Mr. R. Hargreaves on 



y (73) 



426 



equations 1 

 _dK_dG 

 dy dz 9 



i { ,d , d , /An / /d . ,d, d\^ 

 with 



7 = 'It ~1f' • • • and there£ore vi F + ? v/v = o , 



which will he solved for i x a linear function of xyz within 

 the ellipsoid. 



Take the problem of the conductor first. If </> depends on 

 a single parameter X, 



2(*£+«v&) + 3(*3 ,+ *'*-«)-* 



^+2.(D.X,.-0. 



It is proposed to determine the coefficients in the quadric 



u = tax 2 + 2%c*!yz = 1 

 as functions of X in such a way as to make the surface 

 equipotential. If the precise functions were known, X would 

 be defined as a function of xyz by this equation. 



Use a for 



doi 

 3X' 



u for 2#«£ 2 4- 22a / ?/2', then 

 d\ ~^u 



ax qx 



(74) 



and since -=- —il T + =— , the differentiation of (74) gives 

 dx dx ^x' v ' 6 



.^ 2 x ../^x\ 2 n d\aw 



d 2 x 



'/ 



dx~dx 



+ 2a = 0, 



«(£i-- 



„d\d\ d\~du d\~dii 



dx dy dx dy dx~dy dy~dx "' 



The sum of these equations with multipliers p, q, r, 2p\ 2</, 2r' 

 gives 



or if we multiply by m and quote (74), 



= 22,^^— ^- + 22r Urs" + ^~^~ )• • • ( 7o ) 



