Dr. J. R. Mayer on the Mechanical Equivalent of Heat, 507 



garded, the equation just given may be abbreviated into the 



c 

 very convenient form g = - without 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 equation thus radically inaccurate, there are 

 planted in the receptive mind of youth such false notions as, — 

 that gravity is a uniformly accelerating (?) force, a moving (?) 

 force whose action is proportional to the time (?) ; that force is 

 directly proportional (?) 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 fra- 

 ming 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 exami- 

 nation that the retention, under that name, of the conception of 

 force distinguished above by I. has nothing but its origin to 

 recommend it, but much to condemn it, the rest follows almost 

 spontaneously. It accords with the laws of thought, as well as 

 with the common usage of language, to connect every produc- 

 tion 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 produced. 



This definition not only corresponds perfectly with facts, but 

 it accords as far as possible with that which already exists ; for, 

 as I shall show, it contains by implication the conception of 

 force as met with in the higher mechanics, and referred to above 



If a mass M, originally at rest, while traversing the effective 

 space s, under the influence and in the direction of the pressure 

 p, acquires the velocity c, we have /w = Mc 2 . Since, however, 

 every production of motion implies the existence of a pressure 

 (or of a pull) and an effective space, and also the exhaustion of 

 one at least of these factors, the effective space, it follows that 

 motion can never come into existence except at the cost of this 

 product, ]js = Mc 2 . And this it is which for shortness I call 

 "force." 



The connexion between expenditure and performance (in other 

 words, the exhaustion of force in producing its effect) presents 

 itself in the simplest form in the phenomena of gravitation. The 



