204 PROFESSOR WHEWELL's DEMONSTRATION 



which acts upon a free body overcomes its inertia, for it changes its motion ; 

 and this change once effected, the inertia opposes any return to the former 

 condition, as well as any additional change. The inertia is thus overcome by 

 a momentary force. But the weight can only be overcome by a continuous 

 force like itself. If an impulse act in opposition to the weight, it may for a 

 moment neutralize or overcome the weight ; but if it be not continued, the 

 weight resumes its effect, and restores the condition which existed before 

 the impulse acted. 



But weight not only produces rest, when it is resisted, but motion, when 

 it is not resisted. Weight is measured by the reaction which would balance 

 it; but when unbalanced, it produces motion, and the velocity of this 

 motion increases constantly. Now what determines the velocity thus pro- 

 duced in a given time, or its rate of increase ? What determines it to have 

 one magnitude rather than another ? To this we must evidently reply, the 

 inertia. When weight produces motion, the inertia is the reaction which 

 makes the motion determinate. The accumulated motion produced by the 

 action of unbalanced weight is as determinate a condition as the equili- 

 brium produced by balanced weight. In both cases the condition of the 

 body acted on is determined by the opposition of the action and reaction. 



Hence inertia is the reaction which opposes the weight, when unba- 

 lanced. But by the conception of action and reaction, (as mutually deter- 

 mining and determined,) they are measured by each other ; and hence the 

 inertia is necessarily proportional to the weight. 



But when we have reached this conclusion, the original objection may 

 be again urged against it. It may be said, that there must be some fallacy 

 in this reasoning, for it proves a state of things to be necessary when 

 we can so easily conceive a contrary state of things. Is it denied, the 

 opponent may ask, that we can readily imagine a state of things in 

 which bodies have no weight? Is not the uniform tendency of all bodies 

 in the same direction not only not necessary, but not even true? For 

 they do in reality tend, not with equal forces in parallel lines, but to 

 a center with unequal forces, according to their position : and we can 

 conceive these differences of intensity and direction in the force to be 



