PAPER BY PROF. OBERBECK. 195 



Furthermore, if we make the very probable assumption that the vari- 

 ations in pressure here considered depend exclusively on the movement 

 of rotation, that therefore 



P=p a (l+ V 3 ) 



where p & represents the pressure at the equator, then is 



_P-P* 



Therefore 



J/ 3 : 



cos 2 6 



(19) 



cos- a l „ > 



V3= ~J5Z~{ 31 -295- 61.094 cos 2 6 J 



=0.0413 cos 2 #-0.0806 cos 4 9 . . . . 

 But the computation of v 3 had already given 



v,=^cotf \ 3 -^+ X 2-Xi cos 2 } 



wherein the appended constant can be omitted. 



Hence, the two expressions for r 3 can be put equal to each other, 

 and for the computation of the motion of rotation we obtain the two 

 equations 



— r-*! =0.0806 



If in these we put 



then we shall obtain 



E -#(f+*)=0.04 13 



i2=6379600 m ; c=280 m ; 

 6=0.00007292 



Xi =0.0292 e 

 ^=0.0836 X i. 



Hence, the relative angular velocity of the rotary motion of the air is 

 j=0.0292 s { cos 2 0-O.OS36 \ . (20) 



This is small in comparison with e, the angular velocity of the earth, 

 therefore it nowhere leads to improbably large movements of the at- 

 mosphere. If we form the product xi Q we obtain for it the value 

 13.58 metres per second. But the true linear velocity corresponding to 

 the rotatory motion is 



O = x> -R* sin 6. 



The maximum value of this occurs at S. latitude 56° 27' and amounts to 

 4.59 metres per second . From the S. pole to 1 6° 49' S. latitude the average 



