OF THE LAWS OF MOTION. 165 



WJien any forces produce motion in any connected system of matter, 

 the motive quantities of force gained and lost by the different parts 

 must balance each other according to the connexion of the system. ■ 



By the motive quantity of force gained by any body, is here 

 meant the quantity by which that motive force which the body's mo- 

 tion implies (according to the measures already established) exceeds 

 the quantity of motive force which acts immediately upon the body. 

 It is the excess of the effective above the impressed force, and of course 

 arises from the force transmitted from the other bodies of the system 

 in consequence of the connexion of the parts. The motive quantity 

 of force lost is in like manner the excess of the impressed above the 

 effective force. And these two excesses, in different parts of the sys- 

 tem, must balance each other according to the mechanical advantage 

 or disadvantage at which they act for each part. 



This completes our system of mechanical principles, and authorizes 

 us to extend to bodies of any size and form the rules which the 

 second law of motion gives for the motion of bodies considered as 

 points. And by thus enabling us to trace what the motions of bodies 

 will be according to the rule asserted in the third law of motion, 

 (namely, that the motive quantity of forces is as the momentum pro- 

 duced in a given time,) it leads us to verify that supposition by experi- 

 ments in which bodies oscillate or revolve or move in any regular 

 and measurable manner, as has been done by Atwood, Smeaton, and 

 many others. 



18. We have thus a complete view of the nature and extent of 

 the fundamental principles of mechanics; and we now see the reason 

 why the laws of motion are so many and no more, in what way they 

 are independent of experience, and in what way they depend upon 

 experiment. The form, and even the language of these laws is of 

 necessity what it is; but the interpretation and application of them is 

 not possible without reference to fact. We may imagine many rules 

 according to which bodies might move (for many sets of rules, dif- 

 ferent from the existing ones, are, so far as we can see, possible) and 

 we should still have to assert — that velocity could not change without 

 Vol. V. Pakt II. Y 



