47 ON THE ORIGIN OF FORCK. 



stratable that the total amount of vis viva in any moving 

 system abandoned to the mutual reaction of its particles, 

 while depending at every instant of time, solely for its 

 magnitude, on the then ^ relative situation of those par- 

 ticles (or being, in algebraical phrase, a function of their 

 mutual distances), has a maximum value which it cannot 

 exceed, and a minimum below which it cannot descend. 

 Let its state then be what it will, there is sure to be a 

 certain amount of vis viva by which its actual falls short 

 of its extreme possible value ; and to say that the amount 

 of this deficiency added to the actual present amount 

 will make up the maximum, is neither more nor less than 

 a truism : whether expressed in so many words, or by say- 

 ing that the potential together with the actual energy of 

 the system is invariable ; or, again, in other words, that 

 when certain changes have taken place in the relative 

 situations of the parts of the system, what it has lost in 

 actual it has gained in potential energy. When in speak- 

 ing of a mechanical combination we say that what is lost 

 in time is gained in power, though equally a translation 

 in ordinary language of a dynamical equation, the terms 

 uf;cd refer to different modes of viewing the expendi- 

 ture of force. But in the case before us they stand in 

 their nakedness of similar meaning and convey to the 

 mind no equivalence available for any purpose of rea- 

 soning. If, indeed, we could be assured, a priori, that the 

 system is one of simple or compound periodicity in which 

 a certain lapse of time will restore every molecule to 

 identically the same relative situation with respect to all 

 the rest ; we should then be sure that in the nature oi 



