644 
6. SURFACE OF THE CONICS RESTING ON A GIVEN LINE J. Let us 
consider the intersection of this surface with the plane 8. To this 
8’ belongs jifteen times. Further three rays h,,, which intersect / 
and each of which forms with one of the straight lines g,,, a 2’. 
Also the three lines joining the points Az* with the point (/,8) and 
each belonging to two pairs of lines. Then the two rays of the 
plane pencil (4;*, 8), each forming a 2’ with a straight line A; A 
resting on 2; in all six rays. Finally the three lines A;*A;*, each 
of which belongs to a A of which the second component is the 
ray through 4,,** intersecting /. The complete intersection is there- 
fore of order 48. 
The surface in question is accordingly a A** with fourfold lines 
di, As, Aj, fifteenfold curve 8? and three double conics 27; these are 
the conics which have / for a chord and therefore intersect it twice. 
Besides the lines mentioned lying in the plane 8, 4 contains the 
three lines g,,,, two lines g,,, two lines g,, and two lines g,,, all 
crossing the line ¢; further two lines g,,, two lines g,, and two 
lines g,,, intersecting /; then three lines resting on /, successively 
directed to the three points A;**; finally 3 X 16 pairs of lines, the 
components of which each contain one point of 8°; in 3 x 4 of 
them the line gj; and in 3 >< 12 the line / rests on /. 
