THE EEV. GEOEGE SALMON ON QHATEENAEY CIIBICS. 
239 
through the line xy and examining the terms in 0, H, and O, which do not contain x 
or y. I have already noticed ^ that the existence of these twenty-seven right lines may 
be deduced as a particular case of the following theorem, that on a surface of the 7ii\\ 
degree there is a locus of points at each of which it is possible to draw a line to meet 
the surface in four consecutive points, this locus being the intersection of the given 
surface with a surface of the degree — 24. I gave the equation of this surface, but 
in a very inconvenient formf. But I have now to add a simpler form of the general 
equation of this surface, \iz. 
0=4H(a>+«-sp-), 
where 0, H, O have the meaning already explained ; « is a numerical multiplier 
/(n— 2)(n— 3)\ 
and is a covariant obtained as follows: — Let 0 when expanded be 
A 
then 
+ &c. + 2A'§f + &0.. 
that is to say, "L" is the result of squaring the bordered Hessian, introducing differential 
symbols instead of the contravariant variables, and operating with the result on U. In 
the case of the cubic ’L’ evidently vanishes. 
* Cambridge and Dublin Mathematical Journal, vol. iv. p. 258. 
t Quarterly Journal of Mathematics, vol. i. p. 336. 
