64 SCIENTIFIC APPARATUS. 



ing down inclined planes, the law of which he at first assumed, 

 and afterwards proved to be identical with that of the other. The 

 former statement, that the velocity increases uniformly, is directly 

 tested by an apparatus known as Attwood's machine, consisting 

 essentially of a pulley, over which a string is hung with equal 

 weights attached to its ends. A small bar of metal is laid on one 

 of the weights, which begins to descend and pull the other one 

 up ; after a measured time the bar is lifted off, and then, both 

 sides pulling equally, the motion goes on at the rate which had 

 been acquired at that instant. The distance travelled in one 

 second is then measured, and gives the velocity ; this is found to 

 be proportional to the time of falling with the bar on, 



The second statement, that the space passed over is propor- 

 tional to the square of the number of seconds elapsed, is verified 

 by Morin's machine, which consists of a vertical cylinder which 

 revolves uniformly while a body falling down at the side marks it 

 with a pencil. The curve thus described is a record of the dis- 

 tance the body had fallen at every moment of time. 



This investigation of Galileo's was in more than one 



Fluxions. . . 



aspect the foundation of dynamical science :; but not 

 the least important of these aspects is the proof that either of the 

 two ways of stating the law of falling bodies involves the other. 

 Given that the distance fallen is proportional to the square of 

 the time, to show that the velocity is proportional to the time 

 itself; this is a particular case of the problem. Given where a 

 body is at every instant, to find how fast it is going at every 

 instant. The solution of this problem was given by Newton's 

 Method of Fluxions. When a quantity changes from time to 

 time, its rate of change is called \hz fluxion of the quantity. 

 In the case of a moving body the quantity to be considered is 

 the distance which the body has travelled; the fluxion of 

 this distance is the rate at which the body is going. New- 

 ton's method solves the problem, Given how big a quantity is 

 at any time, to find its fluxion at any time. The method has been 



