236 SMITHSONIAN MISCELLANEOUS COLLECTIONS 



and substituting the values of F and F v we shall find 



P = [2 wsin 6 . N - kM - M']lognat r 

 P 



- [2 a) sin . M + kN + N'] <p 



Mr - Nrj' . MW + N? 

 ^_ sin <p + — ' cos <p 



VOL. 51 



(7) 



- \ U 2 + C 



The condition that the isobars are fixed curves requires that 

 2wsmdM+kN+N' = 



(8) 



Equation (7) shows that the isobars are not circles: they are curves 



dependent on £' and j)' 

 which are the compo- 

 nents of the velocity of 

 propagation. The gra- 

 dient no longer coincides 

 with the radius r and the 

 angle ¥ between the ve- 

 locity and the gradient 

 differs from the normal 

 angle a. 



Let a' be the angle 

 between the velocity U 

 and the radius r (see 

 *- fig. 49) by combining 

 - FIG - 49 the equations (3) and (4) 



with the preceding equations we obtain 



tang <p — 



u 



tang a' = tang (<p — i) = 



1 + - . tang^ 



TV 

 M 



(9) 



Determining M and N by equations (5) and (9) we find 



M = — Urcosa' ] 



N = U r sin a' 



(10) 



