new fundamental experiments upon the collision of bodies. by mr. john smeaton, f. r. s. in a letter...

New Fundamental Experiments upon the Collision of Bodies. By Mr. John Smeaton, F. R. S. ina Letter to Sir Joseph Banks, Bart. P. R. S.Author(s): John SmeatonSource: Philosophical Transactions of the Royal Society of London, Vol. 72 (1782), pp. 337-354Published by: The Royal SocietyStable URL: http://www.jstor.org/stable/106465 .

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337 ]

XI New A4ndamental Experimlents upon tha OIIifon of Bodve. ty Mr John Slneaton, F. R. SO in a Lexter tra S°r oI+h-BarlksS B4r* P R. 5;

Read Apxil I 8 I 7820

T0 SR JOSEPH BANKS, BART P R S

S I Rs

THE fubjeEts of the illclofed traR have been the ol#PeEt of X my collfideratiol-l for matly years paIl; arld as they jcon

taial fome matters ttlat have llot only been variou{ly reaSoned about, but variouny concluded uporw; if what is contained therein Ihall appear of fuch a tlature as either to eRabliffi trutht aS it appears to £ne; or to prompt fome more able perfiotl in l^eviewing rlle fubj-ed'c to {hew W}lAt liwks in my chaitl of reau fonillt therwotl are defeAive, fo as to eStablith the whole doErine of moviwg bodies upon olle plain collfiIlent leaI;s, my end will be equally allfwered in offeritlg tlleln to you, to be laid l)efore the Royal Society, in cafe you ihall thitlk tllat the iln portallce of the fiubjeEt thall merit the fame: ftlrthermore I hope tQ be forgiven, if in fome parts of this paper I have exprefl>ed nay-felf svith more pointednefs than I might have dorle, ir I declare9 that it uTas folely OWillg tO lny earneR NG.S that tlle fubjeS of mecllallic tnotiolls and powers ffiould le fully and freely i3zve{tigatee1, and ellablithed UpOI) grounds tllat {llall lle uncolltrovertilule

I have the llollowr to be &cX Gray s-InIl

April I8, I 78.2*

y

Votix LXXII. I.



.Rfe38 M:r. SMEA1tONsS anUmeatal Prisc@s

IT is uiliverfally ackllowledged, that the frI} fmple pritw-

* > * * * 4 * *

clples or iclence callnot be too crltlcal y examlne 7 ln or (ler to tlacir lJeilag firmlJr efl:al)ltthed; more ebecially thofE lstllich relate to tlle p:raaical and operatIve partss of medha- -lliCS, upon which mtlch of the adive bufilleSs -of matlkilld depends. LA fentinleIlt of this kind occafiloned my traA UpOll

Mchvc Power, wehich was publithed in tlle PhiloSophical TratlEdiolls, zzol. LXVI. for tlle year I 776. \Vhat I Ilave llOW

tc) osSer svas inte1lcled as a fipplement theretoX and tIle expe rimellts were thelln in part, tried; lout the colmpletioll thereof sras deRrrad at tlldt tinze partly Dom W81]t of leiXle; partly to ave8id too great a legtll of tlle paper itSelf t and partly tv avold tTle brislglIg forsrard too tnatly pOilltS at ollce. My preferlt perpoSe is to lllexnrS that t:lle true dodl:rille of tlle col

oz qf boXs halags as it urere UpOll the faime hooka as thc doEt:ritle of the gradual geIleratioll of IllOtiOI) Sotn reR) colafi- (3ered itl tlat paper > that is that mThetller lJodies are put itltO gradual lnotion alld ulliformly acceIcInte(l Som reR to any

giltell velocity; or are pUt ill mOtiOli ill it]R2IltAlleQUS

zlSatlilerS sv-1-wew I-)odies of ally T;ind firike o1le allotller; the motion9 or futn of tlle motioIas produced, 11as the Iartle relation to tnech.aaic posver tTlereill t(lefiSledS srilicll is neceIIary to proo (ltlce the 1notiorl defiloeel To prove tlais, atld at the rame tilne to fllow fome capital- tniRakes ill pritlciple, whicl lanve lJeetl @.Svd as itldiI}utable trutI-ls L)y le1l of great learlw llg iS ttlle rtaSVXl Of tNy I10XV purfutag tlle fame fuUe&.

I do not neatl to pClillt QUt tile particular naiR-akes wllich la^.ve lzeell made by particulat Inen7 as t:hat svould lead me itlto too gteat a lellgth: 1 t1ll therefblXe cGIltellt mytetf svith olz- 1WIvl13<XS tllat ttae laws of collifioll) which have l)eell inlrefiiw ()5ateu ljy ->-latilernatical RiloSophersX a}re priIlcipally of thlee kstads S ?ZZ t;tO1E rola,titlg to bodiPs ;re fedly e1vs X to l)adies

peridEly



a¢pOn /zE Colli,/^On ;?f t BODiLSS. 339 peridtls7unelal}cX aIld peri4L;y/5S.S; aIlCi to I)Q41CS peridtly

. .

uIlelaRic aIld p<.rfeEtly bard. W5o avoidprol.X.X.y l -.Sall coilfildel

in each only the limple caSe of two bodtes which ae equal in weight or qualltity of matter fl:rikirlg otwe at<lotiler. RebeEltlb thofe wilich are peridly elaRic, it is utliverIElly agreed that tvhen-two filch bodies fErike one another t30 tnotton ts loR; but that ill all cafes, what is loR by one is acquirexl lv tlle other: alld hetlce, that if an elaRic body in motiotl Itrikes a-Xether at reR, llpOIl the Rrie- the ¢irmer will be rcduced to a i;\4.te of reR, atld tile latter will fly oF with at1 eSqunl velocity.

II1 01ike mantler if a Ilon-elafl:ic /H body IRri3tes anotEler al: reIl, they neither of them remain at reR, lout proceed together Som the pOillt of collifion with exadSy olue half of the vtslou city that the firA had before the IEroke; this is al UlliVS^-

fally allowed to be true, alld is fully proved by every good experiment upon the I;eEt.

3tefpe&;llg tlle third fpecies -of body that is, thoIW tLIat are won-elallicS alld yet periAly hard; the laws of motioll relatiSlg

tO them, 5 laid doxvn ly olle fpecies of philoMphersX T1aVe een lFeJed:ted by another; the latter alledgillgs that tllere alve wo fuch l)odies to be fbulld ill llature wllereotl to t.ty tlle experi- tnent; but tlzoWe wllo have Jaicl dosvIl and adlg;lled tl-we t!rEtrilre that would attetld tEle collitioll of bodies of tllis! liitld (if tcy could be itlIld) have ulliverfally agreed tl¢lat if a 1lotl-eXctliic Aard body svas to firlke another of theX lme kitld at r*>lRX tl-;at itl the iame tnanner as it agreed concertiitlg laotz-eltftc foft bodlesS they Lleither of tt}etn srolllcl remain at rcL}) l)tlF wotlld in like imallner procced from tllC pOillt of collifion ssrith t<gn21v one lialf of the vclocity that tlle firft had befbre the {troke: ill fhortS tlley lay it doss'tl as a rule attellditlg all norl-elaRit bok3iess whether hard orX fofE, that tlle vcloity affer the- firelie vill

Xr v , l.)C.



4O SMEATONtS FanzetaS Etrzens

}e tEle f)tne in bothS fviz. are hatfs of the velocity of Ethe origi+ 21 firiklng boZ. J0Iele i-s tleteilre tlle aXulnptioll of a pritlciples svhicll i

reality is proved !y tao experiment, tlor by any-ir (ledlld:ion O- rtaroll t}lt I kllOW Qg t%+ that tEle vclgity of Ilontelafiic t;rd lzotlies aRer the Rroke muR fkg vl:le Ame as that refulting Svm the firoke of nonwelaRic:@ bodies; and the queRion notJr isS wherlacr it is true or not ?

Here it may be ̂ ?ery pUroyerly afked, what ill efiEts Ctll

reIMlt to pradeical men, If philOphers {hgld ma wrong concerxlin-g the efiEts of what does not exil} iu nature, fince the praAical men call have I10 ruch materlals to work upon or rnigudge d ? But it is anSweredS that thBy svho lEr at1 equa lity o-f e@&s Sbetween the two brts may Sorn thellce be milled themfel+7es, and in caliquenx millead pradrical men in the}r reatIl1ngs atld concluiRons c>rtling the fort with which tT}ey have abutlda-tlt concerIl, to wit, the non-elaItic- K lxodxes, of which water is oney whwh they llave much to do wit}w in their daily pradice.

Previous to the teiIlg my eXperimeIlt OIl- mxlls I 1levex had doulJtect the truth of the dQ:trines that tlae falne velocity re fillted f}om the Ilroke of both Ibrts of non-elaft;c bodies, trut the tr}al of thoIb eXperiments made me clear}y ke at leaIt thB rlcollclufiveI1efi if 1ot the filfity of that (3odrllle b£cauSe I

found a reilt whic! I did IlOt expeA to hEave ariren from either irt; anc3 for the whicl1 wl1en it apwared Dom experime11t, I

could 1ic a ibRantial reaSon hy it Ihould take place iI1 011e

*fortS and that it was impadible tllat it could take place i-n the other t fb1 lf it dsdS the bodies copld not llave been perfe£t1y harg which.would be contrary to the hypothefis Of this deduEtion- I have given notst in my fiid trad on millsS pub-

lifhed



tpos the CollEfot ff Bodies 34r Iiflhed lI1 the EliloXhical T>ral;ions, vol. LE. fg the year }759-$

lt may alSo be faid, that fi1]ce we have n-o bodies perEe&:ly claRlc or perfMtly unel-afl;ic andAoft7 why lBould sve expe& and bodies per-fedly utlelaRic and hard ? Why ma9 I]Ot the eSeAs be fuch as {hould- reSt fiom a: filtpofotion o-f- their 13eillg zmpert #Bly elaF joined with their being werfsSly Spard? 13ut here I tnuR oSferves that tlze fiappofition appears to be a contrao fldiAion iEl terms.

We have-lsodihes which are S nearly perfieAly eIaRicX tbat the :law-s may be very sve11 deduced and confirmed 13y tlaem; alld the fime olzta-i;ns with refpeA to llwotl-elakic vw boc3ies ; but-con cerllitlg boclies of a mixed nattire, which are by fir tlae greatetE Rum13er7 Ib lir as dacy are wYanting ial ellicity, they are XJi atild- brvife, ield) or I-eate a mark-- i-tl -collifon; aizd fo far as t-hey are not perD0edly foft they are elallicX alld obServe a-lmix ture of the law relative to etch ; but impel^fieEtly elattxc bouliesX -£nperfe£lly hard come sn reallty under tize Jafses defcrzptzav as the former mised bodies: for fo ir as- they are imperfedly hard they AIt foft andL either rwifie and yield7 or leave a malk in the firoke ̂ atld fo ir as they sratllt pRer-fed ekfi-ic Xtya t^wey are non-elaRlc; that is tcy fay, they are bodiesS imperfieAiy claIlicg and irrAperfe&;ly Soft o alld itl fid I- llave twe;7er yet iSte any bodies hut what come utuder t11Xs deSc:ptiotlD I:t Iveerasn thereforeS that rebeding the b4rdnMs of bodies t-hey diEer ill degrees of it, ia l?roportiotl ass they llave a greater degree of tenacity- or cohe{;on > that Ls a*e rther-removed fr<3rrl perfcA

* '; The effe2, therefore of overfilot wheeIs>. un-ct:er tht fime cixcumEance of &t quantity axld 11 i5 at a ledilm- clouble to that of tX1e IlIl-erfilot: and as a

4; contiquence- thereofg, that ton<-ela2fit bGdtes whrt &Hz?s<g bXy {heit izpzzpor colZifr, 4 (ommsnicate otby a pare of thrits or;(t,itale potUer; theh cather part beitzgSfpent in

4 vhaz^gag; tA>$Z+ 4¢vrx o COfXtXC£ 8< 27erak<.' Phiio TI anE vo1 LI. p 1- 3e-

YftueS



43 >. SMEATWS Sn&AreazfS f^4g*X;Xer;

wifinefs at the farlle ttirne t:hat their elaltic bri}zgs, g fir as -thev ;reacll are very IlifF; atlcl hence snre may (by«tlle way) con- clude,- tSwat the fime niechanic power that ls required to thall8;e the figtire ili afirs2aXl akgee wof thoS lsodles that l-lave the popiar appellation of bard bodiesS wlould chanWge it itl a great degree itl tI<oIE - bodies -that approach towards bfttwefs - by hav ilg a fmall degree of teliacity or cohefion. In the foriner kind we tnay rank tEle harde-r Izindvs qf cv xroty -atid itl the latter / ezpered c.

Whiie the plwiloSop-Ilical world was divlded by tlle dibute . .

about the old and new-e+X:nzoa a$ it satas called, cotlcernillg tTwe powers of boclies ill tnotic>n) ill proportion to their difEerent veloci- nes: tho<Se who held tilt oId opillion cotiteliding that it was as the srelocityJim.p+7 aIked tiloIi of the twew, HosvS upon their principles tlaCy sNtould get rid of the coticlu;fiolls ariflng So tile dofErille of unelaSc peri&ly- hard bodies > They repliedi tRhey found tao ich bodies In IlatulXe, arld therefbre dil noat

. .

coneern themlblves about-tilem On the otherhalld tholi of the ntw opiXwlotl afked thote of the old, How tiley would account ir tlae cafe of notl^elaIlic bA lsodies svlaere accord- illg to tini tlle whole motloll loR by the Rl-ikilag l)odY VVsIS

loetained in t.lle two after the Itroke (the two lsodies snovilag together witil the half velocity) tElOugh the tsvo llOll- elatic lsodies 1lad leen bruifed and chatagedotileir figule by vlle

Ilroket, f8r if lao tnotion was loI}s the change of-figure muIt le atl efi& svitlolout a cauSe? To olviate thi§, thoWe of the oId opitlion fbrioully fet about-provilig7 tlaat tile todies migllt cluatige riltir figtlrev svithout ally lofs of motioll i< either of the lEriR;ing bo-die-S-.

Neither of theSe atlfwers have appeared to nae fatisE.lAvryS

ebecia-lly fiIlCe my mill experiments: br with rebed to the .z5r{}> 1t is rlo proper argulmellt to urge the impofiibility of find-

z i}ES



uWn the GllEon c?f :Rodies. 343 * .. . . ^ . . *

lllg the- proper materlal tor Atl eXptRlmell:t 111 anier to a eCOI1

clufionbdrawn from:an al)RraEidea. On the pther hatldS if it catl be thewn, that ie figure of a bodyicala te chalzged,< with at a poMWerJ then by the fime law we mi«t be able to make a fbrge hSmwer work upon a mati- of IbE irouls without a-ltr other: power thallJ that necelEary to overcome the friAioll- re- fiRance and origillul vn tnertMs (?f-the parts of tlle machille

. * . r * * *

to e- put ln motlon : tor as no progretilve rnotloll ls g:wll t le

maii of irowlzy the hamrner(it beitlg fupported by the atvil)* no posver call be expcnded that YVay; and if nolle is loIt to twhe hamuler firom cilatlgitlg the figure of the iroll dich is t.lle otllv eSed pioduced? then the w hole power muIt reficie i flle hammer: atld it weould lump leackSagain to the place fioln hich it ills uR itu the me matliler a-s if it7ill upotl a lsody perfidly elaIlicS upon svhich, if it did fills thecaS would really llappell: the po* therefore> to wo-rk tlae hamtner wotllcl le the I)mes whether! it i11 upotr;atl elaftic ar ilotl-elaftic body ; AI1 iden rO ve contrary to a11 experiellce atld estetl apprehtk lion, of lJoth. tlle philoIbpiler ancl vulgar artift that 1* Iha t . . + . .-

here leave 1t tO;ltS n COIlE tinllatIOIl*.

As nothitags llowever, is Io convi1wcing to the mi1ld as expe rlmetlts-olvious to the Senfess I wase very defirou-s of COIltfiVitlg

an experilnent itl: poillt; alld as I fiw no hopos of fitldillg ma£ ter to luake a$direH tspertncllt I tVurned my- mllld towalOds a-} irldireEt one;- fo clrcumfcrlbed, hosrever ao to prove incon- teIlalLulyX that tI<e rtiMlt of tlle firoke of- two lOtu-elaIlic per tedly hard bodies coulul not 1At the 1itne as wouid -leilt fi-om- the col3ifiotwn of two- fofE olles; tlwat isS if i£ CA11 t)C brv X

proved t}lat co7e haof the origilaal ]ror is 1oR>itl t}se firoke of foft bodies by tlae thange of figule (sI.S WSS very RrOtluly figgeRed lly the rnill experiiolents) > tliwetl {iIl£e l}Qv fUl Iops-

.



344 - - Mr. SX4IEAtONtS damSZ mgene cail llappet itl the collifion of bodivs perfidly ilardJ the reiit

aldconiquence of fuch a firoke muR be mrent. The coafeqllence of a Aroke of bodies periAly hard 6u£

roid of ela:Rictty,, muI} doultleX l)-e di-fferellt from that of bo dies perfedly el@c: for having 1lo lprillg the botly at reR could nor be driven oflS tll Ythe velociSy of- the Itrikitlg l)ody, br that is the collfequenc of the ition of the fpring or ela{tic parts letween ttleals as svx11 be Ihewn itl the refult of tlle expeo rients; tlle firiking body will therefore-tlot be Ilopped alld as tlle tnotiorl it lolEs mnIt be commutlicated to the other} firorn the equality of aftion and re-adtiot1, they slYill lJoth proceed together, witll a11 equal welocity, ASvitl the cafe of Iloll-eldic {oft bodies: the quettioIls therefbre, that remaills is, what tElat

sueZoclfy mV be It muR be grea-ter than that of the llotw-

elaIlic loft bodies, becauS& there is 1lo mechanical power loR in Xthe Rrok&. It mul} be leIi than that of the firikitlg bodye

becauIb; if equal iniRead of a logi of motlon by the collifioll, lt svill be cloubled. If; thereSbre, non-ela{tic foR bodies IoSc half tlreir motion, or mechatliccll power ly change of figure in colliiion and yet proceed together tvith hsalf the velocit a1ad tlle noil-elaRic hard bodies call lofe none in any marlne vr31atevers tlletz, as they muR move together their velocity snu{} be fuch as to prelirve the equality of the naechallic posver, uxifireg after the Rzooke the fame as i-t svas before it

For example, let the velocity of the Ilriking body befbre tlle IlroVe be 20, and its mafs ol quantity of matter S; thelz09 accordig to tlle rule deduced from the experitnents i}l the tradt o Cdnf*¢ PoMSer (ie exp. third atld itlr-t}l) tlzat pover svill be expreflexl by zo X Ao-oo w-hict-w x S _ 3zoo; at3d if half of

it is 1wIt ttz the Rroke, in the cak of notl-elaflic Coft bodies it wo11 be 1*ecitzced to t69O; :wllicAl e I *6 tl-le doalble qualatity of rnatter u-ill give I0O ir tlle kuare of tlleir velocity; tE<c

liuare



Vpon tDe Gllifon Cf Adits 345

hiare^root of svllich lDeiIlg t*e, will be the velocity of dle tsvo

non-elaItic foft bodies afier the Ilrokes being Jull one half of

the origital seloct as it ts conRantly bund to beF But it

the non-elafiic hard idies, no power beirxg-loR in the firokes the mechanic power will remaill after it^ as bHe it7 - 3zoo; this in like mantler being divided by I 6, the double quantity of rnatter,- will give 20O @ the uare- of t-he veloce, the

guare root of which is t 4J I4, &c. br their velocity after the firoke svhich is- tb 10 the velocity of the nolz-elaRic ik bodies after tlje Itroke as the fquare RQ0t of 2 tO I > or as -the diagontal

df a<Square to its fide

It remains therefbreznow to be ptoved that prec-ifely lanlf

of the nechatzic power is bf in the colliIioll of 1loll-elaLlic fE

-bodies-; for which purpofe tey mind IiggeReel the fbllowing rreflediolls. Ill the collifion of elaItit botlles the ofteA feenW

fIlgly illlntaneeus is yet perittn-ed in tth7Ze; durillg svhich time the Ilatural Ipritlgs refidillg ill elaffic ledies alld wh-iclo conRitate them !'^i&1 are betlt or irced till the motion of

the Rriking body is divided between itSelf atld tlle lJodY at re(t >- atld ill this Rate the tsro bodies would then proceal together as n the caSe XOf lloll-elaRic fofsc bodies; lzut as the I}rings svill

lmmediately reRore themSelves ill an equal titne all(l witll tlle

-Xame degree of xmp>ve fArce wherewith they Nvere belt in

this Are--alhiorl the motioll that remaixled in the IlriR:ing bodst

tvill lje totally deItrtecl -alld the total exeltion of the twe brings comm>unicated ta dle original relliXag bOdyg NVill caui

t to fly off svith the fatne VC1QCitY wherexvitll it \¢Y2S R1 vlcks Upo this idea if sve could coaRruA ra couple of lJotlies i

i*ucTl a mray that they Ilaould either aft as boklies cridly e]>lftic s

or kthat tlleir brila;s flwoul(l at pleaiire be lsoolied ua X etailwed ar prevetltetl h om reRel+-Xtwg theluIelvesS svhelt at t<ezle extrerne degree of l)etldillg ; and if the l:J£>die.s uader tIleI:e

Sol)* T.XQW1le .-2; jZ circlu<*



3346 ildr. SXAtQnNS 9sXStS>/ E<5erxmvtZs

bodies then it would be provedf that one half oiS the meclaaZ siCesl power, tefiding ln theiRrikin$ b?dy would be 1QIT ill theR adion vf mItiXion; icauSe thesisnpulvc brce or power of thQ

*sw

brinwg 1Il its teRitutwll beitg cut ofW ox IB@etaded fion a&;tag} 1wicll is equal to t:he i)VXYX itC¢. Of pOWRI' tO bend it (an

whsich a1W1e has beeIl employed ta cmptlicate motion Som one iC to the Qther) it would make it eviden.t that olle half of the impulfive irce ls loR iN the aEion as t11e ot}uer half remain+s P&vd e ;11 tlle @rugs. It ali bllows as a ctervS crsvs

j?a$ceS that be the iInpulfive power of the 0?rilag;s svhat Lt

}nay Som firIrt to IzIl, yet as one half of the tme of tlle adiow is ly this mealls cut o; irl this rn- alfW it will fiolt 1e3w- that one Iwalf of the mechanic power is deRroyxd; or sathery i.t] this cai retls lockedS up in th& frings, capabe of beillg UfetHdenever thqam t atliberty and of producing a-ffeXh mechanical eids equivalent to the rnot>ow or mectlalaical posuer of the tWQ IlQu-elafiic ik bodies aRer

e a

* * < > the1r col 1tlon Hence we muR inir tht*the qvantity of mechanical power

expended iI1 dWlaung the parts of noneIaRlc ift boflieds ila

collition) is exad:tly the iRame a5 that expenid ila bellding the brings of periE&ly eJallic bodies; but the diffirence ill the -ultmate e-ffed isX that ta the- 1wor^elaRtc -ft bodies the povrer taXata to di4?lace the parts will lJe totally 1oR and dellroyedS as it would require an equal mechallic powela to be raiKed a-kethX and exerted ilw a ctrar,Y direRion to reIlore the patts btlck again to t3ielr brmer places s whet^eas ill the cai of tlle claRic bodzes the 0j3eration of half the meclzarsic power S as oIJIirved <lreacty onlJr loclied up at-d I;]@ended? alzd capaWe of l)eing reeserted wit}Wout a furtIzer cz;rlgilfl} aceeJot1*



WSON XSU (S ful@o#: 0T BGzdS 3 + 7 Pl^EleSe ideas arofe from thle refule of the experitnetles -trid

upDrl the mach;le defcribed ill my- faid -tra-Et upon Mechanic Power, and were- alfo comlnun;icated to rmy ve-ty svorthy a iid lilgthiOUS frielld WILLIAM RESSELLS EfqX F. R. S at the fame time that I thewed him thofeE experimellts in I 759 ; but the- rnode of putting this matter to-a full and fair mecllanical triaI Ilas fil-ce occurred; arld though fome rough trials, fufE¢ient to Ihew the eiedrs were tndde t}lereon7 prior to the o¢rsng the paper otl mechatlical posver to-the Society irz I776, yet the machille itSelf I had not leifure to complete to my fatisfad:tion till lately; whlch I SnClltiOXl tO apologize for tlle length of time that theSe fpeculations have take-ll in bringing forward.

OEDSCRTPTION OF srz MACISINE FOR COELISION.

Fig. r. Ihews the froIlt of the lmachine as it- appears at reA

wherl fitted for uSe. A is the pedeRal, and AB the pillarX whicK filpports the

whole, Cs D are two compound l)odies of aloout a pouild weight each, but as llearly equal irl sreight as may be. TheSe bodies are alike in conIlruEtioIl) wlwi-cla will be tnore particularly ex-

. . .

plaiIzed byJ fig . Thefe bodies are fufpellded by tsvo white fir1XQDS of aborit half all inch diameter ef and ghs beilig;about four feet long from the point of I:ufpetloll to the cerlter of thne lDodies; ancl thei- tilfpenflorl is upon the croEs-piece II, which is luortoifed tlzroughS to let the rods pafs vwith perfeA freedom; alld tiley hang vlpon two fmall plares filed to atl edge on the ullder fde, arld parS through the upper part of the rodsX Their centers are at k and l7 azaci tlle edges being let illtO a little laotch? otvl each lide the mortoife tTle rods are at libertv to vil)rate freely upoil their refpedtive points (or rather edges) of ftlfpeilficl7 atld are deternaitled to one pIairl of vibration. MN is a ffat arch (3f ssrhite xvoodS which may be covered with

rZI Z 2 paper7



£i.

34 o Afr sEs;Tosss FX&ra</aE Ear;nents

ParerjX tat tele marks the-retlpotl tnay be tlle more CQllbiCtIOUSt

lthe c*twSspitce I1 is talaclewto projed Ib*ir betore tlx pilEar, -tilat tXle. Itodies it- the;r vibratioAls may paEs clear of it without daq;t--of Rrlking it f SslXld alfo the arch MN is brotlgllt

far- fbrwarcl-- as to leave no more rlwatl a cIcaratacc, Iiifficicllt r tXtae rods to vibrate hely svithoR£-touchitXgnitt Fsigie 2* SIlews ozt of tEwe comp<3und boediesS drawn of its

iQlll fit%t AS ts a block o£ wo-od; atld about as much in breadth a5 it: xs repfef9tated i;n heighte thrs:>R;Ighh a hole in whicl; tShe wed rod--CC pais a<d is Sxed tIwerei<* - DS repxIEns a plate of; lead 5QUt threeeiglatEls of an illch

thick, olle on- eacll fide irewed Ola 1);y; way of pving it a com- . .

petelat weight. kSe retDrefents tile cdge of a fpringig plate of lialiS rendered eIailic 1)y hard*hatunzerltig; it ls about i

ei;ghths of an inch ilu lareadtha - alidt about orleZtwelitieth of- an illCtl thtck It is Sxed dosvil upon the wooden blFock -at its eIzT dS by rzleatls of a laridge 7?1ate, svhofe etidtis {hesva h atld is *iLesved down onf tach fide tlie /it^itlg plate by a IEresvs whictti

- l5ring rebxed the fizring can be taken outs at pleaire- atltl ad , . .

JURed t) itS proper fltuation. 41 i5 a light thill flip of a platej whole undEr edge is £Ut into teeth li-ke a fitle IAr or ratchete arad is- atrached to t:he iring w a pi at:< k, which paIRs

.

througil it, and aSo tPsrough a Imall Ilud rivetted itto the back pfart of the brlng aIld upon which pin as a centerS it^Xs Seely moveable . .

7nn ews a finall plite or Rud iiew edgeways raired UpO£1 the bridge plateX through an hole ln vvhicll Itud the ratcEaer paSes, and ille lonver part of the hle is cut to a-tceoth ShaAped pro perly to Gatth tiXe tecth of the ratchet, ansd retai< it tgetllep vith the WrX-jg at- any degree- to svilich it lnay be fuddenly ttIlt; afld br this intelat it is kept beariIlg geIltw dasvnsvard tv; met:s- of a wire^@rin<g ip> nyhicil is 11 reality deubtle t1

lJeal.X;.lg



zlpn /Je-Gllll*on ¢f Bozlie-. 349 bealtiidg palt at o beitlgfemiwcircular; frotnsvhich bra:nchitlg oS oll e^.cla f1de the lod ccX pades to p and fixes at eactl elld -jtlto thewood at q. Idowev<al, to clear tI:Ie ratctletX wllsicll is

eceiJaxiTy i;n the tzlicltlie as well as the rodn tlle latter ls per

f(3rated ,- ailcI-alio tilev blck is cut asvay, ro fzclr as to fet tI<e nlailt lp1*ilg ats e fI-ee of all obfltclcles ti-at wotlld presretlt its play frorn -the poilat B l>1we pal^t tg is thewn thicler tlaan tlie reItX Iy being: covel ed; 6zXlitl<- tflait) liid leather tight Svssred ol] 5 ! to pre- vetlt a certaila jarri1zg tllat otilerwiSe takes place oI1 tiae ubet;Xlg of the- rplillgs iIl colliElOll

LCt -us twosv rettll to to fig. Ie tllO maltS UpOUL tlae arcll IS4N AL*t )ut 011 AS follosvst of tis {(Rt-l arcl- of a -circle Eo1n the center 1, alacl fr a-tw archliof a circle Xfioom tlae cetlter k il-vrerSekzl;itlg each other at s. NTOR the middle line of tlat mark.s tg V9 are at the fame diRance frotn the rniddle litle at s tlnat tlle cellters kl are X

fo that when each body halags in-its owNn fioee poEltion, nvith otlt bearing againIt the ot;her? theE rod ef will covex thc traalak at- tn and the rod-gh will cover the mark at v. Fronxl t:lle pOi--tlt S UpOll- the arches Sp alld S^a refpe&-i-vely fet of points at an es3tlal and corupetetlt difEance from S each svay7 ss7hibh will giye the midblle of the mark: w and z: atld UpOll the arch Sp find a middle poiat betuteexl tlaef nla.rkov aIld vWv xvlaich 1Ctbey; a1ldo<theotherflHde, itl likernatlnerX UpOIl -tliearch Si? tStld a middle poitlt ir tlle nzalk z ;> thetl fet off the cliltaice: Sv Qr St frorxly each \vay7 al-ld fron; z each vvay; alld froln tlleSe points, drawing litltS to the refpeEive centels l alld they sv;11 give tile p;Iace atld po-fi<tion of tlle malks {ln bX allds r i;2 and thus is the trlaclfxIat })re>p?I-ed for ufe. >

son trRIALS ON ETJASTIC BODIES.

iFor this vlfe take aut l:he pitls atad tatcllers frorn eacl] tweli:ec-. tivelyv and the fprings btingf vL-lbil at l;tCrty, vith a flaort Xt

{:)f .



3 ((3 Mto sl^/XA^ronqs hsdaesZaZ B>Xperianes

.

vS fticl (fuppoSe the fCtme fize as the tods) tUS't1 afide tlle rod gh vit:h the r,ht1tlazd carrying t1<e lody D upwards till tlle R-ick is upotl the at-k w) as fuppoSe £ Ot there hold it, and with the left fet tile body 6: pis-fedtly at reR 2 in which caSe t}<e 1ad :f wvill be over tho Xnarle t; ttletl fuddetlly withdraw tlle fiCkS itl the direfl:iou that tE1e rod gh ts to follow itS and the fpring of the body D) ilBpitagillg upOt-l that of fhe bo-dy Cv

tlzey w;11 be both bentw and alfo 3reRored; atL-d the body C: sv;11 fly oiS and mount till it.s rod ef co>7ers tEle marl z; the rod of the Rliling body 1D remaining at relt UpOIl itS propef malk of reR t7 till the body C returtls, whetl tIle body D will fly offin he fane ma1wner; t11e two lzodies thtls reb-outlding a number of times? IofiIlg a part of their vibration each ti-lne f but fo rlearly is the theory of elaflic ledies fulfilled twereby, -that-thc figle ad- vant-age of origillally pU{hilZg the rod gh b@yond the mark w, by the thickLlefs of the RicliS or its osvtl thicknefs, is fufficietlt to calory the rod of the qwekent 130dy C complel:ely to its mark x.

tI>here are feveral othet6 exZsperi-metlts that mtay be m-ade with this apparatus, in confirmat:iotl of- the dodcrine of the colliXiot of-ela{tic bodies,, WliCtl beirg utsiverfally a-greed upon, alld wtelI ktlowIl, it is needltiis further to clwell UpOIl here; but leIpedixlg the applicatiorl to Ilon-elaItic fioR bodies it ;-s fir rnore difficult to come at a fitttefs of material-s for this kitld of experimetlts, vllan it is for thofe fuppoflug perfedly elaRicityX Tlle corlcltlfionsX howeverX nzay be atrained vlth equal cer talllty.

F OR T R X J L S O N NO N-E Ix A S ' I C S OF t B O D I E S

P8or this prpofe the ratclaets rntIR lJe applied and put it order as before defcribed, azld the fprings ljeing both put to -tlatir point of lFeRn lse£ the body D lse put to its m-ark w ill the

fanae



upon tZ3e CollFon o Badies f SI

fame manner as before defcrib;edS and the: body C to reR. rhe body Di being let gos r atld firiking the body f: at rtIlS in coll fequence Qf the Rroke,? the fprings bein; llooked:up by the

ratch;ets, they both nwoove froul their refitn3g marlsks i?, refpec

tively tosvard M : Now if they both tnoved top,elther, ancl- tlle rod + covered tile mark c, a1*wd the rod ,^Zr covered tlle malk e.{

at their UtlMOfi lSitNits th/en they ntotlld trul:y obey the Iaws of non--elaRic foR bed:X-es; becani tltxeir mediutu jaficetlt vould be to the; raairk zS which is jtlI} laulf the aglg of aIc>elat to tllx mark w-> bu; as iIl thigs piece of machitlery) vllovgh tlae z;maiIl or psriilciple fiprinigs are hooked ups ye-t- every part of tllem and a11 tE1e; ma£erials of xvhi£h thDevy are tonapofedX antl t*e which tlwey are attachedX have a degree) or lrtore properly beaklag a cert<win 1npai of -slicxVt -ut-htchX as; -icIaX is pericdy aald ao motfion lo-the-rebye

BTe1mufi twot, therefQre expeEt the tvo cc3lllpound bodies after the Rroke to Iticlk togerhe-r without rfepatatitlg, as svould be the: cafe with bodics truly twotlwelaRtc atad foft; trut that from the claRicity theyX are pofftIRd of; they will by reboulld;^ mg be £iparated; but that elaIl:tcity l:Atilag perfeEt, catl occatioll wa lofs of nOtiotl to the Iim of the two bod1es ffi fo l:hat if the Iody C aScends as lnucla alsove its mark a as the body D £alls ffiort of its mark dX tllen it zvill followX tllat Xtheir lnedium

afdwnt will ffill be to tE}e rnark as it ougllt tQ have I)eelz

tad tlle7been ttuly swot] clafttc roft bodies; alld ttl;Sx 11< feali£yg is

£ruly the cafe ira the experlm-erxtX as llt2t41y as it CAll be- diScerlled.- Azter a few zilratiozasS 1Xy thze tubbing of the fpritags agaillR

6;)Xze atlotherX tlzey are fc>Otl brought tcz reflt; atld laere tlzey would vIwa?ys reS haci ti-atif beetl traly and prot3elely pel^ft& otl-elafti£- Ibft bod}esg 1)ut llere as :tt1 tlle cclie of tlleSe

bod:iesg lJy a chatge of the fig;ure alld fttlczlziotl of the conpo <cllt parts: therc is cxpendd otle half of tlat tne£:hata ica1 povver



35z Mr. SMEATON'S Sn&#ZeWl B#esgXmeS/S

of the firS ulover, yet ill -this*caSe tlle- other half is not Ms but fiffi5en&4 ready to be re-exerted svhetlever it is Ibt 8 liberty > and that it is really atld boxa Ade one hag and 11eitller

;more or- ieIRg appears firm this ullcontt^overted fimple prnclple,, that tlle power of reRitution of a perfUA fl3ring iXs exadly equal Fto tllle posrer that bellds it. And this nzay? -ill a certaill degree be IEe-wn to be fad by experimetlt if there svere any ntecl Qf

ic11 a proof; for ifs when the bodies are at reI} afier the laIt experimetlt the two rods are laShed togetlzer near the l)vttonu with a bit of thread and thetl the ratchets- vIlpinned alld removed, on CUttitlg tlle thread with a pair of fcifiars they wlll each of thetn relsoulld>- C towards M and D tQWaHS N; atld if they reboulldpd rebedis7ely to z atldy the nzechanicat posver exerted- would be the fanle as it was aher the Ltroke when the tnean of their tsva a-fcetlts wxis up to- the mark z; :but here it is not to be expeEted, benufb awot otlly the m£tiot IoIt ty the fiid:tion of the ratcllets is to be deduEted becauSe it had tTwe efid of real noll-elafticity; but alb the elaflicity tlllt parated thm in the Ilroke, svhicll saras loI} in tEle vibra- tions tlzat fucceeded; tweither oiS which hindered the mean akellt to be to z ; 13ut yet ullder a;11 the difadvalltages irl the machitle (if llet ullreaIollably ill made) the red tf will atcend to g atld tgl) to a: alld lletlce [ infir) as a pcz{;tive truth tllast

Atl the collition of noll ela{tic foft bodiesn one lwalf ef the ms cDvn1t-ac >vwcr re9irg zn the /?rzkx7ag boXy xs @ 7a tbe #roke.

J<efpeEtitg bodies uwelallic alld periEtly twardn W& StE

ixzirS tlwa.t Iitice sve are mnavoidably led to a cotzcIstiotl CS)I1-

cerniolg tC1nS -wllich colltracliEts svXat is eReemed a trllth ca palulw of the £}riEteft detr<srlf;ratiotl-; xtZ^Z that the veletit)? of the cetlter of gravity of no IyAem o£ bodies catl be chat-ged iJv atRy collifoll betwixt otle atlotherS fotnethillg meR l)e ;aidunWd that involves a contradiEtiot1. This puSeSly holds

f aCeO.t dilg



rzp tbe s+At of Bggs. 353 accordig to a11 the e{Eab]R{hed rules,, 1)(3t11 of perfeAly ela{tic atld pel+feAly tlonelaRicfiogt lJodles; rules which rnuIt fail it}

tlle perfeEtly IlOllelgiRiC hard t30dies if tEleir velocity after tlle llroke is to tlle velocity of tI<e firiking-body as oIae is to the rquaLre root of z; for thetl t1Ac center <3f gravity of the two lzodies will by the IEroke acqulre a velocity greater thall tlle center of gravity the two bodies 11ad before the firoke it that proportionS - svhich is p-roved thus.

At vlae outWet of the Rrikin:g body, the center of gravity of

the tssro bodies itl our caSe will be exadly in the middle be tweet3L the two; a-rld when they rgleet it will have uloved fi^om their half diRance to their point of co<taRS fo the velocity of the cetater of gravity before tlae l;odies meet will lJe exadly one half of the velocity of the Itriking 13ody; andS tlaerefore-5, if w the velocity of the firikig lJody is zs the velocity Qf the center of gravity of both will be oLle After the Itrokeg as both lsodies are fuppofed to move in coIlta&, the velocity of the ceil ter of gravity will be the fame as that of the bodies ;* aild as their velocity is proved to be the fquare root of , the velocity of their center of gravity will le increafed froln X . to the fquare root of 2*, that is frorn I . to I4I 4 &c;

The falr inference fiom tlaeIc co:atradiAory corlclufi1ons there° R fiore is, that an unelaRic hard l)ody (perfEEtly fo) is a repuglaatl-t idea, ar:d contai1ls in itCelf a contradidcion; for ito make it agree vi-th the iir conclufiolls that may be drawn on teach fide, flom clear premiCesX we fhall be obliged to define its properties thus : that in the Itroke of uslelallic hard bodies they -Ca11I1Ot poffibly lofe any mechanic ponver in the Rroke; becaufW no otller imp;rei1o11 is made than the commerlicat-on of motion; and yet they mvfl loJ^e; a qntizy of mechanic power in the Rroke R

-becauSe7 if tlley dc) IlOt tlleir common center of gravity, as \TOL LXXIL A a a abore



3S4 MtXe SMEATONsS SX&eatsl Expgrtaanes &C9

aboxre fhexvilS will acquire an igcree of velocit--by their llro)<e nI)oll each other

1f a ike lncnnner the idea of a perpef>l zno-fon perJhaps, at firll fight, 1nay 1zot av3pear to involve (w £ontvaf3idioil i1-l terms 5

btlt wc illall be obliged to coilEeIs tllat it does, svhen9 otl exa tntlig its requitltes fbr executior me fild we allf^ratat l)o- dies havitlg the followilag properties, that s^7hen they are made

to of ve-ncS a-gai;ll} gravitalt;ffn thetr abSeltlte weightr Ihall be leJ§, aIld tlat when they dWcend by gravitation (through atl equal fpace) their abSolute weight ffiall be greate-r; which, according to alf we 21QW of natur> is a repUva ar canradiSory iAO <



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new fundamental experiments upon the collision of bodies. by mr. john smeaton, f. r. s. in a letter...

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