-18 Statics. 



Moreover, as the particles of matter of whatever kind tend by 

 the force of gravity to move with the same velocity, or exert the 

 same power, the combined action arising from this cause will be 

 proportional to the number of particles ; that is, the weight of a 

 body is as its density, other things being the same. The relative 

 weights of the different kinds of matter under equal bulks, are 

 called the specific gravities of the bodies respectively, the weight 

 of pure water, in a vacuum, at a particular temperature, being 

 taken as the unit. Thus, if a cubic inch, a cubic foot, &c., of 

 gold be 1 9 times heavier than the same bulk of water, under the 

 same circumstances, as to temperature, &c., the specific gravity 

 of gold is said to be 1 9. 



Of Equilibrium between Forces directly opposite. 



31. We shall represent forces, as we have said, by their ef- 

 fects, that is, by the quantities of motion which they are capable 

 of producing respectively in a determinate mass. But not to 

 embrace too many objects at once, we shall consider each mass, 

 or body, as reduced to a single point, at which we suppose the 

 same quantity of matter as in the body of which it takes the 

 place. We shall see hereafter that there is in fact in every 

 body a point through which motion is transmitted as if the whole 

 mass were concentrated there. We shall, moreover, unless the 

 contrary is expressly stated, consider bodies as composed of 

 particles absolutely hard, and connected together in such a man- 

 ner as not to admit of any change in their respective situations 

 by the action of any force whatever. 



32. This being premised, let us suppose two bodies m, n. 

 to be put in motion, the first from A toward C, with a ve- 

 locity w, the second from C toward A with a velocity v. When 

 these bodies come to meet, they will be in equilibrium, if the 

 quantity of motion in ra is equal to the quantity of motion in n ; 

 that is, if m u is equal to n r. 



Indeed it is evident, that if m is equal to n, and the velocity 

 u is equal to T;, there must be an equilibrium ; for in this case, 

 whatever reason there may be for supposing m to prevail over 



