MOVEMENT OF AIR IN ANTICYCLONES POCKELS 597 



average value: (this is all the more allowable in proportion as the 

 average latitude is nearer the pole). 



(4) We shall study only the movement over the earth's surface, 

 of^a layer of air of moderate depth assuming that it experiences 

 a frictional resistance opposed to the direction of its movement 

 and proportional to the velocity of the current. 



(5) That a descending current of air prevails over a surface 

 bounded by a circle of radius R and that its descending velocity is 

 directly proportional to the altitude above the earth's surface and 

 is the same, for any given altitude, over the whole of this region. 



(6) That purely horizontal motions prevail outside the circle 

 whose radius is R. 



From this last assumption combined with the second and third it 

 follows at once, that the atmospheric pressure, the velocity of the 

 current and the angle that the current makes with the radius-vector 

 depend only on the distance, r, from the center of the descending 

 current. Designate by V n the radial component of the velocity V 

 positive inward ; by V t the velocity component tangential to the 

 isobar counted positive in case the rotation is directed contrary 

 to the movement of the hands of a watch; let p be the atmospheric 

 pressure expressed in absolute units of force, p the average density 

 of the air, k the coefficient of friction, and X the product of the 

 angular velocity of rotation of the earth multiplied by the sine 

 of the geographic latitude; then in the case under consideration 

 of concentric circular isobars, the hydrodynamic equations of 

 motion can be written 2 



l£-*r* + Yl + i r, + kv m da) 



p dr dt r 



= *?± - VtVn -XV n +kV t (lb) 



dt r 



which equations moreover can be deduced directly from very simple 

 considerations. Because of the assumption of a stationary condi- 

 tion, the total acceleration is identical with the acceleration depend- 

 ing on a change of location, that is to say, a change in the distance 

 from the center of the whole system of winds, consequently in our 

 problem we have 



dV n dV n dr . dV. d'V, dr 

 3 = 3 . . and = . — 



dt dr dt dt dr dt 



2 See Sprung's Lehrbuch der Meteorologie, Hamburg, 1885, p. 135. 



