( 583 ) 
So a surface S2+1 with two w-fold lines can admit of still (u +1) 
simple crossing lines, or of (u +2) lines two of which intersect 
each other. 
In the first case the (w + 1) lines c taken two by two determine 
with m and m’ a number of (4 + 1)e lines a situated on S2+1 , Of 
these lines evidently 2 resting on m, m', ¢,41 form with these three 
lines ‘the intersection of S2%*! with the quadric skew surface 
(cu+1,;m,m'); so the latter contains still one line a cutting m, m’. 
So in all (w + 1)? lines a cut at least one of the lines c, the 
remaining ? lines a have no point in common with a line c. By 
choosing for (u + 2) lines ¢ the sides of a skew polygon of (4 + 2) 
sides it is seen in a corresponding manner that w°—u—l lines a 
have no point in common with any line c. 
The condition that a surface S¢+’+! with a ge-fold line m and a v-fold 
line » contains vy + 2 given right lines ¢ counts for (u + v + 2)(v + 2) 
points. Now 
Quy + 8(etytl)—(etr42) Darl 
and this number is positive for u >>. So at least (» + 2) lines c 
can be chosen for u >; it depends on the value of (w — v) whether 
it be possible to choose arbitrarily a greater number or not. 
§ 12. After the assumption of three multiple lines /,m, « of the 
multiplicity 4, 4, respectively of a surface S**"'’ we can dispose 
of (A+1) (+1) (vy+1)—1 more points. Probably a general rule refer- 
ring to the maximum number of lines ¢ does not exist. In the case 
A=u=y on a S* still (A+1) right lines can be assumed for 
ODE AED Gij ke i 
and this is positive for À > 1. 
Then the hyperboloid (J), /2, /3) contains 3À right lines a situated 
on S%*; on each of the (A+1) lines ec rest two of these. 
In the preceding lines only a few fundaments for a general treat- 
ment of surfaces with a limited number of right lines have been 
indicated ; a more complete study about the subject will be published 
elsewhere, 
