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



" force," and also, in order to distinguish between this and the 

 following conception, u dead force" (vis mortua). 



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

 space through which it acts, or, again, the product — or half-pro- 

 duct — 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" (JVirkungsraum) : 

 and in this case a magnitude which is proportional to the " push- 

 ing 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 motion," or " moving force." 



With the generic conception of "force," the higher mechanics, 

 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 obtained runs thus — 

 " Force is everything 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 pos- 

 sibility combined into a generic conception. Pressure or attrac- 

 tion is, in the theory of motion, what affinity is in chemistry — 

 an abstract conception: living force, like matter, is concrete; 

 and these two kinds of force, however closely connected in the 

 region of the association of ideas, are in reality so widely sepa- 

 rated 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 diffi- 

 culty. For instance, just as we speak of absolute weight, specific 

 weight, and combining weight, without its ever entering any 

 one's head to want to construct a generic idea out of these 

 distinct notions, so two or more meanings may be attached to the 

 word force. This is what is actually done in the higher mecha- 

 nics, and hence in this branch of science we meet with no men- 

 tion of a generic conception of "force." 



There has been no lack of recommendations to carry, in like 

 manner, the notions of " dead " and " living force " as distinct 

 and separate through the other departments of science ; it has, 



