i^6 Journal of the Mitchell Society. [Nov* 



\ y'B {B'x - a!u>) - h'A {y'y — $ z) = 

 | yB (8x - aw) — 8A (yy — $z) = 



Now, in general, four given lines have a pair of tractors. 

 Since the five lines 1, 3', 4', 5', 6 already have a single trac- 

 tor 2, they have, in sets of four, five more tractors, thus: — 

 the lines 1, 3, 4, 5, 6 are tractors of the sets (3', 4', 5', 6'), 

 (1', 4', 5', 6'), (1', 3', 5', 6'), (1', 3', 4', 6'), (1', 3', 4', 5') respec- 

 tively. 



Let us proceed to determine the equations of the five lines 

 1, 3, 4, 5, 6. Recalling- the values of A, B, C and D above, it 

 is obvious by inspection that the equations of lines 1 and 3, 

 meeting the quadruples (3', 4', 5', 6') and (1', 4', 5', 6') respec- 

 tively, are 



1 : x = 0, w — 



3 : y = 0, z = 0. 



The equations of line 4, since it meets the lines 5' and 6', are 

 of the form 



x y z w 



A f_A = 



a' $ y' 8' 



x y z w 

 A— + /* = 



a X 8 





The conditions that this line meet the line 1', written in 

 the form 



(x z iv \ 1 / x z vj \ 1 

 - + J kl - + 1— = 0,y = 

 y' 8' Jay \ a y 8 Ja'y' 



are given by 



X = l, /*=1. 



Then the line 4 has the equations 



