194 SMITHSONIAN' MISCELLANEOUS COLLECTIONS VOL. 5 1 



y and z with respect to t and introducing u, v and w (see §19) equa- 

 tion (8) and eliminating the arbitrary constants, we have 



(6) 



For a< o, the air flows in to the center and for a > o the air 

 flows away from the center. 



In any horizontal plane (z = constant) the gradient G is found 

 by equation (3), by noticing that 



... (7) 



Let us consider a horizontal plane at the distance z = — h = z Q , 

 and study the phenomena along this plane, which can represent the 

 surface of the earth. 



Denoting the absolute velocity at the point A by V Q , we shall have 



Writing 



we shall find 



Denoting by p ' the pressure at a point so distant that we can con- 

 sider the velocity V as zero [V = — from equation (6)] we place 



R 2 



d = p: - Po = i p v 2 



and 



p —p = — . U, 



(1 + ey 



