581 
congruence [g*] contains seven systems of o' curves g’, each of 
which is degenerated into a conic £* and a straight line d. 
In the first place the conic 4? can pass through the points A, and 
A, and therefore lie in a plane 2 through the straight line A, A,. 
Such a plane intersects the lines a,,a, and a, in three points A,, 
A, and 4,, which together with the points A, and A, define one 
conic £?. The ruled surface yw? formed by the common transversals 
of the lines a,, a, and a,, intersects this conic £’ besides in the 
points A,, A, and A, in one more point D; the transversal d 
passing through D, forms with 4? a degenerate g°. The surface w’ 
is intersected by the line A, A, in two points B, and B,; the 
generatrices 6, and 5, of yw? passing through these points, form each 
with the line 4, A, a degenerate 4? of the system just considered. 
The transversal d, which completes the degenerate ?, formed by the 
lines A,A, and 6, to a gy’, is apparently no-other than the line b,. The 
three lines b,, A, A, and 6, form therefore together a degenerate 9’. 
[t has just appeared that to every conic &’ there belongs a definite 
transversal d; is the reverse also the case? In order to examine 
this we remark that the line A, A, is twice a component of a 
degenerate &*, and is therefore nodal line of the surface formed by 
these conies 47. A plane a through A, A, intersects this surface 
along the nodal line and along a conie k?; it is therefore of order 
four. A transversal d intersects this surface besides in the lines a,, 
a, and a, in one point D and so forms together with one conic £? 
a degenerate Q’. 
$ 3. In order to get a second series of degenerate 9’, we draw 
the transversal 6,,, mentioned in § 1 and bring throngh the point 
A, and the line a, a plane a,,. This plane intersects the transversal 
b,,, in a point D,, the lines a, and a, in two points C, and C, 
The points A,, D,, C, and C, determine a pencil of conics each 
of which forms with the line 5 
. B 8 
ia, à degenerate o°. 
As we can take one of the transversals 6,,,, boss, Orsa Onas Osis 
instead of the transversal 5,,,, we get in all sir pencils of conics 
degenerated in this way. 
Each of the corresponding pencils of conics contains three pairs 
of lines; for the pencil lying in the plane e,, they are the pairs 
(A, D,, C,C,) (A, C,, D,C,) and (A,C,, D,C,). Each of these pairs 
forms with the transversal 6,,, a @’, which has degenerated into 
three straight lines. 
Lying in the plane «,, the line A,C, intersects the line a, and is 
therefore the transversal 6 
e E N . 7 Ì = 
aay; in the same way the line A,C, is the 
