RELATIONS OF APPLIED MATHEMATICS 595 



only arise to repel them when they attempt to belittle mine. But 

 one can scarcely give as complete an account according to subject- 

 matter, and an exposition of the inter-relations of all ideas in the 

 views of another, as in his own. 



I shall therefore select as the goal of my lecture to-day not merely 

 the kinetic theory of molecules, but, moreover, a highly specialized 

 branch of it. Far from denying that it contains hypotheses, I must 

 rather characterize it as a bold advance beyond the facts of observa- 

 tion. And I nevertheless do not consider it unworthy of this occa- 

 sion; this much faith do I have in hypotheses which present certain 

 peculiarities of observation in a new light or which bring forth rela- 

 tions among them which cannot be reached by other methods. We 

 must indeed be mindful of the fact that hypotheses require and are 

 capable of continuous development, and are only then to be aban- 

 doned when all the relations which they represent can be better 

 understood in some other manner. 



To the above-mentioned problems, which are as old as the science 

 and still unsolved, belongs the one if matter is continuous, or if it 

 is to be considered as made up of discrete parts, of very many, but 

 not in the mathematical sense infinite, individuals. This is one of 

 the difficult questions which form the boundary of philosophy and 

 physics. 



Even some decades ago, scientists felt very shy of going deeply 

 into the discussion of such questions. The one before us is too real 

 to be entirely avoided ; but one cannot discuss it without touching on 

 some profounder still, such as upon the nature of the law of causation, 

 of matter, of force, and so forth. The latter are the ones of which it 

 was said that they did not trouble the scientist, that they belonged 

 entirely to philosophy. To-day the situation is different, there is 

 evident a tendency among scientists to consider philosophic questions, 

 and properly so. One of the first rules of science is never to trust 

 blindly to the instrument with which one works, but to test it in 

 all directions. How, then, are we to trust blindly to inherited and 

 historically developed conceptions, particularly when there are 

 instances known where they led us into error ? But in the examina- 

 tion of even the simplest elements, where is the boundary between 

 science and philosophy at which we should pause ? 



I hope that none of the philosophers present will take offense or 

 perceive an accusation, if I say boldly that by assigning this question 

 to philosophy the resulting success has been rather meagre. Philo- 

 sophy has done noticeably little toward the explanation of these 

 questions, and from her own one-sided point of view she can do so just 

 as little as natural science can from hers. If real progress is possible, 

 it is only to be expected by cooperation of both of these sciences. 

 May I therefore be pardoned if I touch slightly upon these questions 



