1905] Henderson — A Memoir. 83 



of a double-six are discussed and a practical method is there 

 given in detail. 



In §§20 to 45 the general problem of constructing thread or 

 wire models of the configurations of the lines upon all twenty- 

 one types of the cubic surface is fully considered, and a com- 

 plete solution of the problem given. 



In §46 is given a discussion of the derivation of the 

 Brianchon configuration from two spatial point triads, and 

 in §§47-8 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) and a 

 graphic representation of the same. 



Finally, in §49 appears a theorem on the number of cubic 

 surfaces with one conical point passing throug-h the lines of 

 mutual intersection of two triheders. 



CHAPTER I. 



PRELIMINARY THEOREMS. 



§1 Existence of Straight Lines upon a Cubic Surface. 



In order to find the conditions that any straig-ht line, whose 

 equations are 



x — x n y — v z — z 



lie entirely upon a surface, we substitute x = x o -f Xr, 

 y = y -f /xr, z = z o + v in the equation of the surface, 

 arrange the terms of the resulting equation according" to 

 powers of r and then set all the coefficients of r equal to zero, 



