ii8 HERMANN VON HELMHOLTZ 



last decade of his life, is intimately connected, though the 

 latter was of course considered from an altogether different 

 point of view. 



Helmholtz fully recognized the importance of an attack 

 upon this particular part of his treatise on the Conservation 

 of Energy, because this was his main advance on the investiga- 

 tions of Robert Mayer, and the chief significance of his own 

 work rests upon the same considerations. Both engineers and 

 physicists had for a long time defined the product of the 

 mass of a weight raised, and the height it is raised to, as 

 the measure of work done ; this conception of quantity of work, 

 as the product of force into a distance, had to be transferred 

 from the case in which there is a force of constant magnitude 

 acting in a constant direction, viz. gravitation, to the cases 

 where a large or even infinite number of particles, acting 

 upon each other, undergo relative displacement, so that work 

 is done along the path of each individual particle by the 

 forces exerted by the other particles. 



Green had defined this amount of work as potential, for attrac- 

 tive and repulsive forces, the intensity of which is inversely 

 proportional to the square of the distance of the interacting 

 masses, and applied its mathematical properties to the explana- 

 tion of electrical and magnetic phenomena. It was then seen 

 that this same quantity of work, taken negatively, is a factor 

 to be considered in all problems of mechanics and physics : 

 it was named potential energy to distinguish it from the product 

 of half the masses into the squares of the velocity, which was 

 termed vis viva, or actual energy. By this conception Helmholtz 

 was able to proceed from the earlier law of the ' Conservation 

 of Vis Viva', as laid down in the mechanics of ponderable 

 masses, to the great law of the 'Conservation of Energy ', 

 which, in addition to asserting that matter can neither be 

 destroyed nor added to, affirms the constancy of energy as 

 the sum of actual and potential energy. The old formula, 

 the so-called ' law of the conservation of vis viva ', only dealt 

 with cases in which the potential energy was unchanged, and 

 therefore disappeared in the final result. 



Clausius protested against the derivation of the law of the 

 1 conservation of vis viva ', as given by Helmholtz in his memoir, 

 where he takes it as the point of departure for his own great 



