DISCOVERY OF THE LAWS OF MOTION. 327 



The Law of Velocity was hitherto, as we have seen, treated as a law 

 of phenomena, without reference to the Causes of the law. "The 

 cause of the acceleration of the motions of falling bodies is not," Gali- 

 leo observes, " a necessary part of the investigation. Opinions are dif- 

 ferent. Some refer it to the approach to the centre ; others say that 

 there is a certain extension of the centrical medium, which, closing 

 behind the body, pushes it forwards. For the present, it is enough for 

 us to demonstrate certain properties of Accelerated Motion, the accel- 

 eration 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 free- 

 ly 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 Casrseus 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 com- 

 pared 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 given time, without 

 taking into account the velocity they have already. If we communi- 

 cate velocity to a body by the hand or by a spring, the effect we pro- 

 duce in a second of time is lessened, when the body has already a 

 velocity which withdraws it from the pressure of the agent. But it 

 appears that this is not so in the case of gravity ; the velocity added 

 in one second is the same, whatever downward motion the body al- 

 ready possesses. A body falling from rest acquires a velocity, in one 

 second, of thirty-two feet ; and if a cannon-ball were shot downwards 

 with a velocity of 1000 feet a second, it would equally, at the end of 

 one second, have received an accession of 32 feet to its velocity. 



•This conception of Gravity as a Uniform Force, — as constantly and 



« Gal. Op. iii. 91, 92. 



