826 HISTORY OF MECHANICS. 



The Force of Gravity which thus produces deflection and curvature 

 in the path of a body thrown obliquely , constantly increases the veloci- 

 ty of a body when it falls vertically downwards. The universality of 

 this increase was obvious, both from reasoning and in fact ; the law of 

 it could only be discovered by closer consideration ; and the full anal- 

 ysis of the problem required a distinct measure of the quantity of 

 Accelerating Force. Galileo, who first solved this problem, began by 

 viewing it as a question of fact, but conjectured the solution by taking 

 for granted that the rule must be the simplest possible. " Bodies," he 

 says, 7 " will fall in the most simple way, because Natural Motions arc 

 always the most simple. When a stone falls, if we consider the matter 

 attentively, we shall find that there is no addition, no increase, of the 

 velocity more simple than that which is always added in the same 

 manner," that is, when equal additions take place in equal times ; 

 " which we shall easily understand if we attend to the close connection 

 of motion and time." From this Law, thus assumed, he deduced that 

 the spaces described from the beginning of the motion must be as the 

 squares of the times ; and, again, assuming that the laws of descent 

 for balls rolling down inclined planes, must be the same as for bodies 

 falling freely, he verified this conclusion by experiment. 



It will, perhaps, occur to the reader that this argument, from the 

 simplicity of the assumed law, is somewhat insecure. It is not always 

 easy for us to discern what that greatest simplicity is, which nature 

 adopts in her laws. Accordingly, Galileo was led wrong by this way 

 of viewing the subject before he was led right. He at first supposed, 

 that the Velocity which the body had acquired at any point must be 

 proportional to the Space described from the point where the motion 

 began. This false law is as simple in its enunciation as the true law, 

 that the Velocity is proportional to the Time : it had been asserted as 

 the true law by M. Varro (De Motu Tractatus, Genevse, 1584), and 

 by Baliani, a gentleman of Genoa, who published it in 1638. It was, 

 however, soon rejected by GalUeo, though it was afterwards taken up 

 and defended by Casra3us, one of Galileo's opponents. It so happens, 

 indeed, that the false law is not only at variance with fact, but with 

 itself: it involves a mathematical self-contradiction. This circumstance, 

 however, was accidental : it would be easy to state laws of the increase 

 of velocity which should be simple, and yet false in fact, though quite 

 possible in their own nature. 



Dial. Sc. iv. p. 91. 



