1062 
coincidences, we find that the complex contains (n—5)(n—6)(n—‘7) 
(n—8)(9n?+37n—72) curves with a tangent te2,2,. 
The correspondence (MS, MS’) has as characteristic number 
HN --5)(n—6)(n—7)(n—8)(n—9)(7n? +-7n — 30); each tangent f2202 
Tt | 
passing through J/ represents (2—8)(n 
9) coincidences. From 
2 (n—5)(n—6)(n—-7)(n—8(n—9)| (Tn? +- 72—30)— 2n(n—4)] ensues that 
49(7—5)(n—6)(n—:7)(n—8(n—9)(n?4-38n—6) curves of IT possess a 
quintuple tangent t99,29. 
10. The curves c” with a twice osculating tangent 433 form a 
system with index $(—4)(n—5)(n?+-7n—9) *), their tangents 433 
(§ 4) a system with index 9n(n—4)(n—5). The figure produced by 
these projective systems consists of three times the curve (Js)s,3, 
containing the points of contact ($ 6) and the locus of the points 0, 
which each c” has moreover in common with its é 3. For the order 
of (O) we find 3(n—4)n—5)(n?+7n—9)+ In (n —4)(n-—5)— 3(n— 5) 
(9n?+39n+135) = $(n —5)(n—6)(3n?+-7n— 21). 
The correspondence (MR, MO) has as characteristic numbers 
n—5)(n—6(Ou*439In—135) and 9(n—5)(n— 6)(38n? H7n—21); each 
tas passing through JM/ represents 2(n—6) coincidences. From this 
we find, that the complex contains 6(n— 5)(n — 6)Bn° J-29n—54) 
curves with a tangent tss. 
The correspondence (MO, MO’) has as characteristic number 
$(n—5) n—6)(n—7)(3n? + 7n—21) and possesses in each f3,3 passing 
through Jf an (n—6)(n—7)-fold coincidence. From this ensues that 1 
possesses 9(72—5)(n —6)(n—7)(2n? +11 n—21) curves with a tangent taz. 
11. The curves c” with a tangent ty» form a system with index 
6(n —4)(n——5)(n?-+-11n—14) *), their tangents t2 (§ 1) a system with 
index 16n(n—4)(n—5). These projective systems produce a figure, 
composed of four times the curve (/t4)42, see § 6, twice the curve 
(Re), see § 7, and the locus of the points S, which each c” has 
moreover in common with its ty». 
For the order of (S) we find 6 (2 —4)(n—5)(n?+11n—14) + 16n? 
(n — 4) (n — 5) — 4 (n—5) (4n?+ 46n—138) — 2(n—5)(12n* + 40n— 
132) = (n — 5) (n — 6) (22n? + 70n — 192). 
From (MR,, MS) we find again the number of the fa {§ 3), 
from (MR, MS) the number of the #34 ($ 10). 
The symmetrical correspondence (MS, MS’) produces one new. 
characteristic number. Its characteristic number is apparently (2—5) 
(n—6)(n—7) (22n?=-70n—192), while the 16n (n—4) (n— 5) lines #42 
1) N p. 942. 
3) N p. 938. 
