202 CELESTIAL MECHANICS. I. V. Ip. 



This equation is analogous to the simpler equation v^zi 

 c-\-2(p(g) (264), and expresses algebraically the law of 

 living forces [or energies. Dr. Wollaston has given to 

 this function of a moving body the very appropriate name 

 of impetus ; a short time before, the term energy had been 

 proposed, and either or both of these words may be em- 

 ployed with advantage : energy is perhaps more hkely to 

 be misconstrued in a moral sense, but it is more convenient 

 when a plural is wanted]. 



320. Scholium 1. This principle is, 

 however, only applicable when the motions 

 of the bodies concerned are changed by im- 

 perceptible degrees. 



For if the motions undergo abrupt changes, the impetus 



is diminished in a manner which may be thus determined. 



We may employ, in this case, the character A (317) as 



denoting a finite variation of the velocity, and we shall 



have for the part of the force P not accelerating m, m 



I djc\ 



fP — A-T-l» and the equation (P) will become 0=2?;* 



> d^' 



In this equation we may substitute for Sar, dx + Adx, for 

 ^y, dy + Ady, and for ^z, dz + Adz, since it is perfectly 

 consistent with the conditions of the system, to make the 

 arbitrary variations such as actually happen, the variations 

 preserving the proportions of these fluxions though they 

 rem2dn infinitely small. The equation will then become 



