ON A CERTAIN SEXTIC TORSE. 
[From the Transactions of the Cambridge Philosophical Society, vol. xi. Part in. (1871), 
pp. 507—523. Read Nov. 8, 1869.] 
The torse (developable surface) intended to be considered is that which has for its 
edge of regression an excubo-quartic curve, or say a unicursal quartic curve. I call 
to mind that (excluding the plane quartic) a quartic curve is either a quadriquadric, 
viz. it is the complete intersection of two quadric surfaces; or else it is an excubo- 
quartic, viz. there is through the curve only one quadric surface, and the curve is the 
partial intersection of this quadric surface with a cubic surface through two generating 
lines (of the same kind) of the quadric surface. Returning to the quadriquadric curve, 
this may be general, nodal, or cuspidal; viz. if the two quadric surfaces have an 
ordinary contact, the curve of intersection is a nodal quadriquadric; if they have a 
stationary contact, the curve is a cuspidal quadriquadric. 
The unicursal quartic is a curve such that the coordinates (x, y, z, w) of any point 
thereof are proportional to rational and integral quartic functions (*]£$, l) 4 of a 
variable parameter 6; and the general unicursal quartic is in fact the excubo-quartic; 
but included as particular cases of the unicursal curve (although not as cases of the 
excubo-quartic as above defined) we have the nodal quadriquadric and the cuspidal 
quadriquadric. The torse having for its edge of regression a unicursal curve is a sextic 
torse; and this is in fact the order of the torse derived from the excubo-quartic, and 
from the nodal quadriquadric; but for the cuspidal quadriquadric, there is a depression 
of one, and the torse becomes a quintic torse. The equations have been obtained of 
(1) the sextic torse derived from the nodal quadriquadric, (2) the quintic torse derived 
from the cuspidal quadriquadric, (3) the sextic torse derived from a certain special 
excubo-quartic; but the equation of the torse derived from the general unicursal quartic 
has not yet been found. To show at the outset what the analytical problem is, I 
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