32 HISTORY OF MECHANICS. 



closing behind the body, pushes it forwards. For 

 the present, it is enough for us to demonstrate cer- 

 tain properties of Accelerated Motion, the accelera- 

 tion being according to the very simple Law, that 

 the Velocity is proportional to the Time. And if 

 we find that the properties of such motion are 

 verified by the motions of bodies descending freely, 

 we may suppose that the assumption agrees with 

 the laws of bodies falling freely by the action of 

 gravity 8 ." 



It was, however, an easy step to conceive this 

 acceleration as caused by the continual action of 

 gravity. This account had already been given by 

 Benedetti, as we have seen. When it was once 

 adopted, gravity was considered as a constant or 

 uniform force ; on this point, indeed, the adherents 

 of the law of Galileo and of that of Casraeus were 

 agreed; but the question was, what is a Uniform 

 Force ? The answer which Galileo was led to give 

 was obviously this ; that is a Uniform Force which 

 generates equal velocities in equal successive times ; 

 and this principle leads at once to the doctrine, 

 that Forces are to be compared by comparing the 

 Velocities generated by them in equal times. 



Though, however, this was a consequence of the 

 rule by which Gravity is represented as a Uniform 

 Force, the subject presents some difficulty at first 

 sight. It is not immediately obvious that we may 

 thus measure forces by the Velocity added in a 

 8 Gal. Op. iii. 91,92. 



