PHYSICAL CUR\nES. 99 



branch, physics, is a science of discovery and concerns nat- 

 ural laws beyond the control of man. If, however, a com- 

 parison be made between these two lines of investigation, the 

 reason for the existence of the common boundary region is 

 easily found. The fundamental concepts of mathematics are 

 practically only two, namely, magnitude and direction. The 

 former includes all variations of size under the given law in 

 question, the latter all matters of composition and opposition, 

 positiveness and negativeness, etc. These fundamental con- 

 cepts underlie all branches of mathematics. In the field of 

 physics, it is found that all force, motion, energy and such 

 other entities as are met with in nature, are governed by laws 

 which group themselves around two fundamental ideas, first, 

 that these quantities var}- in magnitude in certain determined 

 ways, and second, that they act sometimes in one direction 

 and sometimes in the other, sometimes in conjunction with 

 one another, sometimes in opposition, sometimes inward, 

 sometimes outward, etc. In other words, again we have the 

 same two concepts of magnitude and direction. Hence, with 

 identical fundamental ideas in both mathematics and physics, 

 it naturally results that many identical relations should have 

 been evolved in one case and discovered in the other. 



