124 



Journal of the Mitchell Society. 



12 3 4 5 6 



8' 



4' 



LM 



01 



• • • • 







• • • 



• • • 







• • • 







• • • • 



and determine thirty planes n# ', (formed by the lines i and 



Using- quadriplanar co-ordinates, I choose for the lines 1', 

 3', 4', 5', 6' the following- equations: 



V : 8B'Cx + WAz - (a'y'8 - ayB')w = 0, y = 



3' : yy' By — (fi'yS' — K/2y'8> -f yy'Bw = 0, # = 



4' : # = 0, w = 



5' : B'x — a! zv — 0, yy — (3'z = 



6' : Sx — aw = 0. yy — fiz = 



where we set 



A, B, Q D = (a' - Ka), (/?' - A3), (y' - Ky\ ($' - AS) 



respectively. 



These five lines have a common tractor* since the determ- 

 inant 



•Cayley uses the word 'tractor' to denote a line which meets any given 

 lines. 



