AT THE PHYSICO-TECHNICAL INSTITUTE 385 



inspired. To be in contact with him always gave one the 

 sense of extraordinary benevolence and cordiality.' 



After moving in 1889 from the official quarters which he had 

 previously occupied in Berlin to the residence assigned to the 

 President of the Physikalisch-Technische Reichsanstalt, in the 

 Marchstrasse, in Charlottenburg, Helmholtz temporarily laid 

 aside all other scientific work, in order to devote himself, 

 as far as was compatible with his duties at the Reichsanstalt, to 

 meteorological research. On May 31, 1888, and on July 25, 

 1889, he communicated two papers to the Academy ' On 

 Atmospheric Motion ', the contents of which were in part, and 

 in a somewhat altered form, the subject of a lecture given in 

 September, 1889, to tne Heidelberg Congress of Natural 

 Science, ' On the Movements of the Atmosphere/ 



In the first place, Helmholtz applied to Euler's hydrodynamic 

 equations for a fluid subject to friction the consideration of 

 which he had so frequently availed himself, viz. that its 

 particular integrals held good also for the case in which the 

 co-ordinates, the time, and the friction-constants were multi- 

 plied by an arbitrary factor n, while the forces, the pressure, 

 and the components of velocity remained unaltered. It was 

 found that the motion proceeded analogously, only more 

 slowly, if in the motion of the magnified masses the friction- 

 constants were correspondingly magnified. But if the value 

 of these last be unaltered, the influence of friction upon the 

 magnified mass will be much less, and the large mass will 

 have the effects of inertia much less affected by friction. Since 

 the density and the potential remain unaltered, and the forces, 

 inasmuch as the entire process takes n times as long, must be 

 reduced to the n\h part of their previous value, Helmholtz 

 concludes that the different densities of the air at different 

 heights cannot be reproduced in reduced models, since we 

 cannot alter gravity proportionately. 



He showed by special cases how extraordinarily insignificant 

 the effects of friction at the surface of the earth, which would 

 ensue in the course of a year, must be for the upper air-layers. 

 The destruction of vis viva by friction can only occur at the 

 surface of the earth, and at the separation surfaces of vortex 

 motions. So too for heat exchange : hardly anything except 

 radiation and convection of heat comes under consideration in 



