RELATIONS OF APPLIED MATHEMATICS 599 



In saying that such judgments as "everything is red or is not red" 

 are results of experience, I do not mean that every person checks this 

 empty truth by experience, but that he learns that his parents called 

 everything either red or not red and that he preserves this nomen- 

 clature. 



It might seem as if we had gone somewhat deeply into philosophical 

 questions, but I believe that the views we have reached could not 

 have been attained in a shorter and simpler manner. For we have 

 reached an impartial judgment how the question of the atomistic 

 structure of matter is to be viewed. We shall not invoke the law of 

 thought that there is no limit to the divisibility of matter. This law 

 is of no more value than if a naive person were to say that no matter 

 where he went upon the earth the plumb-line directions seemed 

 always to be parallel and therefore there were no antipodes. 



On the one hand we shall start from facts only, and on the other 

 we shall take nothing into consideration except the effort to attain 

 to the most adequate expression of these facts. 



Regarding the first point, the numerous facts of the theory of 

 heat, of chemistry, of crystallography, show that bodies which are 

 apparently continuous do not by any means fill the entire volume 

 indistinguishably and uniformly with matter. Indeed, it appears 

 that the space which they occupy is filled with innumerably many 

 individuals, molecules, and atoms, which are extraordinarily small, 

 but not infinitely small in the mathematical sense. Their sizes can 

 be computed in different manners and always with the same result. 



The fruitfulness of this line of thought has been verified in the 

 most recent time. All the phenomena which are observed with the 

 cathode rays, the Becquerel rays, etc., indicate that we are dealing 

 with diminutive, moving particles, electrons. After a vigorous 

 battle, this view vanquished completely the opposing explanation of 

 these phenomena by the theory of undulations. Not only did the 

 former theory give a better explanation of the previously known 

 facts, it inspired new experiments and permitted the prediction of 

 unknown phenomena, and thus it developed into an atomistic theory 

 of electricity. If it continue to develop with the same success as 

 in past years, if phenomena, such as the one observed by Ramsay 

 on the transmutation of radium into helium, do not remain isolated, 

 this theory promises deductions concerning the nature and structure 

 of atoms as yet undreamed of. Computation shows that electrons are 

 much smaller than the atoms of ponderable matter; and the hypo- 

 thesis that the atoms are built up of many elements, as well as 

 various interesting views on the character and structure of this com- 

 position, is to-day on every tongue. The word atom should not 

 lead us into error, it comes from a past time; no physicist ascribes 

 indivisibility to the atoms. 



