CHAPTER VI. 



OP THE LAWS OF THE MOTION OF A SYSTEM 

 OF BODIES, ACCORDING TO ANY RELA- 

 TION MATHEMATICALLY POSSIBLE BE- 

 TWEEN FORCE AND VELOCITY. 



§ 24. New principles corresponding ^ on this more en- 

 larged hypothesis, to those of the preservation of impetus, 

 the constancy of areas, the motion of the centre of gra- 

 vity, and the least action. Forces reduced to a given 

 direction : referred to an axis ; and combined with the 

 elements of the spaces. 



335. Theorem. The sum of the products 

 of the masses of any system of bodies, into the 

 fluent of the product of the velocity into any 

 function of the velocity, which may be sup- 

 posed to represent the force, is constant with 

 regard to the intervals between any two places 

 of the system. 



There are many conceivable relations between force 

 and velocity, which imply no mathematical contradiction, 

 although the simplest is their being directly proportional 

 to each other, as we find that they actually are in nature. 



