GENERAL EQUATION OF A CUBIC SURFACE. 
57 
We shall call such a set of six lines, if there are no other intersections, or if the 
whole truth with respect to their intersections is conveyed by the following figure, a 
“ double three.” 
Such a combination as 
/ 
e 
d 
G 
h 
d 
C 
h 
* * 
* * 
* * 
a b c d e / 
^ ^ ^ 
^ * 
^ ^ ^ 
^ f g h 
where the rows and the columns necessarily represent diderenb lines, we shall call 
a “ double four.” 
If any pair of non-intersecting lines, such as a, h be omitted, the remaining six 
form a closed hexagon, of which each of the omitted lines intersects three alternate 
sides. 
The figure conveys the whole truth with respect to the intersections of the eight 
lines. 
It may also be interpreted as representing a couple of closed quadrilaterals, 
a, e, 6,yand c, g, d, h, each side of either of which intersects one—and only one— 
side of the other. 
Such a combination as 
e 
d 
* ^ ^ ^ ^ 
* * 
***** 
¥ * * 
* * * * 
is called a “ double five.” 
AIDCCCXCIV.—A. 
/ g 
