FOR
FOR
. bodies UuygenS means Aich as are elaftic, as appears from his treatife De motu corporum & percuflione, oper. vol. u, d MacLanrin, lib. cit. art. 533.]
But it is to be obferved, that though it be true, that in the collifion of elafh'c bodies the vis viva, or afcenfional force is preferved before and after the fhock ; yet during the mock, while the elaftic bodies are bending and prefs on each other, there feems to be a diminution of this force, which is after- wards reftored by the action of their elafticity; though the followers of Leibnitz do not allow that any force is loft even during the fhock. They fay, the vis viva is communicated to the fpring while it is bending, and then is recommunicated to the bodies by the unbending of the fpring. They alfo de- ny that any force is loft in the percuflion of foft bodies. For though the force of the bodies impelling each ether be dimi- nifhed, yet their force does not perifh, but is communicated to Tome other matters fuch as the fubtle fluid caufing cohelion and elafticity f - — [ e Vis viva qua in percujjionc amittitur, non pent, fed confervaiur. Wolf Cofmol. §486. In toto univer- fo temper confervatur eadem virium vivarum quaniitas. ibid. § 4.87. Vis viva • — ■ dum figura corporum in contaclu mutatur, in alia materia confervatur. Ibid, demonftr. § 486. f Mr. Dan. Bernoulli, fpeaking of this principle of the preservation of the vis viva, obferves, $htamvis principium univerfale fit, non tamen efl fine circumfpetiione adfabmdmn, quia fapc contingit ttt mot us tranfeat in ?nateriam altenam. lta verbi gratia pofitio ittius valet pro regidts motunm ex percu]Jio?ie cruendis, fi modo corpora fint perfecle elajlica ; fed cum taiia non funi, facile ejl videre, partem virium vivarum five afcenfus potentialis in com- prelfionem corporum impenfam corporibus non rcjlitui, fed materia emdam Jubtili, ad qitamtranf.it, imprejfam harere. Hydrody- nam. p- 12, 13. And Mr. Daniel Bernoulli, in this trea- tife has affumed the prcfervation of the vis afcendens of Huy- «j;ens, or, as others exprefs it, the confervatio virium virarum ; and, in Mr. Bernoulli's own cxprcilion, ecqualitas inter def- tenfum aclualem afcenfumque polentialem, as an hypothefis of wonderful ufe in mechanics. But a late author contends that the conclufions drawn from this principle are oftner falfe than true. See De confervat. virium vivarum dhTcrt. Loud. 1 744. quarto.]
As to the eftimaticn of the force of bodies in motion, Mr. Euler obferves, that a body in motion may meet with two kinds of obftacles, one oppofing its velocity only, the other its direction. In either cafe, the body exerts its force on thefe obftacles. When the velocity only of the body is changed, as it happens when two bodies in motion meet each other directly, the change refulting is then faid to happen by fhock, percuflion, or collifion. If the obftacle be of fuch a nature as only to oppofc the direction of the body, as when it re- volves in a fling, or moves in an incurvated tube, the ob- ftacle then acts by preffure, and this preffure is called centri- fugal force. Hence a double force is the refult of the inertia of bodies : that produced by an obftacle to its velocity is de- nominated force of pcrcuifion, and the other arifing from the change of its direction is called force of preflure s. — [ e Euler, Mem, Acad. Berlin, p. 25.]
Leibnitz and his followers make a great difference between thefe two kinds of forces. They c?\lfo?-ce of preflure vis mor- tua, and the force of percuflion vis viva. By this opposition of terms, they not only fignify that there is a difference be- tween thefe forces, but alio that they are heterogeneous or not comparable. Hence, though we have an exact meafure of preffures, they invented new rules for the meafure and companion of percuflions, and have thereby occaficned great (lifputcs in the philofophical world.
Philofophers have ftated this queftion fbmewhat vaguely : to fix our notions, let us confider the body B at reft, and an- other body A linking it with a given velocity, in the di- rection ab ; it is manifeft that A exerts an action of a cer- tain force on B to difturb its ftare. The queftion is, what
is the force exerted on B ? Plnlofophers have given them- felves little trouble to determine the true meafure of this force : They have confined themfelves to the cbmparifon of differ- ent forces of the lame kind. In efHmating the quantity of force of the body A, by the quantity of the alteration which happens in the ftate of the body B, they eafily perceived that this change would be greater, according as the body A had a greater mafs, or a greater velocity. The Newtonians, or rather the Cartcftans, and Lcibnltians could not agree how to exprefs-the rcfults of the mafs, and velocity of the finking body : the firft infill, that the force fhould be expreffed by the pro- duct of the mafs by the velocity. Leibnitz, on the other hand, pretends, that the meafure of this force is the pro- duct of the mafs by the fquare of the velocity. The difpute ha; been carried on with gre*t warmth on both fides ; but it
feems almoft needlefs to relate the various arguments brought by them in fupport of their different opinions : for as they have never agreed about the effect, the quantity of which was to be the meafure of the force, the difpute often degene- rated into a logomachy.
It is evident, that neither the one nor the other of thefe opi- nions admit any comparifon between the force of percuilion and that of preffure : for this is neither comparable to the product of the mafs by the velocity, nor to the prouucSr of the mafs by the fquare of the velocity. The Leibnitians particularly deny the vires mortua and viva: to be homogeneous ; they make the fame difference between them as between a line and a furface. It feems to them that experience confirms their notions ; a fm all blow, as that of a hammer on a nail, often producing an effect fupeiior to that of the greateft pref- fure, efpecially if the fame effect is to be produced in fo fhort a time as that of driving in the nail by the hammer. But thofe who lay a ftrefs on this example feem to think, that percuflion is inftantaneous. If this were true, there could be no doubt of the heterogeneity of the vires mortuts and viva ; for no preffure, however great, can produce the leaft fenfible effecT: in an inftant. Befides, although the effect of percuf- lion were not inftantaneous, there Hill appears fo great a dif- ference between tiie effects of ftriking and thofe of prefling, that whether the force of percuflion be proportional to its ve- locity, or to the fquare or other power of its velocity, we can never produce a preffure equivalent to a percuflion : all which confirms the Leibnitians in their notion that preflure and per- cuflion are heterogeneous h . — [ h Mem. Acad. Berlin. 1745. p. 29.]
Mr. Euler obferves, with refpecT; to this difpute concerning the meafure of vivid force, that we cannot absolutely afcribe any force to a body in motion, whether we fuppofe this force proportional to the velocity, or to the fquare of the velocity : for the force exerted by a body, ftriking another at reft, 13 different from that which it exerts in ftriking the fame body in motion ; fo that this force cannot be afcribed to any body conlidered in itfelf, but only relatively to the other bodies it meets with. There is no force in a body abfolutely conlider- ed, but its inertia, which is always the fame whether the bo- dy be at reft or in motion. But if this body be forced by others to change its ftate, its inertia then exerts itfelf as a force, properly fo called, which Is not abfolutely determin- able i becaufe it depends on the changes that happen in the ftate of the body. Suppofe, for inftance, a body A forced to move in an incurvated tube, or along the curve furface EaF, the body in this cafe will prefs the furface wherever it touches it in a direction a a normal to the curve; and with a certain force commonly determined in mechanics, by the mafs of the body, its velocity, and by the radius of curva- ture Oa. Now the body exerts a preflure, or vtsikprtua;
yet it would be abfurd to afcribe a certain and determinate force of preffure to this body confidered In itfelf, fince this pref- fure may vary very much, acording to the difference of the curvature of E<?F. In like manner "it feems unreafonable to place a certain abfolute force of percuflion in bodies, iince it principally depends on the external circumftances accompany- ing the Ihock.
A fecond obfervation which has been made by feveral great men, is, that the effect of a fhock of two or more bodies is not produced in an inftant, but requires a certain interval of time. If this be fo, the heterogeneity between the vires vi- va and mortua vanifhes ; fince a preflure may always be af- figned, which in the fame time, however little, fhall produce the fame effect. If then the vires viva be homogeneous to the vires mortua, and fince we have a perfect meafure and knowledge of the latter, we need require no other meafure of the former than that which is derived from the vires mortua. equivalent to them.
Now that the change of ftate in the fhock of two bodies does not happen in an inftant, appears evidently from the experi- ments made on foft bodies: in thefe, percuflion forms a fmall cavity, vifible after the fhock, if the bodies have no elafticity. Such a cavity cannot certainly be made in an inftant. And if the fhock of foft bodies require a determinate time, we muft certainly fay as much of the hardeff, though this time may be fo fmall as to be beyond all our ideas. Neither can any inftantaneous fhock agree with that conftant law of nature,
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