with the point of contact 5,. Consequently the locus of the points 
R, has in B a 35-fold point; as a plane passing through B contains 
(n—9)\(n —4) points R,, (2,) is a curve of order (n?+5n—1). 
Any és» intersects the surface ®”, which it osculates in B, more- 
over in (n—5) points S. If one of these points comes in B, fzo 
passes into a fy. with point of contact B,. The number of these 
tangents amounts to (6nH46(n —5); the order of the curve (S) is 
therefore (6n-+46)(n— 5) + (n+-9)(n—A4)(n—5S) or (n?+11n+10)(n - 5). 
To the curves (#,) and (S) we now apply the process (a). A 
plane 9 passing through « intersects (R,) in (n?--5n—1) points R,, 
is therefore associated to the (2°+-5n—1)(n—5) planes 6, which 
project the corresponding points S out of a. To a plane 6 (m?+11n 
+10)(n—5) planes 6 evidently correspond. The axis a meets 
(n-+-9)(n—4) generatrices of the cone (t52); in the plane passing 
through « and such a generatix lie a point Zl, and (n—5) points S 
associated to it, so that this plane is an (#—5)-fold coincidence 9 — 6. 
As the remaining coincidences must arise from coincidences R, = S, 
it ensues from (2? + 5n—1) (n—5) + (nv? + 11u + 10) (n—5) — 
-— (n? + 5n—36)(n—5), that (n?-+ 11n-+ 45)(n—5) twice osculating 
tangents 13,3 have one of their points of contact in B. 
If the process (a) is applied to the pairs of points $,$S’ of the 
straight lines 432, we find from 2(n* + 11n + 10) (n—5) (n—6) — 
(n?+5n—36)(n—5), that the number of the straight lines ts,22 
osculating in B amounts to 3(n?-+-17n-+56)(n—5)(n—6). 
§ 7. Let us now consider the locus (#,) of the points R, on the 
tangents “3, which have a point of contact B. As we found that 
they form a cone of order (8n-++-9)(n—4), and (&,) will evidently 
pass 35 times through £4, the order of this curve is equal to 
(3n? 
sn —l). On each tangent 453 with points of contact A, and R, 
one of the points S is united with B; the curve (S) is consequently 
of order (2?--11n+45)(n—5)-+(8n-+9)(n—4)(n—5) or of (4n?+8n + 
+9)(n—5). 
By means of the process (a) we now find from (38?—8n—1) 
(n—5) + (4n? +8n-+-9)'n—5)-— (8n? —3n—36)(n—5), that there will 
be (4n°4+-8n+44)(n—5) straight lines to with point of contact B, 
And from 2(4n* + 8n + 9)(n —5)(n—6)—(3n +-9)(n—4)(n—5)(n— 6) 
it ensues that (52°--19n--54) (n— 5)(n——6) tangents t2,2,3 have a point 
of contact B. 
The straight lines #22» with points of contact B,, R, and R’,, 
form a cone of order 2nH3)(n—4)(n—5). The points R, lying on 
it form a curve, which passes (6n+46)(n—5) times through B 
