DISCOVERY OF THE LAWS OF MOTION. 31 



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 Galileo, though it 

 was afterwards taken up and defended by Casraeus, 

 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-con- 

 tradiction. This circumstance, however, was acci- 

 dental : 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. 



The Law of Velocity was hitherto, as we have 

 seen, treated as a law of phenomena, without refer- 

 ence to the Causes of the law. " The cause of the 

 acceleration of the motions of falling bodies is not," 

 Galileo observes, "a necessary part of the investiga- 

 tion. Opinions are different. Some refer it to the 

 approach to the center; others say that there is a 

 certain extension of the centrical medium, which, 



