344] 
ON CERTAIN DEVELOPABLE SURFACES. 
283 
The curve ae — Qbd — 0, ad 2 + 6b 2 e = 0 is made up of the lines (a = 0, b= 0), 
(d = 0, e = 0), and of au excubo-quartic, and the curve ae — Qbd = 0, ad 2 + \ b 2 e = 0 is 
u 
made up of the same two lines and of an excubo-quartic. 
34. Hence we see that the intersection of the developable and the Prohessian 
which is of the order (6+ 10=) 60 is made up as follows, viz., 
cuspidal curve ae — 4bd = 0, ad 2 + b 2 e = 0, 
taken 6 
times, 6x6 = 
36 
line (a = 0, b = 0) 
„ 4 
„ 1x4 = 
4 
line (d = 0, e = 0) 
„ 4 
„ 1x4 = 
4 
nodal curve (excubo-quartic) ae + 2bd = 0, ad 2 — b-e 
= 0 „ 2 
„ 4x2 = 
8 
excubo-quartic ae — Qbd = 0, ad 2 + db 2 e = 0 
» 1 
„ 4x1 = 
4 
excubo-quartic ae — Qbd = 0, ad 2 + ~b 2 e = 0 
u 
„ 1 
„ 4x1 = 
4 
60 
35. It is to be added that a generating line of the developable meets the Pro 
hessian in the ineunt on the cuspidal edge taken 6 times, in a point of the nodal 
line taken 2 times, viz. the r — 4 points (r being here = 6) of the general theorem, in 
a point of the excubo-quartic ae — Qbd = 0, ad 2 + 0b 2 e = 0, and in a point of the excubo- 
quartic ae — Qbd = 0, ad 2 + ^ Z> 2 = 0, (these being the 2?^ — 10 points of the general theorem) ; 
we have thus (6 + 2 + 2 =) 10 points of intersection of the generating line with the 
Prohessian.