SOME USES OF MATHEMATICS 127 



The illustration in question indicates well the manner 

 by which science grows, that is, by accretions or con- 

 tributions. These have been made in the history of 

 science by many men whose names have long been 

 forgotten or, as hi the case of some of the earliest dis- 

 coverers, by men who probably had no names at all. 

 Such contributions have been made by men of all 

 races and nationalities. In the case of radio-telegraphy 

 it is to be recalled that Maxwell was an Englishman, 

 Hertz a German, and Marconi an Italian. 



While the individual who makes any advance in 

 science is deserving of great credit it must not be for- 

 gotten that such discoveries are rarely if ever made until 

 the time is ripe for them, that is, until the whole body 

 of scientific knowledge and methods has prepared the 

 way for the discovery of genius or of accident, as the 

 case may be. The man who actually makes the dis- 

 covery is usually but a little time ahead of his foremost 

 contemporaries. 



In our illustration this is true and was so recog- 

 nized, for example, by Hertz. In the preface to the 

 collected papers on his work, which were published some 

 years later, he generously but truly states that if he 

 had not happened to make the discovery, some other 

 scientist would have done so shortly. He mentions 

 Lodge, the English scientist, who was then working 

 along somewhat similar lines, as most likely to have 

 made the advance. 



