148 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 51 



§11. Influence of the variation of latitude on horizontal currents 

 of air with rectilinear isobars 



We consider only the case in which the gradient coincides with a 

 meridian. The latitude 8 is expressed by the following equation 



e = e a + x x 



x = ± - - . — 



10 6 180 



(1) 



(2) 



FIG. 5 



The coefficient X is positive when the gradient is directed toward 

 the north and negative when it is directed toward the south. 



The equations developed in §10 now hold good by considering 

 6 as variable. 



Equation (8) of §10 becomes 



d (tan (/>) 2 to sin — k tan if> 

 dx v cos c> 



For the sake of abbreviation we write 



V COS (j) 



tau e = X 



(3) 



(4) 



Placing the arbitrary constant equal to zero, as we have done in 

 §10, we find that the integral of (3) is 



2 w 



tan d) = ~ - cos e sin (6 — s) 

 k 



(5) 



