HELMHOLTZ IN BERLIN 



movements of fluids. It was in 1858, while he was 

 Professor of Physiology in Bonn, that he published his 

 famous paper on Vortex Motion. 1 The paper was 

 adversely criticised by the French mathematician 

 Bertrand ; and, in 1868, Helmholtz replied in such 

 a manner as to silence controversy, in three papers 

 published in the Comptes Rendus de V Academic des 

 Sciences de Paris. In the same year appeared a valu- 

 able paper on the discontinuous motion of fluids ; 

 in the following year, one on stationary streams ; 

 and, in 1873, an important theoretical paper, in 

 which is developed a theorem with respect to geo- 

 metrically similar movements of fluid bodies, and their 

 application to the mechanical problem of steering 

 balloons. There are also remarks on the mechanism 

 of flight. Undoubtedly the most important of these 

 contributions to science is that on vortex motion, 

 an investigation that had baffled such great mathe- 

 maticians as Euler and Lagrange, on account of 

 inherent difficulties. Stokes first pointed out the 

 real distinction between vortex and non-vortex 

 motion ; but it was reserved for Helmholtz to dis- 

 cover the fundamental laws which govern vortex 

 motion. 



A fluid differs from a solid body in that its particles, 

 within certain limits, can move relatively to one 

 another. Practically, even in the most mobile or 

 least viscous of fluids, relative motion of contiguous 



1 Wissenschaftl. Abhandlungen, Bd. i., s. 101. 



