326 
PEOFESSOE CAYLEY ON CUBIC SUEFACES. 
each three times, in the point g= 0, A=0 twice, and in the four points 
{ 16/% 4 - 27(y 2 + 4a% 2 A 2 + 27j3 2 A 4 = 0, 
l (y 2 + 4«% 2 + /3 2 A 2 - 2/%/A- 4j3SA/= 0 
each once. Or reverting to the proper significations of (a, b, c,f\ g, A), instead of points, 
we have 2 lines each three times, a line twice, and 4 lines each once ; the line ^=0, A=0, 
that is, <7=0, A=0, a= 0, being, it will be observed, the line drawn from 
(a, /3, y, h) to the point ^=0, z=0, w= 0, which is the reciprocal of the uniplane X=0 : 
the twelve lines are the aid lines of intersection of the circumscribed cone a 1 with the 
cuspidal cone d, viz. a!d = [<?'<?'] + 3d -f- ; [a!d~\ = 4 referring to the last-mentioned four 
lines; d=2 to the two lines; and %'=2 to the line <7=0, A=0, <z=0, which it thus 
appears must in the present case be reckoned twice. 
