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 II. On the Methods of Theoretical Physics, 



By LUDWIG BOLTZMANN *. 



[This Article was written for and published in the ' Catalogue of the 

 Mathematical Exhibition/ which the Association of German Mathema- 

 ticians had arranged to be held last year at Niiremburg, but which was 

 at the last moment postponed to September in this year at Munich. 



It contains such a clear exposition of the views held at different times 

 about the methods in Mathematical Physics, and more especially of 

 Maxwell's views, and of his use of models and apparatus constructed to 

 imitate dynamically natural phenomena, that the Council of the Physical 

 Society have thought it desirable to make it more easily accessible to 

 English Physicists by publishing this translation.] 



CALLED upon by the Editors of the Catalogue to deal 

 with this subject, I soon became aware that little which 

 is new could be said, so much and such sterling matter having 

 in recent times been written about it. An almost exaggerated 

 criticism of the methods of scientific investigation is indeed 

 a characteristic of the present day ; an intensified Critique of 

 Pure Reason we might say, if this expression were not perhaps 

 somewhat too presumptuous. It cannot be my object again 

 to criticise this criticism. I will only offer a few guiding 

 remarks for those who, without being specially occupied with 

 these questions, nevertheless take an interest in them. 



In mathematics and in geometry it was at first undoubtedly 

 the necessity for economizing labour which led from purely 

 analytical to synthetical methods, as well as to their illus- 

 tration by models. Even if this necessity appears to be a 

 purely practical and obvious one, we here find ourselves on 

 ground on which a whole species of modern methodological 

 speculations have grown up, which have been expressed by 

 Mach in the most definite and ingenious manner. He, indeed, 

 directly maintains that the sole object of Science is economy 

 of labour. 



Seeing that in business affairs the greatest economy is 

 desirable, it might, with equal justice, be maintained that this 

 is simply the object of the sale-room, and of money in general, 

 which in a certain sense would be true. Yet when we search 

 into the distances, the motions, the magnitudes, the physical 

 and chemical structure of the fixed stars, when microscopes 

 are invented and we thereby discover the origins of disease, 

 we shall not be very apt to describe this as mere economy. 



But it is after all a matter of definition what we denote as 

 an object, and what are the means for obtaining that object. 

 It in fact depends on our own definition of existence what 



* Communicated by the Physical Society. 



