PAPER BY PROP. OBERBECK. 



191 



tion of 6 aud of r or also of a the altitude above the earth's surface. The 

 first system of equations is therefore transformed into the following: 



<^~ = &+X) x*, 



dz 

 Since ^ is a function of r and 0, or of p aud z if we put 



z = r cos 6 

 p = r sin d; 



therefore, we can not find one function v 3 that shall satisfy the three 

 equations. If x were independent of z we should find 



c 2 v 3 = constant + 1 (2e+x) XP &P- 



Since however this is not the case we must therefore conclude that 



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the above-given system of equations still needs a supplement; that 

 therefore a movement of rotation of a fluid to the exclusion of all other 

 movements can only exist when the angular velocity in the direc- 

 tion of the axis of rotation is everywhere the same. If this is not the 

 case then further currents occur perpendicular to the rotary motion. 

 In our case these latter would consist of vertical and meridional move- 

 ments. Their components may be designated by u 3 v 3 w 3 . These are 

 to be introduced into the above system of equations as was done in the 

 corresponding fundamental equations (3) of the first memoir which now 

 become 



( ? ;) £=(2e+x)xy + »^ 

 Oy 



c 2 — 3 = kAw 3 

 dz 



dx + dy dz ' 



(2) 



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If the component motions indicated by the subscript 3 that directly 

 depend on the movements subscript 1 are materially less in intensity 

 than the movements of rotation, then in any computation of the pressure 

 their introduction ought not to be omitted. The former memoir gave 



