PAPER BY PROF. OBERBECK. 181 



The following- system of equations relating- to the phenomena of mo- 

 tion proper now remains : 



du aGR 2 dT, 2 >, . , 



-51=- — . — — c 2 ^ + «J»+2ev, 

 dt r Jx dx 



dv aGR 2 dT x 9 dv , 



. dt r t ty dy 



(3) 

 dw aGR 2 t Tl T i _ dv A 



dt=' r ■ -?z- c2 K+" A "'' 



dx 2y dz 



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=u 1 +u 2 ; ti=vi + v 2 ; w 

 =Wi + w 2 ; r=v l -{-v 2 -i r v^ then will the following two systems of equa- 

 tions be those that are first to be discussed: 



and 



c 2 1^= — 2 f «., -f nAv % ; 



dy 



c 2 dv : i =H/iw 2 . 

 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 : 



c 2 — +m - — h v ~ -fw?^-=2 ev 2 ', 

 Jx^ dx^ dy dz ' 



o dV-i d® d® , dV o 



jy ^ aar dy dz 



d* A 3 die , duo , dw _ 

 /* — +u - — \- v ~ — \-ic --= 0. 



6 dz^ dx^ dy dz 



The first two systems of equations are linear. When therefore T t 

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



