144 REV. T. P. KIRKMAN ON THE 



The constant d x must disappear in this subtraction (C); for 

 if it be a circulator, it can depend only on the value of c in 

 equation (A) combined with the circulators in [ 6 Pjr]'; that is, 

 it can have only 42 values, and d x must be the same with 



The circulators 2^ 2 , 2 <r _ 16 , &c, 6 x _ l9 6 x _ l39 &c, standing 

 vertically under each other, are equal, if #740 ; supposing 

 then that a=42(/— 1)+?, (7 70, Z43), and that /7l, we 

 have, by equating co-efficients, 



3.42a = -^.3(2, + 2^)=-?- 135 ° 135 ° 



720 2 v * ' *~~ v 720 2 42.720 2 



_3.42 2 a+84S=-^V^ { (2+30+58)2_ 2 



+(16+44+ 72).2 ; _ 1 J 



+ ^(7926— 8424— 1674+1176— 1674— 8424). (6^+ 6^ 



+6^+6^+6^+6*), 



• fuh— _ 3^2 2 .1350 , 90.1350 , 42.1350 2 ___ 27294 

 i.e. B4G- 42 720 2 + 720 2 + 720 2 • -1 7202 ! 



fl = —37947+28350.2^, 



42.720 2 



a.42 3 -5.42 2 +c.42=-^((l+15 2 +29 2 )2,+(8 2 +22 2 +36 2 )2 a> _ 1 ) 



+w( (1+15+29)2 * +(8+22+36)2 '- 1 ) 



5 -I(— 7926+8.8424+15.1674— 22.1176+29.1674+36.8424) 



720 1 



+.|g± 2 (8424— 8.7926+15.8424+22.1674— 29.1176+36.1674) 

 ^-£-^(1674+8.8424— 15.7926+22.8424+29.1674— 36.1176) 

 +%±(— 1176+8.1674+15.8424— 22.7926+29.8424+36.1674) 

 + ^£=» 2 (1674— 8.1176+15.1674+22.8424— 29.7926+36.8424) 

 +Jk. 2 (8424+8.1674— 15.1176+22.1674+29.8424— 36.7926). 



