734 COSMICAL PHYSICS 



great ingenuity expended upon this problem by Ferrel, Guldberg, 

 Mohn, and others, it has not advanced beyond the first stages of 

 solution. Although the problem in its complete generality may 

 never be solved, an adequate treatment of it is tolerably well as- 

 sured if the practically important factors are taken into consid- 

 eration, while, on the other hand, the less important aspects of 

 the problem are neglected. In other words, the problem is reduced 

 to the working-out of an ideal case, which, although never pre- 

 sent in nature, will approximate to the actual case as nearly as 

 possible. 



In this connection, the working-out by Bjerknes of the so-called 

 circulation theory for the atmospheric case has attracted much 

 attention. He considers the density and the pressure at each point 

 along a closed curve in a given mass of air, and derives the conditions 

 of motion in a simple manner. Sandstrom, a student of Bjerknes, 

 has computed practical cases. The successful application of the 

 method depends very much upon choosing the closed curve in such 

 a way that the calculation may be carried out with facility and 

 clearness. Bjerknes and Sandstrom, with this end in view, choose, 

 in preference, two perpendicular lines whose end points are con- 

 nected by two isobaric lines (along which the atmospheric pressure 

 is constant). The necessary integrations may be then easily carried 

 out and lead to easily interpretable results. The circulation theory 

 indicates that the influence of the earth's rotation, which in general 

 complicates very much the theoretical treatment, may be treated 

 in an extremely clear, simple, and elegant manner. In this con- 

 nection, perhaps the greatest difficulty involved is in the considera- 

 tion of the effect of friction. In consequence of its magnitude, the 

 friction of the air with reference to the surface of the earth plays an 

 important role. It is not a question here of the generally small 

 internal friction of the air, but of the restriction of the motion 

 through the formation of vortices, a phenomenon which, up to the 

 present time, has been but little investigated; and probably extended 

 empirical work will be necessary before it can be satisfactorily 

 treated. 



Bjerknes, like his predecessors in the study of the motions of the 

 air, disregards the time-intervals in which the accelerations per- 

 taining to these motions occur. He therefore investigates only the 

 so-called stationary state, whereby important simplifications are 

 introduced without disregarding the practically important cases. 



The application of the circulation theory to the treatment of the 

 motion of air in cyclones and anticyclones, as well as to atmospheric 

 circulation in general, has already led to very interesting conclusions. 

 It is, therefore, of the greatest interest to apply this theoretical 

 method of treatment to the great mass of empirical data which has 



