444 
PROFESSOR CAYLEY ON THE TRANSFORMATION 
!& A B C ®um. 
0 
0 
0 
+ 
1 
1 
+ 
l 
+ 
1 
+ 1 
+ 
4 
2 
+ 
1 
+ 
1 
+ 1 
+ 
4 
3 
_ 
l 
+ 
1 
0 
0 
0 
4 
+ 
1 
+ 
1 
+ 1 
+ 
4 
5 
+ 
l 
+ 
1 
+ 
2 
+ 2 
+ 
8 
6 
+ 
l 
— 
1 
0 
0 
0 
7 
— 
l 
— 
1 
- 1 
— 
4 
8 
— 
l 
1 
— 3 
— 
12 
9 
+ 
l 
— 
1 
— 
1 
— 
1 
— 3 
— 
12 
10 
+ 
2 
+ 
1 
— 
1 
+. 
2 
+ 2 
+ 
8 
11 
— 
1 
— 
1 
— 
2 
— 4 
— 
16 
12 
— 
2 
— 
1 
— 
1 
— 
4 
- 8 
- 
32 
13 
+ 
2 
+ 
2 
+ 2 
• + 
8 
14 
+ 
2 
— 
1 
+ 
1 
+ 3 
+ 
12 
15 
+ 
i 
— 
1 
+ 
1 
+ 
1 
+ 8 
+ 
32 
16 
— 
2 
+ 
2 
+ 
2 
+ 
2 
+ 9 
+ 
36 
17 
— 
2 
— 
2 
+ 
2 
— 
2 
- 6 
— 
24 
18 
+ 
i 
+ 
1 
+ 
2 
+ 
4 
+ 13 
+ 
52 
19 
+ 
2 
+ 
2 
+ 
2 
+ 
6 
+ 24 
+ 
96 
20 
— 
3 
+ 
1 
— 
2 
- 6 
_ 
24 
21 
— 
2 
+ 
2 
— 
1 
— 
1 
- 8 
_ 
32 
22 
— 
2 
+ 
1 
— 
2 
— 
3 
- 20 . 
_ 
80 
23 
+ 
2 
— 
4 
— 
3 
— 
5 
— 24 
_ 
96 
24 
+ 
3 
+ 
3 
— 
4 
+ 
2 
+ 16 
+ 
64 
25 
— 
1 
— 
4 
— 
5 
— 33 
_ 
132 
26 
— 
4 
— 
3 
— 
3 
— 
10 
- 62 
— 
248 
27 
— 
2 
+ 
5 
— 
1 
+ 
2 
+ 16 
+ 
64 
28 
+ 
4 
— 
3 
+ 
1 
+ 
2 
+ 19 
+ 
76 
29 
+ 
5 
— 
1 
+ 
3 
+ 
7 
+ 46 
+ 
184 
30 
— 
3 
+ 
6 
+ 
5 
+ 
8 
+ 56 
+ 
224 
31 
— 
7 
— 
6 
+ 
7 
_ 
6 
— 40 
160 
32 
+ 
l 
+ 
1 
+ 
7 
+ 
9 
+ 77 
+ 
308 
33 
+ 
9 
+ 
5 
+ 
4 
+ 18 
+ 144 
_j_ 
576 
34 
+ 
3 
— 
8 
+ 
1 
— 
4 
- 38 
_ 
152 
35 
_ 
9 
.+ 
5 
_ 
1 
— 
5 
- 42 
_ 
168 
36 
— 
7 
+ 
2 
— 
5 
— 
10 
- 99 
_ 
396 
37 
+ 
7 
— 
9 
— 
9 
— 
11 
— 122 
_ 
488 
38 
+ 11 
+ 10 
— 
11 
+ 10 
+ 88 
+ 
352 
39 
— 
4 
— 
3 
— 
10 
! 
17 
-168 
672 
40 
— 
13 
— 
8 
— 
7 
— 
28 
-310 
1240 
41 
— 
2 
+ 13 
— 
3 
+ 
8 
+ 82 
+ 
328 
42 
+ 13 
— 
8 
+ 
3 
+ 
8 
+ 88 
+ 
352 
43 
+ 
.8 
— 
3 
+ 
9 
+ 14 
+ 204 
+ 
816 
44 
— 
11 
+ 14 
+ 14 
+ 17 
+ 252 
+ 1008 
45 
— 
14 
14 
+ 16 
— 
12 
- 182 
— 
728 
46 
+ 
5 
+ 
4 
+ 15 
+ 24 
+ 344 
+ 1376 
47 
+ 17 
+ n | 
+ 12 
+ 40 
+ 632 
+ 2528 
48 
+ 
3 
-20 
+ 
5 
— 
12 
— 168 
— 
672 
49 
■ — 
17 
+ 13 
— 
5 
— 
9 
-175 
— 
700 
50 
- 
13 
+ 
5 ! 
14 
22 
-401 
-1604 
64., As already mentioned, the foregoing expressions of the coefficients in terms of q 
may be applied to the determination of the coefficients as rational functions of u, v. 
Representing by Q any one of the coefficients a, (3, y ... or, consider the sum 
