130 Journal of the Mitchell Society. [Nov. 



yy'(a(3' — a'/3)D yy' D y' y 



(3/3'(y'S — yB')A Pl'y — Kfiy' (3' (3 



A - A, A 4 - A 



Calculating- the value -. of the anharmonic 



A — A A — 7 



32 4 '2 



ratio of these four parameters numbered in the order in which 

 they are written, we find 



(3'V ((3(y'S — yS')A—y(af3' — a'P)D) 



(P ,P , P , P ) 



»/' ^ x S /' * K ^ \/3>( y '8 — y S')A — y'{a(S' — a'(3)D 



Let us now determine the co-ordinates of the points of 

 intersection of the lines 1, 2, 3, 5, 6 with the line 4'. These 

 follow in the table below: 



F : 







1 











P : 



34' 



A 



B 











P : 



34' 



1 















P : 



S4' 



ayD 



08C 











F : 



64' 



a'y'D 



0'S'C 











The anharmonic ratio of the four collinear points P , P , 



• 24' 34' 



P ,'P , is identical with the anharmonic ratio of the four 



54' 64' 



parameters 



# /38C p$C 

 0, , . 



A ayD a'y'D 



Calculating- the value s- of the anharmonic 



/* 3 "-" **. ^4 — P. 

 ratio of these four parameters numbered in the order in which 

 they are written, we find 



