ME. A. CAYLEY ON THE CONIC OF FIYE-POINTIC 
376 
and the third equation o£ the system of conditions for a five-pointic contact is therefore 
which leads to the value of A. 
13. We have in general 
3;u =^<i>u 
a:u 
m— 1 
■{m-iy 
1 
’ (m— 1)^ 
DH.^% 
(3;+33 A)U~ D®. U- DH .y, 
(3;+63?aju=^(23,<t+D''®+sli n)u 
■(^l2a,H+D>H+.-;Ai ° -'Wr 
the last two of which have not yet been demonstrated. The value of 'djl (which, how- 
ever, is not required for the present purpose) is 
-3(m — 2) 
m — 1 
HO- 
ID 
m — - 1 
which also is not yet demonstrated. 
14. Putting U=0, we have 
bfU 
= -7-AT2I)H.&^ 
(m — 1)^ 
1 
(3;+ 33,3,)U= -pfyp DH . y, 
(3;+63;3JU=-r^423.H+B--H+,-;4v ° 
S{m-2) 
and substituting, 
3(»i-2) 
23.H+D’H+— 
H<I> 
-tS*)' 
where the term involving baH disappears ; the equation may be written 
A = 3H (D’H+ -ly □ ho) - 4(DH)«. 
which I will represent by 
j^,A=3E,Tl.-4K|, 
