ch. v.] THE TWO METHODS. 109 



omitted elements of the case were brought before the mind, 

 he discovered " that the seeming possibility was a fiction." 

 The other alternative, that velocity is proportional to time, 

 was found to be the true one, and the only one which could 

 withstand the application of the test of truth. The counter- 

 proposition, that the velocity is not proportional to the time, 1 

 is strictly unthinkable. For it involves the assertion that 

 the same amount of gravitative force will cause, in a given 

 second of time, an increment of velocity which is either 

 greater or less than the increment of velocity which it will 

 cause in the succeeding second. We are required to suppose, 

 in the first case, an addition to the velocity without any 

 addition to the force which causes it ; in the second case, we 

 are required to suppose a subtraction from the velocity 

 without any subtraction from the force ; and therefore, in 

 either case, we are required to frame in thought an equation 

 between something and nothing, — which is impossible. 



Thus the objective method starts by verifying its premise ; 

 and, not content with any apparent congruity in its syllogistic 

 processes, it does not definitely accept the conclusion until 

 that also has been confronted with the phenomena. And, if 

 in the verified conclusion there is involveu an unexplained 

 residuum, far from giving up its conclusion out of deference 

 to some imaginary subjective necessity, it acknowledges the 

 need of a new search in order to account for such residuum. 

 The old conclusion, that planetary motion is circular and 

 uniform because motion is naturally circular and uniform, left 

 no unexplained residual phenomenon. As an explanation it 

 was complete, though utterly false. If asked why the 

 olanets move in circles with a uniform velocity, the ancients 



1 To spenk of the velocity as proportional to the time is, however, a some- 

 what lax use of mechanical terminology. Strictly speaking, the velocity is a 



inction of t. s time and of gravity. Since gravitative force increases as the 

 body approaches the earth, there are increased increments of velocity in suc- 

 cessive equal times. Introducing this correction into the sentences which 



ollow, the reasoning becomes strictly accurate. 



