ON THE THEORY OF INVOLUTION. 
312 
[348 
e 
which is a curve of the order S(n— 1): and the eliminating of \ 2 , g?, v-, gv, v\, \g 
from the six quadric equations gives 
be-f\ b'c -p, b"c" - f"\ b'c" + b"c' - 2ff, b"c + be" - 2ff'\ be' + b'c - 2 ff 
ca — g 2 , &c., 
which is a curve of the order 12 (n — 2); the two curves would intersect in 
36 (n — 1) (n — 2) points, but as this is precisely three times the number 12 (n — 1) (n — 2), 
I infer that these are in fact the 12 (n — 1) (n — 2) points three times repeated, that 
is, that each of these is a point of threefold intersection of the two curves. 
Cambridge, 7th November, 1863.