222 
group of 60 positive substitutions, of which the first only is 
expanded in page 145, each group to be followed by its 
negative derivate of 60, 
12345 
12345 
12345 
23145 
21435 
23451 
31245 
34125 
34512 
43215 
45123 
51234 
12345 
12345 
12345 
12345 
12345 
12345 
23145 
21543 
23451 
14352 
21354 
23451 
31245 
35142 
34512 
15324 
45312 
34512 
53241 
45123 
54321 
45123 
51234 
51234 
12345 
12345 
12345 
12345 
12345 
12345 
12453 
32154 
23451 
12453 
13254 
23451 
12534 
42513 
34512 
12534 
14523 
34512 
52431 
45123 
15432 
45123 
51234 
51234 
The specific difference of these five forms of the same 
group of 3-4-5 = 60 lies in the group of 3*4=12. The 
four functions in lines 2, 4, 8, 9 of p. 147 are to be con- 
structed in all their five values on these five forms. 
Page 143, lines 21 and 24, for ambiguous read unambiguous . 
„ 141, over C, for 4123 read 4231 ; 
„ 144, line 14, for a(# 5 -# 2 ) read a(a? 4 -a? 2 ) ; 
„ „ line 15, for a(x 6 -x 3 ) read a(x 5 -x 3 ) ; 
„ ,, line 17, for cube read sixth. 
P.S. — Sept. 7. I have to confess that my attempt in the 
preceding number to solve the quintic, &c., is, like all such 
efforts, a failure. My friend, Professor Harley, has proved 
to me that P t> &c., pages 142, 143, though symmetrical 
in x x x*x 3 x i} are not so in XqX x x 3 x 3 x^ in spite of the cyclical 
character of the values of H. But, I trust that what I have 
written is not utterly useless in connection with the values 
