1905] Henderson — A Memoir. 131 



F? ( pBAC — ayBD ) 



(P ,p ,P ,p ) = — \ V 



* * *' " £8 (P'B'AC—a'y'BD) 



Recalling- the fact that 



A, B,QD= (a' - Ka), (/?' - Kfi\ (V -Ky\ (8' - KB) 

 respectively, it is easily verified that 

 (M j fty'B - yB')A - y(a/3' - a!&)D j 

 K/3B\ p\y'B — y B f )A — y'(a/3' — *'p)D ) 



Accordingly 



PW I (3B A C— ay BD I 

 = PBipB'AC—a'y'BD) 



(P , P , P , P ) = (P , P , P . P ) y 



12' 13' 15' 16' 24' 34' 54' 64' 



or expressing- this in a briefer fashion 



(2', 3', 5', 6'), = (2, 3, 5, 6) 



4' 



Since the configuration is a symmetrical one, we have the 

 general conclusion 



and this theorem may be phrased as follows: — 



The anharmonic ratio of the points in which any four out of 

 jive co-tractorial lines cut the common tractor of all five is equal 

 to the anharmonic ratio of the -points -where the fifth line is 

 intersected by the correspondents of the first four. 



Let us designate the anharmonic ratio of the four planes 

 formed by the plane i* witk the lines i 3 , i A , i s , i 6 by the symbol 

 (Y 3 , i 4 , * s , i 6 )i' t . Recalling next the known theorem concerning 

 the two tractors of four lines, viz. that the four points of 

 either tractor and the four planes of the other tractor have 

 the same anharmonic ratio, we obtain 



