MOVEMENTS OF ATMOSPHERE GULDBERG AND MOIIN TQ9 



Constant Latitude 



We have already in §10 discussed the systems of parallel winds 

 with rectilinear isobars and constant velocity. We now write 



U cos <p = c + c x 



(2) 



in which the distance x is measured along the gradient. 



Differentiating this equation and introducing the value of U 

 and of d Uin place of v and d v in equations (2) and (3) of §10, we 

 shall have 



G cos <p = U ( k + c + U sin <p ~ 

 p \ dx 



11 G sin <p = U ( 2 to sin d - U cos </> - ) 

 p \ dx) 



. . . (3) 



(4) 



If we eliminate G from these equations, we shall have the equa- 

 tion 



d</> 



= (k + c) sin <l> — 2 co sin 6 cos <p + U 



dx 



in place of which we can write 



JL d A=U ens / (tang J) = 2 co sin 6 - (k + c) tan 4, (5) 

 cos ^ dx dx 



We see that we can satisfy this equation by placing the last term 

 equal to zero. Then we have 



tang $ = 



2 co sin 6 

 k + c 



The angle of inclination ^ becomes constant, and the first term of 

 equation (5) also becomes zero. Equations (3) and (4) become 



P 



G sin <p = 2 co sin 6 . U 

 P 



(6) 



