= 



128 Journal of the Mitchell Society. [Nov. 



y ( 8' — kh 

 for "which n = — 



B y — ky 



and accordingly 



hi y' — ky x W I y z 



y 8' — kl a 8 ' £ y 



Applying similar reasoning to the equation 



: — \zv = 

 with respect to the lines V and 3', we finally obtain 



/ 



A = — . 



8' 



Then the equations of line 5 are 



( h'z — iw = 



5: 



I fSC(Bx — aar) — aZ^yv — 0z) = 0. 



Determining in a precisely similar fashion the equations of 

 . we find 



( Bz — yw = 



6: J 



( fCP* — «'*0 — ■?/?(/? — pz) = 



It remains to show that the five lines 1, 3, 4, 5, 6 have a 

 common tractor (in other words are collinearj. 



Writing out the various determinants ( ij) and substituting 

 in the formula for A., vre obtain (after reduction) 



-\ =0 



and hence these five lines have a common tractor (but are not 

 mutually intersecting, since no (?)') = 0). 



Determining now the equations of the line, called 2', which 

 meets these five lines, we find 



