48 
MR. H. M. TAYLOR ON A SPECIAL FORM OF THE 
r 
J 
It will be observed that each of the lines 13, 14, and 15 lies in the plane 
- + f + - + -^ = 2T: 
these three lines therefore meet each other and form a triangle, 
§ 5. Each of the remaining six groups 
1 
4 
7 
10 
a) 
1 
5 
8 
12 
(ii.) 
2 
5 
9 
10 
(iii.) 
2 
6 
7 
11 
(iv.) 
3 
6 
9 
12 
(v.) 
3 
4 
8 
11 
(vi.) 
represents a set of non-intersecting lines. 
Two straight lines can he drawn to meet four non-intersecting straight lines ; there¬ 
fore two straight lines can be drawn to meet the lines of each group, and all straight 
lines so drawn will lie entirely on the surface. We are thus supplied with twelve 
more lines on the surface. 
From what has preceded it will be clear that there is no other way of drawing a 
straight line on the surface. We have now obtained the whole of the twenty-seven 
lines which it is well known lie on the surface. The lines which meet the groups 
i., ii., iii., iv., v., vi., will be called 16, 17 ; 18, 19 ; 20, 21 ; 22, 23 ; 24 25 ; 26, 27 
respectively. 
§ 6. We will now proceed to find the equations of the lines 16, 17 which intersect 
the lines, 1, 4, 7 and 10. 
Any line intersecting 1 and 7 is represented by equations of the form 
X — aT = \y 
z — cT — jxu 
(16) or (17). 
Since this line intersects (4) whose equations are 
y — bT = 0 
z-0 
