58 



SCIENTIFIC THOUGHT. 



40. 



Helmholtz's 

 investiga- 

 tions. 



vortex theory of matter. As this is one of the most 

 remarkable instances of the fruitful reaction of abstract 

 mathematical reasoning on the progress of physical re- 

 search, it will be useful to consider for a moment by 

 what gradual steps this novel idea was evolved or 

 suggested. The immediate occasion which led to it was 

 the publication, in 1858, by Helmholtz of a purely 

 mathematical investigation of some peculiar forms of 

 fluid motion. 1 About a hundred years before Helmholte 

 published his memoir, Euler had laid the foundation of 

 theoretical hydrodynamics i.e., of the theory of the 

 motion of fluids. In doing so, it was necessary to define 



1 Helmholtz's memoir, " Ueber 

 Integrale der hydrodynamischen 

 Gleichungen welche den Wirbel- 

 bevvegungen entsprechen," appeared 

 in the 55th volume of Crelle's 

 'Journal fur die reine und ange- 

 wandte Mathematik. ' It was trans- 

 lated into English by Prof. Tait in 

 the ' Philosophical Magazine ' for 

 1867. Helmholtz's occupation with 

 the subject had originated in the 

 acoustical researches which he was 

 carrying on at the time. These 

 necessitated an analysis of the 

 more complicated conditions which 

 the motion of incompressible and 

 elastic fluids presents in actual 

 experience. The hydrodynamical 

 equations had been solved under 

 certain simplifying assumptions. 

 Discontinuity of motion and in- 

 ternal friction had been left out 

 of consideration. Helmholtz's re- 

 searches led him to the study of 

 these more complicated phenomena ; 

 and he successfully applied the 

 mathematical methods which had 

 proved useful in other branches of 

 physical science for the solution of 

 these problems. Notably in the 

 paper on whirling motion, lie came 



upon very remarkable and unex- 

 pected results, which ten years later 

 led in this country to the novel 

 speculations of Lord Kelvin. It is 

 interesting to note how at that 

 time researches in England or Ger- 

 many could for many years remain 

 unnoticed in the other country. 

 The result was that the same prob- 

 lems were frequently taken up in 

 ignorance of the fact that they had 

 been treated before. See Hicks's 

 "Report on Hydrodynamics," ' Brit. 

 Assoc. Reports, '1881-82. Especially 

 the labours of Stokes seem to have 

 been little known to German 

 writers, who usually started from 

 the better-known French researches. 

 Stokes had anticipated some of 

 Helmholtz's results referring to 

 whirling and discontinuous motion 

 of fluids. About the middle of the 

 century the periodical " Fortschritte 

 der Physik" was started by the 

 " Physikalische Gesellschaft " of 

 Berlin. Helmholtz himself contrib- 

 uted several valuable reports on 

 acoustical subjects. See the 

 ' Wissenschaftliche Abhandlungen,' 

 vol. i. passim. 



