SOME USES OF MATHEMATICS 117 



remember but one of them, since any one is obtainable 

 from another by the simplest algebraic process. In 

 passing from one form to another we have reasoned 

 mathematically. 



In the case of any law of science which may be ex- 

 pressed in the form Z = XY where X, Y, and Z are the 

 magnitudes with which the law deals we may always 



reason by the same mathematical processes as we 



y 

 employed above and arrive at the results of Jf = and 



17 



Y = . Now, it happens that in an ordinary elemen- 

 X 



tary course hi physics, such as that of a high school, 

 the student meets about forty physical laws which are 

 expressible by just this simple relation. In our dis- 

 cussion we have arrived quickly at the general and 

 abstract case. Partly because of the immaturity of 

 high-school students and partly because of certain 

 traditions and inhibitions of their teachers it too fre- 

 quently happens that each of these laws is dealt with 

 as a special concrete case. The result is that the simple 

 mathematical transformations which we have indicated 

 above occasion what is perhaps undue difficulty, and 

 overemphasize what are popularly considered the 

 mathematical difficulties of the subject. 



There are two reasons why this typical equation 

 should be carefully studied. The first is the obvious 

 one that it would make the subsequent work of the 

 student much easier, for whenever he meets a law 

 expressible hi this form he knows that he may apply 

 the same mathematical processes of reasoning with 

 similar results. The second advantage is that he may 



