352 



Mr. T. Craig on Steady Motion in 



Instead of (35), we may write 



and 



dy J dz 



TT di$: d$i 



\i = x— - — z -j — , 

 dz dx 



WdiS: d$i 



* da dy J 



(36) 



U=SB,U„ V=SR,V,, W=SB I W,. . (37) 



We have now for u, v, w 





(38) 



W 



-S + sW-|Wr J 



Since is expressed by a series of the same form as those giving 

 U ; V, and W, we may write 



00 



</>=2L t -0 t -. 







For the surface conditions we now have i groups of equations, 

 of which the following is the type : — 



<*(L,ft) + dQMd _ rf(B,V«) _ , 



d.2? (iy cte ' 



<*(L,-fr) d(B,U t ) d(B,W,) =0 . 



dy dz dx ' 



djlnh) , rf(R,-V,-) _ rf(R,U,) =a 

 cfe c?o? dy 



The first one of these can be written in the form 



(39) 



d£ 



dx \ dy 



IWi dV 



dz 



Now 





dWi d&t , ^ 2 S t - 



(40) 



-^T+y 



ePS, 



rfV« = ^Sj _ggj dSt m 



dz L dz 2 * ' dxdz dx ' 



