MOVEMENTS OF ATMOSPHERE GULDBERG AND MOHN 147 



These two equations are transformed into the following 



H I 2 co sin Q \ 



- G = k v cos <p I 1 + t — ~ tan cp J (6) 



v d <p 



= k sin <p — 2 co sin 8 cos d> + -z~ . . . . (7) 



cos (p a s 



introducing 



cos cp d s = d x 



where x is the distance along the gradient and s along the trajectory, 

 equation (7) can be written 



v cos <!> d (tan d>) 2 co sin S 



The general integral of this equation is 



2 00 sin 6 ~ kx , 

 tan 4> = + Ce » cos ^ 



k 



where C is the arbitrary constant. In nature it is necessary to place 

 C = o because the angle <p does not increase to infinity with increas- 

 ing values of x. 



Thus we have (as in §9, eq. 3) 



2 co sin B 

 tan (p = = tan a 



Substituting this value of cp in equation (1) we see that the velocity 

 becomes constant and consequently according to equation (2) the 

 gradient likewise becomes constant, provided that we suppose the 

 density p constant, and in this case the isobars are equidistant. 

 If we wish to consider the variation of the density p we introduce 



d p = — [iG d x 



and by the aid of formula (20) from §5 we can calculate the pres- 

 sure p. In general we can introduce a mean value of the density 

 and consider it as constant. 



