98 G. F. Becker — "Potential" a Bernoullian Term. 



mus . . . Daniel Bernoulli mihi indicasset se universam vim, 

 quae in lamina elastica incurvata insit, una quadam formula 

 quam vim potentialem appellat complecti posse, hancque ex- 

 pressionem in curva elastica minimam esse oportere, etc." In 

 stating his problem lie says again "atque, secundum Bernoul- 

 lium, exprimetur vispote)itialis in laminae portione AM con- 



tenta hac formula /pp," s being the arc of the spring and R 



the radius of curvature.'-'' It is evident that in these passages 

 vis is used in the same sense as in vis viva and that it is to be 

 translated energy, so that Bernoulli's proposition was that the 

 elastic curve must be such as to make something which he 

 regarded as the potential energy of a bent spring a minimum. 



Todhunter in his History of Elasticity, 1886, quotes pas- 

 sages from D. Bernoulli's letters in 1742-3, in which the vis 

 potentialis is mentioned ; but since the historian makes no allu- 

 sion to his earlier remarks on the origin of the name Potential, 

 it must be inferred that no relation between the two terms 

 suggested itself to him. Had Todhunter lived to edit his 

 history, perhaps this omission would have been supplied. 



It is well known that Green's great memoir was not pub- 

 lished in the ordinary manner, but by subscription in Notting- 

 ham, and that it attracted no attention for many years either 

 in Great Britain or on the Continent. Gauss was thus very 

 naturally ignorant of it. On the other hand it is substantially 

 impossible to suppose Gauss ignorant of the famous memoir of 

 Euler quoted above. The methods there developed of finding 

 curves have been superseded by those of the calculus of varia- 

 tions ; but the appendix, Additamentum de ourvis elasticis, 

 from which the passage quoted above is taken, contains the 

 classification of elastic curves into nine species which, so far 

 as I am aware, has received no addition or improvement. 



There can thus be substantially no doubt that Daniel 

 Bernoulli's vis potentialis suggested to Gauss the name poten- 

 tial for a somewhat similar but more general function. Either 

 he considered the change of form of the expression and the 

 increased generality of its significance as sufficient to make 

 any reference to Bernoulli needless ; or, as seems more prob- 

 able, he assumed that his readers were as well read as himself 

 and that an allusion was supernuous.f 



* De Methodis inveniendi lineas curvas maximi niinimive proprietate gaudentes. 

 1744, pp. 246, 247. 



f The potential has received a variety of names in modern times. " Force 

 function,"' which seems to be used by European mathematicians at least as fre- 

 quently as potential, was proposed by W. R. Hamilton in his famous memoir on 

 varying action, Phil. Trans, 1834, p. 249. In the same year B. de Saint- Venant 

 called it "latent dynamic capital" (Lecons de Javier. 1861. p. 786) and Ampere 

 suggested " implicit vis viva." Ann. chim. phys., vol. lviii, 1835, p. 438. 



