STEINER’S EXTENSION OF MALFATTl’S PROBLEM. 
275 
-{g>-(h-f)M 
2hf(h-f)^ 
J 
Kw( 
+{g=(p-g>+h 
=)+(h+f)j(g' 
-(h-fr- 
2fg2h^ 
— 
{g’-(h-ff- 
2hf(h-f)l 
J 1 
>-3> 
+2v/K\A7 
(g._(h_f)“)V: 
-pw—O 
-|h>-(f-g)=- 
1 2fg(f-g)' 
k£i( 
-|h^ (f g)^- 
1 2fg(f-g)l 
1' u 
>-!> 
+ |h’(P+g*- 
h^) + (f+g)j(li 
'-(f-g)' 
2fgh^' 
)}v'c" 
+2yK\/% 
(h»-(f_g)=)ly- 
-pw—0. 
It is obvious, from the equations, that each separator passes through the point of 
contact of a tactor and determinator, it consequently only remains to be shown that 
each separator touches two tactors. Consider the tactor which has been represented 
by ax-\-^y-{-'y%-\-'hw=0, the unreduced values of the coefficients give 
=kV1 
+ £/3+ jTy = + ») 
©<^+4f|3+C7=:7j(6+p.) 
\/a«’+..jS'‘=^(a»+®(3+©7)=K’. 
Represent for a moment the separator 
I— 'gi 1- 
h 
1-J,)*=0 
K 
by lx-\-my-{-nz-\-sw~0. Then putting since 
!3[a/+ ...+^$5— K^|/\/;3[+- 
=^‘{-|f-g)’+h(f+g)-^''|, 
the condition of contact becomes 
□ =- 
