7 
which is the group over A on p. 141, and to each member 
of which we may, I presume, prefix a 0. By the way, 
ought not the group over C to be written 
1423 
4132, not 4123, which occurs over F? 
2314 
3241 
But to proceed to his theory ol sextics. He appears to 
desire to construct his expression for x 0 at p. 144 on the 
groups’ of p. 145. If so, there is an inaccuracy, which may 
be corrected by writing 
0Co=l^+l 
X 0 X 3 -\- &c. | 6 
) s 
+ 
6 
„ « i 
6 \ 6 
}•)* 
+ 
+ 
X 0 # 4 + &c. 
X () X 5 -\- &C. 
x 0 — x l -\-a (x , l — x 3 ) + a 2 (x 5 — x 3 ) 
x 0 — x 2 -\-a (x 5 — x 3 ) + a 2 (^! — # 4 ) 
6 \ 6 
1 
6 \ 6 
there are errors (I think) in the lines corresponding to the 
last two at p. 144. Now Mr. Kirkman says, that H b H 2 , &c., 
after involution are invariable by the cyclical permutations of 
x 0 x 1 x 2 x 3 x^x 5 . But I think that is not the case. If Hj is 
so cyclical, then S-f is so (see p. 144, for meaning of S 
and H). But 
1 , 
S+H 1= 
^ | x o — x z + a ( x i — x i ) + cl 2 (x 2 - — x 5 ) | °y ; 
x 
6 \ 6 
now make the cyclical permutation and 
= k | — (*o— x 3 )+a(x!— x 4 )+a 2 (x 2 — x 5 ) 
for a is an unreal cube root of unity, and a 3 =a 6 =l. Now 
S + Hj and (S 4 - ^ 1 ) 5 1234 ^ differ, for the quantity (x 0 — x 3 ) has 
