PAPER BY PROF. OBERBECK. 181 



The followiug' system of equations relating to the phenomena of mo- 

 tion proper now remains : 



dt r ;)x ,U' ' 



dt r Jy ,^y^ 



dt r Jz Jz^ 



;)x yy"^ ;)z 



One can now compute first those components of the current that de- 

 pend only on temperature differences; after that those that are brought 

 about by the rotation of the earth. If we put u=Ui-^U2', v—v^ + v,; iv 

 = Wi-\-iC2', y=i'\+yt-{-y?.i then will the following two systems of equa- 

 tions be those that are first to be discussed: 



(•^) 



dx r ' ;)x 



+ hJui 



and 



(T ^— ' = . i ' + H/Slh 



Jy r ;)y 



C* - — - = i-f KZ/U'i 



dz r dz 



dy 



dz 



Thus there still remain the following equations which are no longer 

 linear and which will serve principally in the computation of the varia- 

 tions in pressure produced by the motion : 



dx^ dx' Jy Jz 



,ii/^ dx^ dy^ dz ^' 



^' 34-M \ \- V V + M7 V= ^• 



dz dx dy dz 



The first two systems of equations are linear. When therefore Ti 

 consists of a sum of terms we shall obtain corresponding sums for the 



