MEANING OF THE TEEM U FOKCE." 331 



II. On the other hand, the product of the pressure into 

 the space through which it acts, or, again, the product or 

 half-product of the mass into the square of the velocity, is 

 named " force." In order that motion may actually occur, it 

 is in fact necessary that the mass, whatever it may be, should 

 under the influence of a pressure, and, in the direction of that 

 pressure, traverse a certain space, "the effective space" 

 ( Wirkungsraum) : and in this case a magnitude which is pro- 

 portional to the " pushing force " and to the effective space, 

 likewise receives the name " force ; " but to distinguish it 

 from the mere pushing force, by which alone motion is never 

 actually brought about, it is also called the " vis viva of mo- 

 tion," or " moving force." 



With the generic conception of " force," the higher me- 

 chanics, as an essentially analytic science, is not concerned. 

 In order to arrive at it, we must, according to the general 

 rule, collect together the characters possessed in common by 

 the several species. As is well known, the definition so ob- 

 tained runs thus " Force is every thing which brings about 

 or tends to bring about, alters or tends to alter motion." 



This definition, however, it is easy to see, is tautological ; 

 for the last fourteen words of it might be omitted, and the 

 sense would be still the same. 



This erroneous solution is occasioned by the nature of the 

 problem, which requires an impossibility. Mere pressure 

 (dead force) and the product of the pressure into the effective 

 space (living force) are magnitudes too thoroughly unlike to 

 be by possibility combined into a generic conception. Press- 

 ure or attraction is, in the theory of motion, what affinity is 

 in chemistry an abstract conception : living force, like mat- 

 ter, is concrete ; and these two kinds of force, however closely 

 connected in the region of the association of ideas, are in 

 reality so widely separated that a frame which should take 

 them both in must be able to include the whole world. 



There are several conceivable ways of escaping from the 



