PAPER BY PROF. OBERBECK. 193 



The equation of continuity now becomes 



3» 



(8) 



The three first equations lead to the two following 



c 2 v-i = Constant + % — u — (9) 



AM = -. d 3 (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 (9) 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 au 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 Fand N. These are con- 

 nected with L and ill by the equations 



V=*^+ Mcoad ] 



> (11) 



N= -£^ + i¥ sin I 



The equation of continuity now becomes 



£+?7-i{ «*«.*+£} (12) 



Jr r r i dV J 



The elimination of L gives the further equation 



^ '-+ — n =r — sin 6+ -—y cos 6 (Id) 



The calculation gives the following values : 



V= 2 ^R^Xi+^X2-Q( i Xi+X2)GOS 2 d+S5 Xl GOS i 6\.f(ff) . (14) 



F= 2 -R 3 sin 6 cos &-Xi—2xt+1Xi • cos 2 d7.cp(a) . . . (15) 



H ( ' 



In these /((r) aud q> (<j) have a signification similar to that in the 

 previous memoir, namely, 



a 2 



/(<r)=4gr(*-<r)(3*-2<r) 



80 A 13 



