V. 



0\ ATMOSPHERIC MOTIOXS. 

 {FIRST PAPER.) 



Bv Prof. H. VON Helmholtz. 



I. INFLUENCE OF VISCOSITY ON THE GENERAL CIRCULATION OP 



THE ATMOSPHERE. 



The iiitiueiice of fluid friction in the interior of very extended regions 

 that lire tilled with fluid and contain no vortex motion is always rela- 

 tively very small. This can be proved from considerations that are 

 based upon the principle of mechanical similarity. If we form the 

 Enleriau hydro-dynamic ecpiations and in them indicate by «, r, w the 

 components of the velocity parallel to the axes of .r, y, z ; by 6 the den- 

 sity, hy p the pressnre, by Pthe potential of the forces that actt ujion a 

 unit of mass of the fluid; then if we consider P, f , ?>, «, i\ ic as func- 

 tions of X, ij, z, t we have, as is well known, the following partial differ- 

 ential equations for a fluid under the influence of friction + : 



Jx £ Jx~ Jt M' 





Jt c)-» c)l/ .^^ 



Two other equations symmetrical with regard to the other coordinates 

 are to be added to the first of these equations. If now we have found 

 any special integral whatever of these equations, which obtains for a 

 definite region, then the equations will also hold good for a second case 

 where all the linear dimensions x, y, z and also the time t and the fric- 

 tion constant Ti^ are increased by a factor n, but where P, p, e, ti, t\ m 

 retain for every value of the new coordinates nx, 7iy, nz, nt, the same values 

 as they had in the first case for the original coordinates a', y, Zj t. Hence 

 it follows that when in the movement of the magnified mass the friction 

 conistant can be also simultaneously and correspondingly increased, the 



* From the Sitzungsberichte of the Royal Prussiau Academy of Science at Berlin, 

 1888, May 31, pp. 647-663. 



[t Namely viscosity as represented by Maxwell's kinematic coefficient v or Helm- 

 ^ , ,^2 0.0(101878 „ ,.,,,^T 

 holtz' 7=-o:ol;T^=0-l'^'ll'] 



78 



