372 
ME. A. CAYLEY ON THE CONIC OF EIYE-POINTIC 
3. Consider the coordinates of a point of the cuiTe as functions of a single variable 
parameter ; then for the present purpose the coordinates of a point consecutive to [o:. y, z) 
may be taken to be 
y-\-d.y-\-^d^y-{-^d^y-\- -^d^y, 
z-\-dz -\-^d^z -\-^d^z -^^d*z, 
values which, substituted for X, Y, Z, must satisfy the equations 
T=0, D^U-n.DU=0. 
4. I write for shortness 
'd,=dx'd^-]-dy'd^-\-dz 
^2 = d^xb^ + d^yb,j + d'^zb 
Bg = d^xb^ + d^yby + d^zb^, 
B 4 = d*xb^ + d*yb^ + d*zb^, 
then the consecutive value of T is 
exp. (Bi+-|B 2 +:g^B 3 +-^B 4 )U 
(Read exp. z, exponential of z, =e*), which is 
x(l 
+ i ^2) 
X(l 
+¥^3 ) 
x(l 
+■^^ 4 ) 
1 +^1+i^l+^^l +■^^1 
+ ¥^2 + -2^1^2+ T^1^2 
+ ■§■ ^2 
+ 6^3 + ¥ ^ 1^3 
4" "^^4 
>U 
>U 
u 
+ ^.U 
+ ¥ (^1+^2)U 
+ K^?+3B.B2+S3)U 
H" ■^4(^1 “f" 6B 1B2 + 4 B 1B3 + SBa H-B4)U , 
the several terms of which must respectively vanish, and we have therefore 
U=0, 
B,U=0, 
B2U=-B?U, 
B3U=:_(B?+3B.B2)U, 
B 4 U = - (B1 + 6 BIB 2 + 4B .Bg + 3B^)U. 
