170 CELESTIAL MECHANICS. I. iii. 13. 



moving with the velocity mu. In the same manner we 

 may substitute for the system rnf a single point moving 

 with the velocity mV.- but the two systems being supposed 

 capable of destroying each other's motion, the two points, 

 possessing respectively equal quantities of motion, must 

 remain at rest after meeting, consequently their velocities 

 must be equal (A); we have therefore, for the condition of 

 the equilibrium of the two systems, wiwizmV. 



[D.] The mass of a body consists in the number of its 

 material points, and the product of the mass by the velocity 

 is called the quantity of motion of a body: and this product 

 is also [sometimes] considered as the force of a body in 

 motion. In order that two bodies meeting may destroy 

 each other's motion, the quantities of motion in opposite 

 directions must be equal, and consequently the velocities 

 must be inversely as the masses. 



[E.] The density of a body depends on the number of 

 material points which it contains within a given volume or 

 bulk. In order to ascertain its absolute density, it would 

 be necessary to compare it with a body having no pores : 

 but since we know of no such body, we can only compare 

 any given substance with some other as a standard with 

 respect to density. It is obvious that the mass of a body 

 is in the joint proportion of the volume and the density, 

 so that calling the mass M, the bulk t/, and the'density D, 

 we have in general Mz=iDU\ the quantities M, D, and U, 

 relating to different units, each of its own species. 



[F.] In this reasoning we suppose that bodies are formed 

 of similar material points, and that they only differ in the 

 relative situation of the atoms composing them. But the 

 intimate nature of matter being unknown, this assumption 

 is at least hypothetical, and it is perfectly possible that 



