452 



Dr. H. Jeffreys on Periodic 



On account of the condition of symmetry, R and <I> must 

 be independent o£ <j>. Then 



r or qz 



am 



g +2(B R-*(V<I,-*) = 0, 



SR 

 9* 



(ll) 

 (12) 



(13) 



(14) 





-k\J 2 w 



= y*V 



({-3-4 < 15) 



d^\Po 



W -Ja)J?4( rf j=,g + ivi v -g .(i«) 



a \po o J ol ror 0~ Ot dt 



8 being regarded as known in consequence of "V being 

 known, these equations have to determine p', R, <3>, and w. 

 In the previous paper we had 



Y = {be- vZ + ce- mz )J (\r)e^, . . . . (17) 



where m is the root of m 2 = \ 2 + iy/k with a positive real 

 part. In this case V has the same form, and m is unaltered, 

 since in the differentia] equation for the temperature * the 

 rotation does not appear. 



Define the quantities II, W, A, and B, which will be 

 found to be functions of z only, by the equations 



P 



Po 



ID 



R 



Then 



(k\ 2 + iy)A-2coB 



-$k8 = nj (\r)^ I 



= AJ^Xryy 1 , 



d?A 



dz 2 



d 2 B 



{kX 2 + cy)B + 2a)A-k^ :2 = 



XII, 



0, 



(kk* + iy)W 



d 2 W 



dz 2 



ga{be~ vz -\-ce~ mz ) — 



dU 



dz> 



* Equation (2) of the previous paper. 



(18) 



(19) 

 (20) 

 (21) 



