THAT ALL MATTER IS HEAVY. 203 



This truth is indeed one of the laws of motion. That weight is propor- 

 tional to inertia is proved by experiment, as far as the laws of motion are 

 so proved : and Newton's experiments prove one of the laws of motion, so 

 far as any experiments can prove them, or are needed to prove them. 



That inertia is proportional to weight, is a law equivalent to that law 

 which asserts, that when pressure produces motion in a given body, the 

 velocity produced in a given time is as the pressure. For if the velocity be 

 as the pressure, when the body is given, the velocity will be constant if the 

 inertia also be as the pressure. For the inertia is understood to be that pro- 

 perty of bodies to which, ceteris paribus, the velocity impressed is inversely 

 proportional. One body has twice as much inertia as another, if, when the 

 same force acts upon it for the same time, it acquires but half the velocity. 

 This is the fundamental conception of inertia. 



In Newton's pendulum experiments, the pressure producing motion was 

 a certain resolved part of the weight, and was proportional to the weight. 

 It appeared by the experiments, that whatever were the material of which 

 the pendulum was formed, the rate of oscillation was the same; that is, the 

 velocity acquired was the same. Hence the inertia of the different bodies 

 must have been in each case as the weight : and thus this assertion is true of 

 all different kinds of bodies. 



Thus it appears that the assertion, that inertia is universally proportional 

 to weight, is equivalent to the law of motion, that the velocity is as the 

 pressure. The conception of inertia (of which, as we have said, the funda- 

 mental conception is, that the velocity impressed is inversely proportional 

 to the inertia,) connects the two propositions so as to make them identical. 



Hence our argument with regard to the universal gravity of matter 

 brings us to the above law of motion, and is proved by Newton's experiments 

 in the same sense in which that law of motion is so proved. 



Perhaps some persons might conceive that the identity of weight and 

 inertia is obvious at once ; for both are merely resistance to motion ; — inertia, 

 resistance to all motion (or change of motion) — weight, resistance to motion 

 upwards. 



But there is a difference in these two kinds of resistance to motion. Inertia 

 is instantaneous, weight is continuous resistance. Any momentary impulse 



c C2 



