434 TEE POPULAR SCIENCE MONTHLY 



THE THEOEY OF EELATIVITY AND THE NEW MECHANICS 



By Professor WILLIAM MARSHALL 



PURDUE UNIVERSITY 



HE who elects to write on a mathematical topic is confronted with a 

 choice between two evils. He may decide to handle his subject 

 mathematically, using the conventional mathematical symbols, and what- 

 ever facts, formulas and equations the subject may demand — save him- 

 self who can ! Or he may choose to abandon all mathematical symbols, 

 formulas and equations, and attempt to translate into the vernacular this 

 language which the mathematician speaks so fluently. In the one case 

 there results a finished article which only the elect understand, in the 

 other, only a rather crude and clumsy approximation to the truth. A 

 similar condition exists in all highly specialized branches of learning, 

 but it can safely be said that in no other science must one fare so far, 

 and accumulate so much knowledge on the way, in order to investigate or 

 even understand new problems. And so it is with some trepidation that 

 the attempt is made to discuss in the following pages one of the newest 

 and most important branches of mathematical activity. For the writer 

 has chosen the second evil, and, deprived of his formulas, to borrow a 

 figure of Poincare's, finds himself a cripple without his crutches. 



After this mutually encouraging prologue let us introduce the sub- 

 ject with a definition. What is relativity ? By relativity, the theory of 

 relativity, the principle of relativity, the doctrine of relativity, is meant 

 a new conception of the fundamental ideas of mechanics. By the rela- 

 tivity mechanics, or as we may sometimes say, the new mechanics, is 

 meant that body of doctrine which is based on these new conceptions. 

 Now this is a very simple definition and one which would be perfectly 

 comprehensible to everybody, provided the four following points were 

 made clear: first, what are the fundamental concepts of mechanics, 

 second, what are the classical notions about them, third, how are these 

 modified by the new relativity principles, and fourth, how did it come 

 about that we have been forced to change our notions of these funda- 

 mental concepts which have not been questioned since the time of 

 Newton? These four questions will now be discussed, though perhaps 

 not in this order. The results reached are, to say the least, amazing, 

 but perhaps our astonishment will not be greater than it was when first 

 we learned, or heard rather, that the earth is round, and that there are 

 persons directly opposite us who do not fall off, and stranger yet, do 

 not realize that they are in any immediate danger of doing so. 



