ON A SIBI-RECIPROCAL SURFACE. 
255 
671] 
viz. the left-hand side here contains the factor — {ax + (3y + yz + 8w); throwing this out, 
we obtain the required quadric equation T— 0. If for the calculation of T we compare 
the terms containing 8, we have 
Tw = 
w, 
-Z , 
y 
w, w, z, — x 
w, -y, X , 
fi, 3 m ha > > hi, Cj 
y*2> [)% 3 Qj%, b 2 , c 2 
fa, g 3 , K «3, K C 3 
where observe that, writing w = 0, the right-hand side vanishes as containing the factor 
-*> V • 
z, —x 
-y, as, 
Hence the right-hand side divides by w; and one of its terms being evidently w 3 (abc), 
T contains as it should do the term (abc)w 2 : the remaining terms can be found 
without any difficulty, and the foregoing expression for T is thus verified.