126 
PEOFESSOE CAYLEY ON SKEW SUEFACES, OTHEEWISE SCEOLLS. 
a bitangent torse which should in the classification be considered along with the nodal 
curve ; and he enumerates in all 12 species as follows : — 
Deficiency. 
No. of 
species. 
Nodal curve. 
Bitangent torse. 
Corresponding 
to my species 
i 
r 3 
s 3 
10 
2 
H 2 +Ki 
Ko + Ej 
7 
3 
Ef 
k 2 +e x 
-(say, 12) 
4 
R+iq 
Ef 
— (say, 11) 
5 
E 1 +Ei + S 1 
Ex+Ef + S! 
2 
P=0 
6 
Ef+S x 
Ef+Si 
5 
7 
r 3 
Ef 
8 
8 
E f 
^3 
9 
9 
Ef 
Ef 3 
3 
10 
E, 3 
Ef 
6 
JP=1 
11 
Ej+'EJ 
Ej+Ei 
1 
12 
Ef 
Ef 
4 
where T 3 denotes a skew cubic, a torse of the 3rd class (or quartic torse), H 2 a conic, 
K 2 a quadric cone, R,, R', Sj different right lines, Rf, Rf a line counted twice or three 
times &c. I have in the last column added the references to my species 9 and 10 ; 
Professor Cremona notices (what I knew, but did not recollect) that the species 10 had 
been considered by M. Chasles, Comptes Rendus, June 3, 1861. 
I have not yet examined the two new species mentioned in this enumeration ; viz. 
these are (Cremona 3), say twelfth species , a scroll having a triple line, but a bitangent 
torse made up of a quadric cone and a line; and (Cremona 4), say eleventh species , a 
scroll having a nodal conic and line, but for its bitangent torse a triple line : the two 
species are, it is clear, reciprocal to each other ; although properly treated as distinct, 
species 11 may be considered as a subform of 8, and species 12 as a subform of 9. 
