294 GREAT MEN OF SCIENCE 



manifold researches, which are mostly of a kind developing 

 existing knowledge of nature and connecting it together and 

 enlarging it.^ 



The wide range of his gifts included a rare aptitude for 

 mathematics; he thus succeeded in deriving, from the dif- 

 ferential equations of hydrodynamics, the characteristic phe- 

 nomena of eddy formation, and of the structure of jets in 

 liquids and gases, in the most admirable fashion. This was 

 not the achievement of further knowledge of nature, but 

 an unusual mathematical success. ^ For the fundamental 

 equation had already existed for almost a hundred years, and 

 eddies in liquids and their flow as jets had been known for a 

 much longer time; but no one till then had succeeded in 

 showing that these phenomena are not only contained in the 

 fundamental equations - and therefore do not conceal 

 anything fundamentally new, but follow entirely from New- 

 ton's and Galileo's laws of motion, as Newton had already 

 seen - but also that they may be completely deduced in de- 

 tail from the fundamental equation, and represented as they 

 occur, according of course to the fundamental laws, but in 

 gases and liquids having particular properties. This at the 

 same time made clear, in a manner superior to all observa- 

 tion and going beyond Newton's earliest statements, what is 

 the essential and characteristic feature of these phenomena, 

 what are their simplest forms, and what can be further done 

 with them, or thought about them. 



The fact that this achievement was reserved for Helm- 

 holtz, who had never studied mathematics at the university 

 at all, shows, in a striking manner, the complete useless- 

 ness of the extensive mathematical and other courses of 



1 See his collected papers {Wissenschoftliche Abhandlungen) Leipzig, 

 1895. English translations: Oti the Sensations of Tone, trans. A. J. Ellis, 

 London, 1875; The Description of an Ophthalmoscope, trans. T. H.' 

 Shastid, Chicago, 1916. 



2 See what has already been said in this connection under Laplace and 

 Gauss. 



