HELMHOLTZ 295 



training at present-day universities, in which innumerable 

 students are plagued with the most out-of-the-way matters 

 merely for the purpose of examination, and many of these 

 again, as teachers in schools, pass on to the next generation 

 the same endless and useless plague, instead of inculcating 

 modest but accurate fundamental knowledge and the simple 

 great fundamental sense of mathematical thought, whereas 

 only few are capable of originating any kind of progress by 

 means of mathematics, and have no need to waste their time 

 in this way. 



As an example of Helmholtz's gift of correctly deducing 

 the possibility of unknown natural phenomena from known, 

 we may mention his early reference to electrical oscillation,^ 

 six years before this process, so well known to-day, had 

 been calculated by William Thomson on the basis given by 

 Faraday, and ten years before it was actually observed. 

 Then we have his proof that light of sufficiently short wave- 

 length would pass through everything in straight lines, three 

 years before rays for which this is true were discovered, and 

 twenty years before the rays so discovered (and quickly 

 used in medicine), were actually shown to be ether waves of 

 extremely short wave-length. Helmholtz then also pro- 

 duced works of a general description, which contributed 

 greatly to his public reputation, some of these being of a 

 popular character. We may mention his larger works, the 

 Physiological Optics, and his Theory of Sound, and also many 

 lectures and papers, in which his understanding for art, and 

 particularly for music, played a part, and in which he was 

 able to gain a very large circle of readers, since he met the 

 taste and views of his time halfway, as for example, when he 

 allows himself to give an estimate of Aristotle. 



^ In the paper on the conservation of force, 1 847. 



