DISCOVERY OF THE LAWS OF MOTION. 39 



from the theoretical form, the parabola, do, in fact, 

 approach nearer the true paths of a cannon or 

 musket-ball than a parabola would do: and this 

 approximation more especially exists in that which 

 at first sight appears most absurd in the old theory; 

 namely, the assertion that the ball, which ascends 

 in a sloping direction, finally descends vertically. 

 In consequence of the resistance of the air, this is 

 really the path of a projectile ; and when the velo- 

 city is verj great, as in military projectiles, the 

 deviation from the parabolic form is very manifest. 

 This cause of discrepancy between the theory, 

 which does not take resistance into the account, 

 and the fact, Galileo perceived ; and accordingly he 

 says 12 , that the velocities of the projectiles, in such 

 cases, may be considered as excessive and super- 

 natural. With the due allowance to such causes, 

 he maintained that his theory was verified, and 

 might be applied in practice. Such practical ap- 

 plications of the doctrine of projectiles no doubt 

 had a share in establishing the truth of Galileo's 

 views. We must not forget, however, that the 

 full establishment of this second law of motion was 

 the result of the theoretical and experimental dis- 

 cussions concerning the motion of the earth: its 

 fortunes were involved in those of the Copernican 

 system ; and it shared the triumph of that doctrine. 

 This triumph was already decisive, indeed, in the time 

 of Galileo, but not complete till the time of Newton. 

 18 Op. vol. iii. p. 147. 



