PAPER BY PROF. OBERBECK. 103 



The eqiiatioD of continuity uow becomes 



JL= -^-^^ . . , „ „ . . . . . (8) 

 The three first equations lead to the two following : 



c^ vs = Constant + a — « — ^9) 



JM = '^ .^^^ (10) 



If the functions L and M are so determined that they satisfy the 

 boundary conditions then the problem is to be considered as solved 

 and equation (0) gives the desired distribution of pressure. As 

 boundary conditions I have retained those previously laid down, viz, 

 adhesion to the earth's surface, slipping on an upper boundary surface 

 at an altitude R. h above che earth whereby h is to be considered as a 

 small number in comparison with unity. 



For further calculation it is expedient to introduce the vertical and 

 meridional components of the current or F and N. These are con- 

 nected with L and Mhj the equations 



Y=^J^ j^ Mcosd ] 



dr I 



} ■ - (11) 



JV = - L ^J + M sin d I 



The equation of continuity now becomes 



^li+^F=i cot^-.V+'^S (12) 



The elimination of L gives the further equation 



The calculation gives the following values : 



y=~R'\xi + ^X2-Q{^Xi+X2)<iOs'd+35xiCOs'f^\.f{(j) . (14) 



i\r=-i2-^ sin (V cos ^j-Ii—2j2+ 7^1 . cos'' ^ p 99(0-) . . . (15) 



In these /((T) and cp {a) have a signification similar to that in the 

 previous memoir, namely, 



f{ff) = ^{h-ff){Sh-2(T) 

 80 A 13 



