PROFESSOR AT KONIGSBERG 119 



aw. He objected that Helmholtz had, even in the simple case 

 in which two particles act on one another, assumed, in addition 

 to his assumption of the law of the conservation of vis viva, 

 that the magnitude of the force was a function of the dis- 

 tance, concluding therefrom that the direction of the force 

 coincided with the line connecting those points. Helmholtz 

 showed this objection also to be ill-founded, and embraced the 

 opportunity of giving a further and more complete discussion 

 of this point, suggesting a new and interesting treatment of 

 the subject. Starting with the definition that movable points 

 have the same relative position to each other, whenever 

 a system of co-ordinates can be constructed in which all the 

 co-ordinates shall have relatively the same values, Helmholtz 

 expresses the law of the conservation of vis viva in this form : 

 'When any number of particles in motion are only moving 

 under the influence of such forces as they are themselves 

 exerting upon one another, then the sum of the vis viva of 

 all particles at any moment in which all the particles recover 

 their same relative position, is constant whatever their direction 

 and velocity at intermediate times ' ; and in virtue of this law 

 he again refutes Clausius's objection that in certain cases the 

 vis viva may be a purely arbitrary function of the co-ordinates 

 of the system. He states expressly that he made the assump- 

 tion in his treatise that the force exerted by one particle upon 

 another is independent of any other forces that may be acting 

 upon it, a principle which has always been accepted in 

 mechanics. He concludes by saying that he had expected 

 criticism from Clausius in regard to his Theory of Galvanism : 

 1 The chapter on electro-dynamics in my treatise was written 

 under great difficulties. At that time I scarcely had access to 

 any mathematical and physical literature, and was almost 

 wholly confined to what I could discover for myself. It can 

 only be a gain if the ideas which I endeavoured to bring 

 forward in my paper at a time when they were rinding 

 little response from the physicists, are taken up afresh by 

 another thinker, and handled with the same thorough criticism 

 as Dr. Clausius has bestowed on other chapters of the Theory 

 of the Conservation of Energy/ 



He then enumerates the results obtained at a later period 

 under more favourable circumstances, and lays down the 



