166 THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



Consequently 



P a = constant +^1+^2P log r. 



For the inner region the equation (24) is to be used. According- to it 



we have — 



^ = _^+(A+C)^ 

 dr dr v dr 



But according to equation (25) we have — 



dW 



A + C = — » 



d<£> 



Therefore, 



P,= const— Tap— 7c. 



The arbitrary constant cau be considered as determined in that the 

 value of P is supposed to be given for r=0. (For the center of the 



depression we have r=0 and P=2.) Let P„ be this value. Then we 



9 



have— 



P^P^+Pir), 

 Where 



*»-*■ \ ^^^KiT+w^rii)n \ ■ < 31 > 



Since P a and P t must at the boundary merge continuously into each 

 other, therefore the constant in the expression for P a is to be deter- 

 mined in accordance with this condition, and we have — 



P o =P +P ( P) + |(l + ^EMog| . . . (32) 

 From equation 9 we obtain the expression for the pressure — 



P 



If we designate by p , the pressure at the center of the depression, 

 where ca=0, then in the inner region we have— 



l^l=F(r)-$Go 2 (33) 



but in the outer region — 



*^-*W + *f(l + £)*.log£-i* (34) 



