Ogilvie 



'S 

 Similarly, in T55 



y dS n3(4;3 + V . V <^3) = y dS (4>3^4>3- ^Jn^s) = 0. 



J dSng(qjg+ V. V^g) = 0, 



'S 

 In Tjg, we manipulate one integral as follows: 



y dS njCiljg + V ' V <j)5) = J dS (ngijig - m^^^ 



= Jg dS (ng^^g - ci.3^45 + 4>3<}>5^ - %r^) 



= - J dS n34>3+J dS z(n3<j>,^ - n,<j),^). 



Similarly, in T53 and T55, we find: 



^ dSn^(^>^+ v.V^^)=^^ dSn34,3-£ dS z(n3,j»,^ - n,4»,^), 

 The last integrzil in the last two expressions can be rewritten: 

 \ dS z(n3«j>,^ - n,^, ) = j . \ dSznXV<}>, 



= j . y dS [nXv(z<^,) -n X (4.,k)] 



■I ' 



s 



dS n, (^|, 



the last equality following from application of Stokes' theorem to the 

 first term. Combining all of these results, we find for the Tjj : 



T33 = - p(i(o)^ j dS n^^^; 



T35 = - p(lwf y dS n3(|>5 + p(iwU) J dS (n34>3 - n, <|),); 



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