MOVEMENTS OF ATMOSPHERE — GULDBERG AND MOIIN 1 53 



These two equations are transformed into 



- G = v ( k cos (p -f- 2 a) sin 6 sin (J) -\- - 



= k sin <j) — 2 w sin 6 cos ^ — i> 



r 

 ~dr 



(2) 

 (3) 



The last equation can be written 

 d (tan 0) & 



r dr 



tan ^ 



fe 



sin 6 



v r cos ^ 



By integration making the arbitrary constant equal to zero for 

 the same reason as in §io we obtain 



tan d> = — sin 6 tan a 

 k 



(4) 



FIG. 8 



The angle of inclination has therefore the normal value and the 

 trajectory is a logarithmic spiral. Designating by <p the angle be- 

 tween the radius and some fixed direction, the equation of the tra- 

 jectory will be 



log nat r = — <p cot a -\- C (5) 



Let r and v be the values of r and of v for any point whatever, 

 we can transform equations (i) and (2) into the following: 



v r = v >'„ (6) 



kv 



G- - + *- 



p cos a r 



^G = kV ° r ° l \- V ° r ° 2 



o 



(7) 



cos a r 



