424 HERMANN VON HELMHOLTZ 



of fixed associations between the same, and that they were 

 discovered and proved on this assumption only. 



'At a later time it was found by observation that the pro- 

 positions thus derived command a much wider application in 

 Nature than follows from the proof which is given of them, and 

 it was thence concluded that certain universal characteristics of 

 the Newtonian conservative forces of attraction obtain for all 

 natural forces, although no one succeeded in reducing this 

 generalization to a common basis.' 



Helmholtz then points out that Hertz had endeavoured to 

 discover this fundamental conception, inasmuch as, in order to 

 give a perfectly logical derivation for all the laws of mechanical 

 processes that have hitherto been recognized as universal, 

 he had selected the outlook of the oldest mechanical theories 

 as his sole standpoint, and had imagined all mechanical pro- 

 cesses to proceed as though the several associations between 

 the interacting parts were fixed, explaining the forces that 

 exist between bodies not in direct contact by means of the 

 hypothesis that there are a great number of imperceptible 

 masses and invisible motions. Helmholtz's cyclical systems 

 with invisible motions were employed by Hertz for the working 

 out of examples ; indeed the whole structure of his mechanics 

 rests upon the foundation laid by Helmholtz, but the death of 

 this brilliant investigator stopped the advance of mechanics in 

 this direction, possibly for many years. 



1 English physicists like Lord Kelvin in his theory of vortex 

 atoms, and Maxwell in his assumption of a system of cells with 

 rotating contents on which he based his attempt at a mechanical 

 explanation of electromagnetic processes, had obviously found 

 greater satisfaction in explanations of this kind, than in the 

 mere general representation of facts, and the laws that govern 

 them, such as is given by the systems of the differential 

 equations in physics. I confess that, for my own part, I have 

 hitherto adhered to this last kind of representation, and regarded 

 it as the safest ; but I have no substantial objections to make to 

 a method^ recommended by such prominent physicists as the 

 three above named. Certainly there are still great difficulties 

 to be overcome in the attempt 'to explain particular sections 

 of physics on the basis proposed by Hertz. But, as a 

 whole, the Hertzian representation of the fundamental laws of 



