260 
A SECOND MEMOIR ON QUARTIC SURFACES. 
[451 
122. “Considering any 9 points as above; taking any one as vertex, and joining 
it with the remaining 8, these 8 lines determine a dianodal nintliic cone. We have 
thus 9 dianodal cones, which cones pass all of them through the same 22 — to points.” 
123. I am not able to verify these theorems a posteriori. It appears to me that 
the theorem in regard to the enneadic centre subsists for a system of 9 points such 
as referred to in the statement; but that if by possibility the statement be too general, 
the theorem must, at all events, subsist for a more special system of 9 points; and 
that there certainly exist systems of 10 points, such that each 9 of the points have 
as an enneadic centre the tenth point. {I have since ascertained that if a quartic 
surface with 10 nodes has a single node (3, 3), the surface is a symmetroid ; whence, 
by what precedes, the remaining nine nodes are each of them (3, 3). Added 25 March, 
1871.} 
124. I notice, as a subject of investigation, the following system of correspondence 
viz., given any 8 points in space: then to every point in space corresponds a line 
through this point, viz., the ninth line of the ennead obtained by joining the point 
with the 8 given points respectively; and to each line in space a point or points on 
the line, viz., the point or points for each of which the line is the ninth line of the 
ennead obtained by joining the point with the eight given points respectively.