52 
MR. H. M. TAYLOR ON A SPECIAL FORM OF THE 
Hence 
ajh 
rp + — 1 
yQ — 1/5 y 
Again, because this line intersects 12, whose equations are 
the equations 
are true simultaneously. 
Hence 
u — (IT = 0~1 
— X -f- -)- (ijdp u — 0, 
xpU + cjd u = 0 , 
(XX -|- -j- (S — \ jcV^ 'll = 0 
'A 
/3 
(j) -f- (ijcl 
cjcl 
S - Ijd 
These equations of condition may be written 
by^\\f + (5/8 + cy — 1) (f) ~ aS = 0, 
“b (n* d” dS — 1) 'A — ~ 
respectively, and. the values of (/>, xp must be so chosen that they satisfy the 
ecjuation 
(hycpxjj — aS) {ad(j)\jj ■— /3c) = [ctx dS — l) (5/8 + cy — 1) (pxjj, 
or 
ocbyd(f)"iJj^ — {ci(xb^ + c(acy + Cioidh + 5/8cy + 5/8dS + cyd8 
— aa —5/8 — Cy — dS + l) (pyp + a/8c8 = 0. 
It will be observed that the equation to tind in determining the equations of 
24 and 25 is identical with the equation to find X/r in determining the equations 
of 16 and 17. 
Now, it is clear that the equations 
X — uT = Xy and x — «T = (pu 
L = ixit 
- cT = ^y 
