this surface intersects / moreover in a group of (v—4) points S. Ir 
a point S comes in B, ¢ becomes a generatrix of the cone (42,3) found 
above; the surface (S) has therefore in B a(5n+2)(n—4)-fold point, 
and ‘is of order (8n-+9) (n—4) + 3 (n—38)(n—-4) or 6n (n—4). If R, 
comes in B, ¢ has in that point a four-point contact, is therefore a 
generatrix of (f,)"; the surface (#,) is consequently of order (8n—8). 
Applying the process (M) to the pairs (A, S) we find now, that 
there are (8n—3) (n—4) + 6n (n—4) — (8n—9) (n—4) or (6n +6) (n—4) 
coincidences R, =. 
The tangents t,, passing through B, which have their point of contact 
not in B, form therefore a cone of order (6n-+-6) (n—4).. 
Analogously it ensues from 12n(n—4\(n—5)—3(n —3)(n—4)(n —5)= 
= (9n-+9) (n—A4) (n—5), that the tangents ts. passing through B, 
which have their points of contact not in B, form a cone of order 
(9n-+-9) (n—4) (n—5). 
> 
$ 5. As an involution /,;—; contains 2 (n 
3) (n—4) groups with 
two double-points, there are as many surfaces of the net, whieh 
touch the straight line ¢ passing through B in two points A, and 
R, and intersect it moreover in (n 
If ¢ is a straight line, osculating a ®” in B, and touching it else- 
where, it will touch the surface (R,) of the points AR, in B. 
Consequently (#,) has in B an (n+-9) (n—4)-fold point (§ 2), and is 
of order (n+9) (n—4) + 4 (n—3) (n—4) or (5n—3) (n—4). 
If S comes in B, ¢ is a tangent f22, of which one of the points 
of contact lies in B. On the surface GS) therefore B is a (2 + 6) 
(n—4+) (n—5)-fold point (§ 3): the order of S amounts therefore to 
(Qn-6) (n —4) (n—5) + 2 (n—3) (n—A4) (n—5) or 4n (n—A4) (n—5). 
_By means of the process (M) we find from the correspondence 
(R,, R',) again the order (6n-+-6) (n—4) of the cone of the tangents 
t 
5) points WS. 
passing through B, which have not their point of contact in 5 (§ 4). 
If applied to the correspondence (/,,.S), we find again the order 
(On + 9) (n—4).(m—5) of the cone of the #32, passing through B 
without touching in that point (§ 4). 
We can finally apply it to the pairs (S,S’) belonging to the pairs 
‘(R,, R',). From 8n (n—-4) (n—5) (n—6) 2 (n— 3) (n—4) (n-—5} 
(n—6) = (6n-+6) (n—A4) (n—5) n2—6) we find that the tangents he», 
passing through B, form a cone of order 2 (n-+-1) (n—A4) (n—5) (n—6). 
4? 
§ 6. We found that the tangents #32, which osculate in B, form 
a cone of order (n+-9)(n—4). On each of the 35 straight lines which 
have a five-point contact in B, the point of contact A, is united 
