16G THE MECHANICS OF THE EARTK's ATMOSPHERE, 



(joijsequeutly 



7 , 12 



P,= coustaut +V^ ( 1 + ' ., \E- loo- r. 



For the iimer region the eqiuitiou (24) is to be used. Accordiui;' to it 

 we have — 



dr ' dr ' '^^' dr 



Bat according to equation (25) we have — 



A + : = 



Therefore, 



P = const — I- (p — I- 



The arbitrary constant can be considered as determined in that the 

 value ot P IS supposed to be given for >•=(). (For the center of the 



depression we have /=(• aiHKP=''^.) Let P,, be this value. Then we 



P 



have— 



P, = P,+ F(r), 



Since P„ and P, must at the boundary merge continuously into each 

 other, therefore the constant in the exjiression for P„ is to be deter- 

 mined in accordance with this condition, and we have — 



P„=Po+P(K) + ^|(l+^,')PMog^, . . . (32) 

 From equation (9) we obtain the expression for the pressure — 



P 



If we designate by />,,, the pressure at the center of the depressioD, 

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



i>-2)„_ 



P 

 but in the outer region — 



F[r)-hcJ' (33) 



l^ = F{R) + ^(\ + ^;y^^\og'^-^_co^ (34) 



