124 THE REALITIES OF MODERN SCIENCE 



Some of them are obtained by relations of the general 

 form Z = XY, which are not physical laws but defining 

 equations. For example, the velocity with which a 

 body moves is the ratio of the space traversed to the 

 time consumed. Hence the defining equation is 

 V = S/T. The unit of velocity is then 1 cm./l sec., 

 or 1 cm. per sec. as it is usually read. 



Similarly if the velocity changes, that is ; if the motion 

 is accelerated, the measure of the acceleration is de- 

 fined as the rate of change of velocity, and is a change 

 in velocity (expressed in cm. per sec.) occurring in 1 

 second. Of this we shall have occasion to treat more 

 fully in the next chapter when we consider "rates." 



Before doing so it may be of interest to note two 

 illustrations of the importance of mathematics to the 

 student of science. In the development of our knowl- 

 edge of mechanics and hence of astronomy, which deals 

 with celestial mechanics, there came a time about 

 1600 A.D. when further progress had to wait until 

 new mathematical tools were developed. These tools 

 were supplied by Newton, who invented a mathematical 

 method of studying problems which involve motion. 

 This is the method mentioned on page 32. Similar 

 methods were developed independently by Leibnitz, for 

 this was a remarkable age in mathematics. 



The second illustration concerns the discovery of 

 wireless telegraphy. In 1873 Maxwell, who was a 

 prominent physicist, highly trained in the use of mathe- 

 matical tools, announced that light was an electrical 

 phenomenon and traveled as an electromagnetic wave. 

 He further stated the possibility of there being other 

 electromagnetic waves which would not produce the 



