240 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 5 I 



Bv integration we have 



p = 2 5 [(x - 2 + (3' - >/) 2 ] + (M F + -V *')(* - f] 



+ (m r/ -n r) o> - 9 ) + c . . : . . 



Making 



x - £ + 



we shall have 



and 



M c' + N if 



P 



+ 



y - v + 



m // - .v r 

 5 



= * s p + c 



p 

 p - p, 



(21) 



(22) 



(23) 



Hence the isobars are circles about a center different from the moving 

 origin. 



Let the angle between U and r be /?,' we have 



tang ft 



N 



M 



By the aid of the formula 



IP = u 2 + v 2 = {M 2 + N 2 ) r 2 

 we shall have 



U 



M = - ccsB* 

 r 



U 

 N = sin f 



(24) 



(25) 



By aid of equation (18) we shall find 



2 U N' r 



tang /?' = tang a + ~r~ sin fi' - 



k U cos /?' 



(26) 



We conclude therefore that also in a stationary but variable 



cyclone the angle between the gradient and the wind differs from 

 t! e angle t 3 belonging to the permanent cyclone. 



