328 
A THIRD MEMOIR ON SKEW SURFACES, OTHERWISE SCROLLS. [410 
there is 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. 
1 
r 3 
2 3 
10 
2 
H 2 + Ri 
K 2 + R x 
7 
3 
Ri 
A 2 + R x 
— (say, 12) 
4 
H 2 + R x 
Ri 
— (say, 11) 
5 
R 1 + R x ' + S i 
R 1 + R 1 ' + S 1 
2 
p = 0 
6 
R x I 2 + S x 
R 1 2 + S 1 
5 
7 
r 3 
Ri 
8 
8 
Ri 
2 3 
9 
9 
Ri 
R x s 
3 
10 
R> 
Ri 
6 
11 
R x + R x 
R x + R x 
1 
P = 1 
12 
Ri 
Ri 
4 
where T 3 denotes a skew cubic, S 8 a torse of the 3rd class (or quartic torse), H 2 a 
conic, K 2 a quadric cone, R 1} Ri, S x different right lines, Rf, R x 3 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.