The twenty-seven lines upon the cubic surface ... by Archibald Henderson.

INTRODUCTION

9

In ~ 12 are given the definition and number of trihedral pairs, and
in ~ 13 the actual formation of the tables of the 120 forms. In ~ 14
these are grouped together in such a way (sets of three) as to determine
in forty ways all the twenty-seven lines. In ~ 15 is found a formulation of conclusions.
In ~ 16 is given the discussion of a particular form of the general
equation of the cubic surface, together with the determination and
tabulation of the forty-five triple tangent planes. In ~ 17 is found the
formulation of the analytic expression of geometrical results.
In ~~ 18-19 the methods for the construction of a model of a
double six are discussed; and a practical method is there given in
detail.
In ~~ 20-44 the general problem of constructing thread or wire
models of the configurations of the straight lines upon all twenty-one
types of the cubic surface is fully considered. The complete data for
constructing all these models is furnished. Drawings of the configurations of the lines, displaying their collocation with respect to
each other and to the fundamental tetrahedron, have been made to
scale; and these serve to illustrate the text.
In ~ 45 is given a discussion of the derivation of the Brianchon
configuration from two spatial point triads; and in ~~ 46-47 the
discussion of the derivation of the Pascalian configuration from that
of the straight lines upon the second species of the cubic surface
(Cayley's enumeration), with a graphic representation of the combined
configuration.
Finally, in ~ 48, appears a theorem on the number of cubic surfaces
with one conical point passing through the lines of mutual intersection
of two triheders.
There is appended a bibliography of the principal papers consulted
which bear directly upon the present investigation.