372] 
505 
372. 
ON THE RECIPROCATION OF A QUARTIC DEVELOPABLE. 
[From the Quarterly Journal of Pure and Applied Mathematics, vol. vn. (1866), 
pp. 87—92.] 
It is interesting to consider in a particular case the system of equations which 
shows d posteriori that the reciprocal of a torse (developable surface) is a curve (curve 
in space); and the reciprocal system which shows that the reciprocal of a curve is a 
torse. 
Using (cl, h, c, d) and (x, y, z, w) for the reciprocal coordinates, it will be con 
venient to collect the different equations as follows: 
a 2 d 2 — 6abcd + 4ac 3 4- 4h 3 d — 3b 2 c 2 = 0, 
ad 2 — 3 bed 4- 2 c 3 4- \x = 0, N 
— 3 acd + 6b 2 d — 3 be 2 + \y=0, 
— 3 abd + 6 ac 2 — 3 b 2 c — \z = 0, 
a 2 d — 3abc + 2b 3 +\w—0,J 
ax + by + cz +dw = 0, 
3 xz — y 1 — 0, yz — 9 xw = 0, 3 yw — z 2 = 0, 
3 pz — 9 qw 4- a = 0, N 
— 2 py 4- qz 4- 3 rw 4- b = 0, 
3 px 4- qy — 2 rz + c = 0, 
— dqx + 3ry + d = 0.^ 
C. V. 
(1) 
(2) 
(3) 
(4) 
(5) 
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