G. F, Becker — " Potential " a Bernoullian Term. 99 



It is natural to inquire what Enler and Bernoulli meant in 

 terms of modern nomenclature by vis potentialis. Now Saint- 

 Yenan4; has pointed out* that if Mis, Young's modulus and J 

 the moment of inertia of the cross section of the spring, the 

 work done in flexure for a length s is 



MJ r s ds 



so that Bernoulli's function is simply proportional to the 

 potential energy as that expression is now understood and to 

 the Potential, a fact to which the great French elastician calls 

 attention. 



There seems to be a general impression that the natural 

 philosophers of the last century, when, they used the quanti- 

 ties now known as kinetic, potential and total energy at all, 

 regarded them from a purely algebraical or geometrical point 

 of view, failing to perceive their great physical significance. 

 In this respect these physicists seem to have been underrated : 

 as some passages from the first John Bernoulli, Euler's 

 teacher and D. Bernoulli's father, will show. In a paper on 

 the true conception of living forcesf he generalizes the idea of 

 vis viva and defines it as equivalent to capacity for doing 

 work, or facxiltas age?icli, which is simply a Latin equivalent of 

 the Greek energy. In Section I of this paper he says (trans- 

 lated) : 



" Yis viva does not consist in the actual exertion, but in the 

 capacity for doing work ; for it subsists even when it does no 

 work nor has any object whereon it could act ; so for example 

 a strained spring, or again a body in motion, has in itself the 

 capacity of doing work, so that if nothing external to itself 

 come in its way upon which it may exert itself, and so long 

 as there is no object present with which it can come in contact, 

 it infallibly retains it all undiminished by time, and does not 

 do the work which it would be capable of doing if it had the 

 opportunity." 



This seems a clear and even a vivid statement of the law : 

 " When a system is subjected to no external forces, its energy 

 remains constant." 



In Section III he takes a further step. " Yis viva (which 

 would be more aptly named facultasagendi, gallice le pouvoir)^: 



*Lecons de Wavier, edition of 1864. p. cxij. 



f Devera notione virium vivarum, Acta Eruditorum, Leipzig, 1*735, p. 210. 



% The term power is now rarely used for energy, but it is scarcely a generation 

 since this meaning was common enough. Saint- Venant (op. cit., p. 785) in 1864 

 defined the potential of one or more forces as "leur pouvoir moteur total." B. 

 Peirce in his great work on analytical mechanics 1865 always uses "power" 

 instead of "energy." 



