466 ON A SYSTEM OF EQUATIONS CONNECTED WITH MALFATTl’s PROBLEM, [79 
Hence also 
( wa + MB-./v®)y-( o, 
(- + /V23 + cV&) 5 - ( aV& + M3 - g*/<&) X = 0, 
( - V23 + W&)« - (- ¿V& + V33 + /V®) y = o; 
these equations may be written 
{ jva - ewas - py®+v(aa3®» n®+v(®a>i y - (P?+vc^tats)} 2]=o, 
{- jva+«vis - pjv®+V(as3®)) up?+v(W)j * - yf+v(aa®)3 ®]=o, 
I {- jya - ©via+P?v®+v(aa3®)} [{jf+v@s®)) *-{«& + v(®a» y]=o ; 
where, as usual, 
§ =gh-af, & = hf-bg, %£=fg- c h, 
K — abc — af 2 — bg- — ch 2 + 2 fgli; 
(in fact the coefficient of y in the first equation is 
T Kjfffi - ®p?> va+(a® - №) vas -(«sp? - ajF) v®i,=va+vas -/v®, 
as it should be, and similarly for the coefficients of the remaining terms). We have 
therefore 
Lf + V(230D>} 0 = + V(®8)} y = № + V(&33)} 0; 
or, what comes to the same thing, 
yz = i s i JF + V@3<&)}, 
«c = I 5 {ffi + V(©&)}, 
x y = 2 S + V(&23)}. 
Now 
a {№+v(a®» m + V(aj3» = {$+v(J3®» {abc -fgh +/v(J3®> - <v(®a> - v( aaa)}, 
j (p?+v(aas)i {$+v(J3®)( = (® + V(®a» {«u -fgh -/v(3B®>+v(®a> - v(aas», 
c {j + ^(33®)) 1®+v(®a» = (p*+v(a33)j {abc -fgh -/v(i3®) - v(®a>+w(«b»(, 
(as readily appears by writing the first of these equations under the form 
a {ffi+v(a®)) m+v(aaa)} - uf+v<as®)) (a® -/$ +/v(33®) - v(®a) - w(aa3)}, 
and comparing the rational term and the coefficients of V(23(£), sj {(&$&), \/(^33)}-