594 APPLIED MATHEMATICS 



The accusation has been made that physical hypotheses have 

 sometimes proved injurious and have delayed the progress of the 

 science. This accusation is based chiefly upon the role which the 

 hypothesis of the electric fluid has played in the development of the 

 theory of electricity. This hypothesis was brought to a high stage 

 of perfection by Wilhelm Weber, and the general recognition which 

 his works found in Germany did indeed stand in the road of the 

 theory of Maxwell. In a similar manner Newton's emanation theory 

 stood in the w r ay of the theory of undulations. But such incon- 

 veniences can scarcely be entirely avoided in the future. It will al- 

 ways be the tendency to complete as far as possible the prevailing 

 view, and to make it self-sufficient whenever such a theory is self- 

 consistent and does not in any way lead to a contradiction, whether 

 it consist of mechanical models, of geometrical pictures, or of mathe- 

 matical formulas. It will always be possible that a new theory will 

 arise which has not yet been tested by experiment and which will 

 represent a much larger field of phenomena. In such cases the older 

 theory will count the largest following until this field of phenomena 

 is brought into the range of experiment, and decisive tests demon- 

 strate the superiority of the newer one. It is certainly useful, if the 

 theory of Weber be always held up as a warning example, that one 

 should bear in mind the essential progress! veness of the intellect. 

 The services of Weber are not decreased by this, however; Maxwell 

 himself speaks of his theory with the greatest wonder. Indeed, this 

 instance cannot be taken into consideration against the usefulness of 

 hypotheses, since Maxwell's theory contained as much of the hypo- 

 thetical as any other. And this was eliminated only after it became 

 generally known through Hertz, Poynting, and others. 



The accusation has also been raised against hypotheses in physics 

 that the creation and development of mathematical methods for 

 the computation of the hypothetical molecular motions has been 

 useless and even harmful. This accusation I cannot recognize as 

 substantiated. Were it so, the theme selected for my present lecture 

 would be an unfortunate one; and this fact may excuse me for 

 having lingered on this much-discussed subject and for having sought 

 to justify the use of hypotheses in physics. 



I have not chosen for the thesis of my present lecture the entire 

 development of physical theory. Several years ago I treated this 

 subject at the German Naturforscherversammlung in Munich, and 

 although some new developments have taken place since then, I 

 should have to repeat myself a great deal. Moreover, one who has 

 committed himself to one faction is not in a position to judge the 

 other factions in a completely objective manner. I do not refer to a 

 criticism of its value; my lecture shall not criticise, but shall judge. 

 I am also convinced of the value of the views of my opponents and 



