ON COLLISION. 57 



Acta Petrop. iii. II. 106. Belidor, Ingenieur Fran?ais. Fuss, Nova Acta Pe- 

 trop. 1788, vi. 197. Nicholson's Journal, iv. 443. 



Virtual Velocities. Galileo, Dial. 1592. De Caus, les Raisons des Forces Mou- 

 vantes, Antwerp. Bp. Wilkins's Mathematical Magic, 1648. J. Bernoulli, in Va- 

 rignon's Mec. 1717. D'Alembert, Hist, et Mem. 1769, p. 278. Lagrange on a 

 Property of the Centre of Gravity, Ac. Berl. 1783, p. 290. Do. on Virtual Velo- 

 cities, Journal Poly technique, ii. V. 115. Fossombroni sul Principio delle Velocita 

 Virtuali, 4to, Flor. 1796. Essay on Virtual Velocities, Journal de Physique, xlviii. 

 210. Fourrier and Prony on Do. Journal Poly technique, ii. V. 20, 191. Buquoy, 

 Analytische Bestimmung des Gesetzes der Virtuellen Geschwindigkeiten, Leips. 

 1812. Do. Weitere Entwickerung, do. 1814. Do. Exposition d'un Nouveau 

 Principe General de Dynamique, dont le Principe des v. v. n'est q'un cas particulier, 

 4to, Paris, 1815. Pagani, Mem. de 1'Acad. de Bruxelles, 1825, iii. Gauss in 

 Crelle's Journal, Band 4. Mobius Lehrbuch der Statik, Leipz. 1837. 



LECTURE VIII. 



ON COLLISION. 



HAVING inquired into the laws and properties of the motions and rest of 

 single bodies under the operation of one or more forces, and into the equi- 

 librium of these forces in different circumstances, we are next to examine 

 some simple cases of the motions of various moveable bodies acting recipro- 

 cally on each other. In all problems of this kind, it is of importance to 

 recollect the general principle already laid down respecting the centre of 

 inertia [gravity] that its place is not affected by any reciprocal or mutual 

 action of the bodies constituting the system. 



Whenever two bodies act on each other so as to change the direction of 

 their relative motions, by means of any forces which preserve their 

 activity undiminished at equal distances on every side, the relative veloci- 

 ties with which the bodies approach to or recede from each other, will 

 always be equal at equal distances. For example, the velocity of a comet, 

 when it passes near the earth in its descent towards the sun, is the same 

 as its velocity of ascent in its return, although at different distances its 

 velocity has undergone considerable changes. In this case, the force acts 

 continually, and attracts the bodies towards each other ; but the force 

 concerned in collision, when a body strikes or impels another, acts only 

 during the time of more or less intimate contact, and tends to separate the 

 bodies from each other. When this force exerts itself as powerfully in 

 causing the bodies to separate as in destroying the velocity with which they 

 meet each other, the bodies are called perfectly elastic : when the bodies 

 meet each other without a re-action of this kind, they are called more or 

 less inelastic. Ivory, metals, and elastic gum, are highly, and almost 

 perfectly elastic : clay, wax mixed with a little oil, and other soft bodies, 

 are almost inelastic : and the effects of inelastic bodies may be imitated by 

 elastic ones, if we cause them to unite or adhere after an impulse, so as 

 to destroy the effect of the repulsive force which tends to separate them. 



