MOVEMENTS OF ATMOSPHERE GULDBERG AND MOHN 



227 



which equation represents a series of straight lines parallel to the 

 axis Y. We conclude therefore that any isotherm, as m n, moves 

 parallel to this axis. 



FIG. 42 



Second example. Let the trajectories be logarithmic spirals rep- 

 resented by the equations 



r 2 = r 2 — 2at 



<p = <p — tang a log . nat 



in which we have 



dr 



r — = — a = r U cos (p 

 dt r 



Assume that the isotherms for the initial time t — o be straight 

 lines parallel to the axis X. The equation of an isotherm a b 

 (fig. 43) assumes the form 



r sin <p = f (t) 



Eliminating r and <p we shall find 



r 2 

 r 2 + 2 at 



sin ( (f + ^ tan a kg nat 



fjr) 



1 r + 2 at 



