl[ ( liquid 9 non-uni=m tubes1 #ff ---- ---- 9 tubes1 #fe ---- ---- 9 uni=m tubes1 #fe ,fog-signals1 #abc ----1 influ5ce ( w9d ^u di/ance at :i* !y are he>d1 #abd ----1 p[] absorb$ 9 mak+1 #abe ,free p]iod ( vibration1 influ5ce ^u =ce requir$ to move a body1 #aea1 #aeb ,fr\de1 ,mr4 ,william1 #ha ,fr\de's exp]im5tal tank1 #ha ---- exp]im5ts at ,torquay1 #ha ,g ,gamut1 #afj ---- ( !r waves1 #bfj ,gravitation wave1 #dj ,gr\nd swell1 #ca ,h ,h>monic curve1 #ajh ---- motion1 #ajg ,h>monics1 #aef ,hele-,%aw1 ,pr(essor1 #fb ---- ----1 discov]y ( means ( produc+ irrotational motion 9 liquids1 #fc ---- ----1 inve/igations on liquid motion1 #fc ,helmholtz's inve/igation into nature ( musical tones1 #afg ---- !ory ( discords & concords1 #afe ,h]tz oscillation1 #bjg ,h]tz's rese>*es4 ,exp]im5ts ) electric waves1 app>atus =1 #bcd ,hughes1 ,pr(essor1 inve/igations on electric waves1 made by1 #baj ,human e>1 !1 #aha ,hydraulic gradi5t1 #fe ,i ,illu/ration ( diff]5ce betwe5 wave-velocity & wave-gr\p velocity1 #bh ,inaudible s\nd1 #adj ,index ( refraction1 #ed ,inductance1 #bad ,induction coil = wireless telegraphy1 #bfg ,ineffici5cy ( pres5t me?ods ( manufactur+ light1 #bfe ,in]tia ( ! air1 #aaa ,int]f]5ce ( air waves1 #aci ---- ( electric rays1 #bdh ---- ( ripples & waves1 #dh ,irrotational motion1 #ei ,k ,kelv91 ,"l1 inve/igations on %ip waves1 #gg ,k9etic en]gy1 #be ,krakatoa1 eruption (1 #aaf ----1 s\nd produc$ by ! eruption (1 #aaf ,l ,laplace1 calculation (1 conc]n+ s\nd-velocity1 #fi ,law connect+ velocity & pressure 9 liquid motion1 #fg ,l5g? ( wave1 def9ition ( ! t]m1 #g ,light1 velocity (1 #ahg1 #ahi ,liquid fl[ 9 con/rict$ tube1 #ff ,lodge1 ,sir ,oliv]1 coh]] inv5t$ by1 #baa ,long wave1 #g ,longitud9al waves1 #g ,lum9\s effici5cy1 #bfd ---- rays1 #bed ,m ,magnetic =ce1 #bbh ,major ?ird 9 music1 #afa ,m>coni coh]]1 #bgf ---- a]ial wire1 #bff ----1 exp]im5ts ) wireless telegraphy across ! ,atlantic by1 #bhj ---- sy/em ( wireless telegraphy1 #bgf1 #bgi ,matt]1 #bb ,maxwell's electro-magnetic !ory ( light1 #bfb ,me*anical explanations ( electrical ph5om5a1 #bbb ,me?ods ( manufactur+ light1 #bfe ,m9or ?ird 9 music1 #afa ,model illu/rat+ longitud9al wave1 #aad ---- ---- nature ( an air wave1 #aac ,models1 illu/rat+ wave-motion1 #e1 #f ,morse alphabet1 #bgd ,motion1 h>monic1 #ajg ----1 irrotational1 #ei ---- ( wat] 9 sea waves1 #c ----1 p]iodic1 #ajg ----1 rotational1 #ei ----1 vortex1 #ei ,movem5t ( ! air 9 ! case ( a s\nd wave1 #aab ,music1 !ory (1 #aei ,musical beats1 #afc ---- scale1 notes ( !1 #afj ---- tones & noises contra/$1 #aaj ---- ----1 %>p & flat1 #afa ,n ,natural p]iod ( vibration ( a body1 #adh1 #aej ,node1 #aei ,non-conductor1 electric1 #aig ,non-resi/ance to body mov+ ?r\gh p]fect fluid1 #gb ,o ,octave1 #afj ,op5 electric circuit1 #bag ---- organ-pipe1 #aga ,optical pro( t a s\nd+ body is 9 vibration1 #aje1 #ajf ,organ-pipes1 con/ruction (1 #afi1 #aga ----1 di/ribution ( air-pressure 91 #agb ----1 ov]tones (1 #agc ----1 relation betwe5 l5g? ( pipe & l5g? ( wave1 #agc1 #agd ,oscillations1 electric1 #ahe ---- ( a /ret*$ /r+1 #aed ,oscillator1 ,h]tz1 #bjg ,oscillatory electric sp>ks1 photographs (1 #bjb ,ov]tones1 #aef ,p ,p5dulum1 iso*ronism ( !1 #adi ,p]fect fluid1 #ei ,p]iodic motion1 #ajg ---- "t1 #i ,phonograph1 action ( !1 #adb ,photographic /udy ( ! production ( waves1 #af ,photographs ( ripples on a m]cury surface1 #ea ,plane wave1 #ee ,pot5tial en]gy1 #be ,p[] requir$ to propel %ips1 #ij1 #ia ,prism = refract+ a beam ( s\nd1 #acf ,production ( a s\nd wave1 #aaa ,q ,quality ( s\nd1 #aae ,r ,radiation1 electric1 #bch ----1 nature (1 #bfc ---- ( en]gy f ! sun1 #bhd ,rayleigh1 ,"l1 an ac\/ic exp]im5t ) an op5 pipe by1 #agd ,receiv] = wireless telegraphy 7,m>coni71 #bge ,reflection ( a beam ( s\nd1 #acb1 #acc ---- ( an electric ray1 #bda ---- ( a wave1 #ee ---- ( ripples1 #df1 #dg ,refraction1 explanation (1 #ec1 #ed ---- ( a beam ( s\nd1 #acc1 #acd ---- ( an electric ray1 #bdc ---- ---- by an ice prism1 #bdb ---- ( ripples1 #eb ,refractive index1 #ed ,relation ( wave-velocity & wave-l5g?1 #i ,relay1 telegraphic1 #bcf ,resi/ance curves ( %ips1 #ib ---- to a body mov+ ?r\gh a fluid1 causes ( !1 #fh ,resonance1 #adh ----1 an exp]im5t on1 #aeh ,ripple & wave1 di/9ction betwe51 #dj ---- m>k1 #cj ----1 reflection ( a1 #de1 #df ----1 sci5tific def9ition ( a1 #db ,ripples1 #a ----1 app>atus = produc+1 #dc ----1 int]f]5ce (1 #dh ----1 int]sect+1 #di ---- 9 ! air1 #ajc ---- on a lake1 photographs (1 #ai ----1 photography (1 #ea ----1 by ,j4 ,h4 ,v9c5t1 #ed ---- produc$ by /one ?r[n into wat]1 #ai ----1 velocity (1 #da1 #db1 #dc ,rotational motion1 #ei ,russell1 ,scott1 ,mr41 #ha ---- exp]im5ts (1 on canal-boat waves1 #aja ,s ,scale1 musical1 notes ( !1 #afj ---- ( equal temp]am5t1 #afb ,sea waves1 #b ---- ----1 motion (1 #c ---- ----1 relation ( velocity & l5g? 9 case (1 #aj ,semitone1 #afa ,s5sitive flame1 influ5ce ( s\nd ^u a1 #abi ,sev]n bore1 #ch ,%amrock ,,ii41 trials (1 #ig ,%ip b[ wave1 mode ( production1 #ge1 #gf ---- design1 #hg1 #hh ---- ----1 ! problem (1 #gc ---- models1 ! te/+ (1 #he1 #hf ---- resi/ance1 ,fr\de's law (1 #hb1 #hc ---- waves1 #eg ---- ----1 complete sy/em (1 #gh ---- ----1 v>i\s sy/ems (1 #gc ,%ort wave1 #g ,s9e curve1 mode ( draw+ a1 #ajh ,s++ flame1 #age ,sir51 #abc ,sk9 friction1 #ei1 #fh ---- ---- = v>i\s classes ( %ips1 #ia ,soap film ?r[n into vibration by air waves1 #ade ---- solution = mak+ bubbles1 #add ,solit>y wave1 #bf ---- ---- & wave-tra91 diff]5ce betwe51 #bf ,s\nd1 & music1 #adg ----1 causes 9 v>iation 9 quality (1 #adb ---- due to air waves1 #ajc1 #ajd ---- l5s1 me?od ( mak+ a1 #acj ---- prism1 #acf ----1 quality (1 #aae ---- signals1 #abc ----1 velocity (1 9 v>i\s cases1 #abf ,s\nd+ body is 9 vibration1 #ajd1 #aje ,spe$ ( a fall+ body1 #ce ---- ( s\nd1 #aae ,/ation>y waves1 #aee1 #aef ,/one fall+ into wat]1 photographs ( a1 #ag ,/ream-l9es1 #fd ---- ---- r\nd an ovoid1 #ga ,/roh viol91 #agi ,/ructure ( ! human e>1 #aha ,surface t5sion ( liquid1 #dj ,t ,temp]ature1 effect (1 on s\nd-velocity1 #aah ,tesla coil1 #bje ,tidal wave1 #ch ---- ----1 spe$ (1 #ci ,tides1 #ci ,"t ( vibration ( a /ret*$ /r+1 #aed ,tone1 #afa ,torp$o1 motion (1 9 wat]1 #fg ,transf]5ce ( wave-motion1 #bg ,transv]se %ip wave1 #gi ---- wave1 #g ,true wave1 conditions = produc+ a1 #ae ---- ----1 def9ition ( a1 #ab ,tubes ( fl[1 #fd ---- ---- 9 a liquid1 #ga ,u ,utilization ( ! !r1 #bhd ,v ,v>i\s k9ds ( resi/ance to a body mov+ ?r\gh a fluid1 #fh ,velocity ( electric radiation1 #bdi ---- ( light1 #ahi ---- ( sea waves1 rule = calculat+ !1 #aj ---- ( s\nd1 h[ affect$ by temp]ature1 #aag ---- ---- 9 diff]5t gases1 #abf ---- ----1 influ5ce ( specific heats ^u !1 #aai ---- ----1 measurem5ts ( !1 #aaf ---- ----1 !oretical det]m9ation ( !1 #aah ---- ( s\nd wave1 #aae ---- ( waves 9 wat]1 air1 & !r comp>$1 #bhc ,v]non ,boys1 ,pr(essor1 in/ructions by1 = mak+ soap solution1 #add ,vibration rates ( musical tones1 #afj ---- ---- ( v>i\s !r waves1 #beb ,vibrations1 =c$1 #adi ----1 free1 #adi ---- giv+ rise to musical tones1 #afj ,v9c5t1 ,mr4 ,j4 ,h41 #ea ,viol91 improv$ by ,mr4 ,augu/us ,/roh1 #agi ,viol91 /ructure (1 #agg1 #agh ,viscosity ( liquids1 #eh ,vortex motion1 #ei ---- r+ 9 air1 #fa ---- ----1 production (1 9 air1 #fa ,w ,wave amplitude1 def9ition (1 #h ----1 causes ( break+1 #bi ----1 electric1 nature ( an1 #ahe ---- frequ5cy1 #h ----1 gravitation1 #dj ---- gr\p1 velocity ( a1 #bj ---- l5g?1 #g ---- l5g?s ( v>i\s k9ds ( !r waves1 #beg ----1 longitud9al1 #g ---- motion1 #b ---- ----1 def9ition (1 #d ---- ---- model1 #e ---- ----1 model = illu/rat+1 #ac1 #ad ---- ----1 v>i\s k9ds (1 #d ---- produc$ 9 a canal1 #cc ----1 reflection ( a1 #ee1 #ef ---- resi/ance1 #fh ,waves1 #a ---- & ripples 9 ! !r1 #bcb ----1 conditions (1 = int]f]5ce (1 #di1 #ej ----1 electric1 #ahe ----1 int]f]5ce (1 #dh ---- 9 ! air1 #ajc ---- made by canal-boats1 exp]im5ts on1 #aja1 #ajb ---- made by %ips1 #eg1 #eh ---- on a sn[ surface1 #ca ---- on cl\ds1 #cj ---- produc$ by high-spe$ %ips1 #gi ----1 refraction (1 #eb1 #ec ----1 sea1 #b ----1 /ation>y1 #aee ---- tra91 #bj ---- ----1 velocity (1 #bj ----1 transv]se1 #g ---- velocity1 a rule = det]m9+1 #i ,w9d1 influ5ce (1 ^u di/ances at :i* s\nds are he>d1 #abj1 #aba1 #abb ,wireless telegraphy across ! ,atlantic1 #bhj ---- ----1 app>atus =1 #bfg ---- ----1 explanation (1 #bgc ---- ----1 ,m>coni's sy/em (1 #bfi ---- ----1 me?od ( conduct+1 #bgd ---- ----1 transmitt] =1 #bga ---- ----1 utility (1 #bha ,wor?+ton1 ,pr(essor1 photographs ( spla% ( drop1 #af1 #ag ,y ,ya*t-design1 object (1 #if ,ya*ts ent]$ = ! ,am]ica ,cup race1 pictures (1 #id1 #ie ,"y1 ,dr4 ,?omas1 inve/igations (1 on int]f]5ce ( light1 #aij ,,! ,,end4 ,,pr9t$ ,,by ,,william ,,cl[es ,,& ,,sons1 ,,limit$1 ,,london ,,& ,,beccles4 ---------------------------------- ,end ( ,book ---------------------------------- ,transcrib]'s ,note 7cont9u$7 ,errors 9 punctuation & simple typos h be5 correct$ )\t note4 ,v>iations 9 spell+1 hyph5ation1 acc5ts1 etc41 h be5 left z !y appe> 9 ! 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s9 ( t expression is requir$ x w\ld be r5d]$ unambigu\sly z s977x #a7_/b74 ,= consi/5cy ?is also means t a simple s9 function t w\ld normally be display$ z #8s9 x' w in/ead be r5d]$ z #8s97x7'4 ,a l>ge radical 77 symbol is n available ei!r s 9 ord] to make ! radic& expression unambigu\s a simil> approa* to ! above is us$4 x #a ,?us ! squ>e root ( ! fraction ---------- is r5d]$ 9 ?is text z #b 77x #a7_/b74 ,aga9 ?is means t1 = consi/5cy1 ! simple squ>e root (1 say1 ! natural numb] #e1 :i* w\ld normally be display$ z #8#e' w in/ead be r5d]$ z #87#e7'4 ,9 o!r expressions & equations "s additional bracket+ may h be5 add$ to make ! mean+ cle> & unambigu\s or consi/5t ) bracket+ z us$ 9 imm$iately surr\nd+ equations & expressions4