44 On the Methods of Theoretical Physics, 



branches of theoretical physics. As mechanical analogies 

 may be cited Maxwell's gas molecules which repel each other 

 with a force inversely proportional to the fifth power of 

 their distance, and at first investigators were not wanting 

 who, not understanding Maxwell's tendency, considered his 

 hypothesis to be improbable and absurd. 



The new ideas, however, gradually found entrance into 

 all regions. In the theory of heat I need only mention 

 Helmholtz's celebrated memoirs on the mechanical analogies 

 of the second law of thermodynamics. It was seen indeed 

 that they corresponded better to the spirit of science than 

 the old hypotheses, and were also more convenient for the 

 investigator himself. For the old hypotheses could only be kept 

 up as long as everything just fitted ; but now a few failures 

 of agreement did no harm, for it can be no reproach against 

 a mere analogy if it fits rather loosely in some places. Hence 

 the old theories, such as the elastic theory of light, the theory 

 of gases, the schemes of chemists for the benzole rings were 

 now only regarded as mechanical analogies, and philosophy at 

 last generalized Maxwell's ideas in the doctrine that cogni- 

 tion is on the whole nothing else than the discovery of analogies. 

 With this the older scientific method was defined out of the 

 way, and Science now only spoke in parables. 



All these mechanical models at first existed indeed only 

 in idea ; they were dynamical illustrations in the fancy, and 

 they could not be carried out in practice, even in this general 

 form, yet their great importance was an incitement to realize 

 at any rate their fundamental types. 



In the second part of this Catalogue is a description of such 

 an attempt made by Maxwell himself, and of one by the 

 author of these lines. Fitzgerald's model is also at present 

 in the Exhibition, as well as Bjerknes' model, which owe their 

 origin to similar tendencies. Other models which have to be 

 classed with these have been constructed by Oliver Lodge, 

 Lord Rayleigh, and others. 



They all show how the new tendency to relinquish perfect 

 congruence with Nature is compensated by the more striking 

 prominence of points of similarity. To this belongs the 

 immediate future ; yet, mistaken as it was to consider the old 

 method as the only correct one, it would be just as one-sided 

 to consider it, after all it has accomplished, as quite played out, 

 and not to cultivate it along with the new one. 



