MOVEMENTS OF ATMOSPHERE GULDBERG AND MOHN 149 



Substituting this value of tan </> in equation (6) of §10 we shall 

 have 



^ G = k v cos 4> I 1 + ( — V cos e sin 8 sin (8 - e) ) . . (6) 



P 

 In order to obtain the equation of the trajectory we introduce 



d y = tan <f> d x 

 Substituting herein the value of tan (p and integrating, assuming 

 y = o for x = o, we get 



4 oj cos s , / 8 — 8 \ ( 8 — 8 Q 



y = — . — stn[ - a[- 



dp 

 Introducing [xG = — -j- into equation (6) Ave shall by integration find 



the pressure p. Finally by graphically constructing the curve of the 

 gradient we shall easily determine the curve of the pressure. 



According to equation (5) the angle of inclination <p depends on 

 the quantity e : e being so small that cos e does not differ sensibly 

 from unity, we conclude that ^ approaches the normal angle a, 

 when the latitude 8 has a large enough numerical value. As for 

 the winds that cross the equator, 8 has small numerical values, and 

 the angle </> can be very different from the normal angle of inclina- 

 tion. It is necessary to distinguish two cases: 



(1) The gradient is directed towards the north. 



In this case X and s are positive; the angle </> is negative for south- 

 ern values of 8 and for northern values until 8 = e. When 8 is 

 greater than e, the angle </> becomes positive and approaches more 

 and more to the normal value a. We see then that the winds that 

 come from the south have turned to the left even after crossing the 

 equator, that the deviation is nothing at the latitude £ and that 

 beyond this point the deviation is to the right. 



We recognize this law of deviation in nature in the trade winds of 

 the Atlantic and of the Indian Oceans during the summer. 



(2) The gradient is directed towards the south. 



The value of X and that of e become negative. In this case the 

 angle <l> remains positive north of the equator and also south of the 

 equator to latitude 8 = e; then (p becomes negative and approaches 

 more and more nearly the normal value a. 



We see then that the winds that come from the north have devi- 

 ated to the right even after crossing the equator and until 8 = e; 



