MOVEMENTS OF ATMOSPHERE GULDBERG AND MOHN 239 



Interior portion 



We have assumed that in the interior portion (see § 14) the ve- 

 locity and the gradient diminish proportionally to the radius and 

 that the angle ft between the direction of the wind and that of the 

 gradient is connected with the normal angle a by the equation 



2 U 



We make 



tang a = tang ft [ 1 — — — cos ft 



Consider a variable cyclone and assume that the velocities u and 

 v have the form 



» = Mix - £) + N (y - 9) J 



v = M (y - i)) - N (x - f) J 



It is evident that the conditions under which equations (1) and 

 (2) are integrable are satisfied when we have 



d 2 p 



= 



dxdy 



Introducing u and v into equations (1) and (2) we shall find the 

 condition 



2 a) sin 8.M + k N + 2 M N + N' = (18) 



Making 



S = 2(osin8 N - kM - M 2 + N 2 -M' . . . . (19) 



we shall have 



1 dp n 



- . -/ = S (x - f) + M & + N 7)' 



p dx 



1 dp f 



(20) 



