118 . THE REALITIES OF MODERN SCIENCE 



then concentrate his attention more on the physics 

 of the relation and not so much on the mathematics. 



In other words, mathematics to the scientist or 

 engineer is merely a tool, which he should use like a 

 good workman almost by second nature, thinking not 

 of the tool but of the work which he wishes to do. Of 

 course, a workman selects the tool required for the 

 particular job which he has in mind, but he does so as 

 the result of previous knowledge as to how the work 

 is to be done and of previous experience with his tools. 

 In this chapter we shall consider briefly relations sym- 

 bolized by equations of the form Z = XY, which proves 

 so troublesome to the high-school student, and in the 

 next chapter we shall consider another illustration of 

 mathematics which frequently proves unnecessarily 

 difficult to his college brother. 



One familiar case of the relationship Z=XY has 

 been illustrated by the area of a rectangle. Let us 

 consider another in the expression of the law for the 

 volume of a rectangular box. We derive the law for 

 the volume by noticing that if the area of the base is 

 increased, e.g. doubled, the volume is proportionately 

 increased, e.g. doubled. Symbolizing the volume by 

 V and the area as before, we express this fact as 



V oc A i (4) 



Similarly, if the area of the base is kept constant and 

 the height changed the volume is altered proportion- 

 ately ; thus, representing height by H 



V oc H (5) 



1 The symbol oc obviously means "is proportional to." 



