1 80 Dynamics. 



can never become zero, whatever be the values assigned to m, n, 

 and u ; the only case where u can be infinitely small, is that in 

 which n is infinitely great. Thus, if in nature we see bodies 

 lose the motion that they have received, it is because they com- 

 municate it to the material parts of the bodies which surround 

 them. Now it is evident from the formula, 



u = 



that the greater the mass of the impinged body ?i, the less (other 

 things being the same), will be the velocity M', n being consider- 

 ed as the sum of the material particles among which m parts 

 with its motion. It will be seen, therefore, that the velocity u' 

 may soon be so reduced as to escape the notice of the senses, even 

 when it is not opposed by immoveable obstacles, as friction, &c. 



291. The force of inertia, being a force peculiar to matter, 

 exists equally in every equal portion of matter, and consequent- 

 ly in a determinate mass it takes place according to the quanti- 

 ty of matter, or in proportion to the mass ; and as the mass is 

 proportional to the weight, the force of inertia may be regarded 

 as proportional to the weight. But we must take care not to 

 infer hence, that the force of inertia arises from gravity ; it is 

 altogether independent of it ; indeed, if while a body is falling 

 freely, it be forced forward by the hand with a velocity greater 

 than that of its natural descent, the hand will experience on 

 overtaking the body, a blow, or resistance, that manifestly can- 

 not be attributed to gravity, which acts only downward. Still 

 less can it be ascribed to the resistance of the air ; for the resist- 

 ance of the air, being capable of acting only on the surfaces of 

 bodies, cannot, like the force of inertia, be proportional to the 

 quantity of matter. 



The force of inertia, therefore, is a force peculiar to matter, 

 by which every body resists a change of state, as to motion and 

 rest. The force of inertia is proportional to the quantity of matter, 

 and takes place in all directions according to which an effort is made 

 to move a body* 



