NEWTON'S CONCEPTION OF FORCE. 335 



ics is required. On the other hand, it is quite true that, so 

 long as we have to do only with cases in which the space 

 fallen through is so small in comparison with the earth's semi- 

 diameter that it may be disregarded, the equation just given 



c 



may be abbreviated into the very convenient form g = ~i with- 

 out any considerable error ; but this expression can never be 

 mathematically exact so long as the space fallen through has 

 any calculable magnitude. But on the strength of an equa- 

 tion thus radically inaccurate, there are planted in the recep- 

 tive mind of youth such false notions as that gravity is a 

 uniformly accelerating ( ?) force, a moving ( ?) force whose ac- 

 tion is proportional to the time ( ?) ; that force is directly pro- 

 portional ( ?) to the velocity produced ; and many other like 

 errors. 



It would certainly be a great merit if authors of treatises 

 on physics would help to remedy this state of things, and in 

 framing their definitions would start only from thoroughly 

 exact determinations of magnitudes ; for elementary physics 

 in its present form, instead of being a well-grounded science, 

 is only a sort of half-knowledge, such that on passing to the 

 higher and strictly scientific departments the student must 

 try to forget its principles and theorems as quickly as he can. 



If we have once convinced ourselves by unprejudiced 

 examination that the retention, under that name, of the con- 

 ception of force distinguished above by I. has nothing but its 

 origin to recommend it, but much to condemn it, the rest fol- 

 lows almost spontaneously. It accords with the laws of 

 thought, as well as with the common usage of language, to 

 connect every production of motion with an expenditure of 

 force. Hence " force " is 



Something which is expended in producing motion; and 

 this something which is expended is to be looked upon as a 

 cause equivalent to the effect, namely, to the motion pro- 

 duced. 



