373] 
511 
373. 
ON A SPECIAL SEXTIC DEVELOPABLE. 
[From the Quarterly Journal of Pure and Applied Mathematics, vol. vii. (1866), 
pp. 105—113.] 
The present paper contains some investigations in relation to the special sextic 
developable or torse 
(ae — 4 bd) 3 — 27 (— ad 2 — b 2 e)' 2 = 0, 
considered Nos. 26 to 35 of my paper “ On Certain Developable Surfaces,” Quarterly 
Mathematical Journal, t. VI. (1864), pp. 108—126, [344]. 
The cuspidal curve is 
ae — 4 bd = 0, ad 2 4- b 2 e — 0, 
and the nodal curve is 
ae + 2 bd = 0, ad 2 — b 2 e = 0, 
viz. to put this in evidence, the equation is to be written in the form 
(ae + 2bd) 2 (ae — 16bd) — 27 (ad 2 — b 2 e) 2 — 0. 
The coordinates of a point on the cuspidal curve may be taken to be 
a = 2, b = —t, d = + t i , e — — 2i 4 , 
and then if A, B, D, E are current coordinates, and a, ¡3, 3, e arbitrary coefficients, 
the equation of a plane through the tangent line is 
A, B, 
D, 
E 
2, -t, 
+ t 3 , 
— 2i 4 
. -1, 
+ 31 2 , 
-81 3 
« , /3, 
8, 
e