OF THE LAWS OF MOTION. 157 



consequence of the action of a hand pushing it with a constant effort, 

 or of a spring, or of a stream of fluid rushing in the same direction, 

 the accelerative effect of such agents would be smaller and smaller 

 as the velocity of the body propelled was larger and larger. We can 

 learn from experience alone that the effects of the action of gravity 

 do not follow the same rule. 



We assert that the accelerative quantity of the same force of gra- 

 vity is the same whatever be the motion of the body acted on. It 

 may be asked how we know that the force of gravity is the same 

 in cases so compared ; for instance, when it acts on a body at rest 

 and in motion ? The answer to this question we have given already. 

 By the very process of considering gravity as a force, we consider 

 it as an attribute of something independent of the body acted on. 

 The amount of the force may depend upon place, and even time, for 

 any thing we know a priori ; but we do not find that the weight of 

 bodies depends on these circumstances, and therefore, having no evi- 

 dence of a difference in the force of gravity, we suppose it the same 

 at different times and places. And as to the rest, since the force is a 

 force which acts on the body, it is considered as the same force, 

 whatever be the circumstances of the passive body, although the ejects 

 may vary with these circumstances. If the effects are liable to such 

 change, this change must be considered separately, and its laws investi- 

 gated ; but it cannot be allowed to unsettle our assumption of the 

 permanence of the force itself. It is precisely this assumption of a 

 constant cause, which gives us a fixed term, as a means of estimating 

 and expressing by what conditions the effects are regulated. 



It appears by observation and experiment, that the accelerative 

 quantity of the same force is not affected by the velocity or direction 

 of the body acted on : for instance, a body falling vertically receives, 

 in any second of time, an accession of velocity as great as that which 

 it received in the first second, notwithstanding the velocity with which 

 it is already moving. The proof of this and similar assertions from 

 experiment produced, historically speaking, the establishment of the 

 second law of motion in the sense in which we now assert it. And 

 here, as in the case of the first law, we may observe that an important 

 Vol. V. Part II. X 



