915 
915] 
ON THE PARTITIONS OF A POLYGON. 
95 
ïa Xs+ rls< l! >' + rm (I,) " + - - { x + oW' + îxî( i ‘)" + - 
Ling, 
aber 
the 
ides, 
ition 
r hich 
r= 
fc = l 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
3 
1 
4 
1 
2 
5 
1 
5 
5 
6 
1 
9 
21 
14 
7 
1 
14 
56 
84 
42 
8 
1 
20 
120 
300 
330 
132 
9 
1 
27 
225 
825 
1485 
1287 
429 
10 
1 
35 
385 
1925 
5005 
7007 
5005 
1430 
11 
1 
44 
616 
4004 
14014 
28028 
32032 
19448 
4862 
12 
1 
54 
936 
7644 
34398 
91728 
148512 
143208 
75582 
16796 
13 
1 
65 
1365 
13650 
76440 
259896 
556920 
755820 
629850 
293930 
58786 
14 
1 
77 
1925 
23100 
157080 
659736 
1790712 
3197700 
3730650 
2735810 
1144066 
208012 
15 
1 
90 
2640 
37400 
302940 
1534896 
5116320 
11511720 
17587350 
17978180 
11767536 
4457400 
742900 
r— 
k = 2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
4 
1 
5 
2 
4 
6 
3 
14 
14 
7 
4 
32 
72 
48 
8 
5 
60 
225 
330 
165 
9 
6 
100 
550 
1320 
1430 
572 
10 
7 
154 
1155 
4004 
7007 
6006 
2002 
11 
8 
224 
2184 
10192 
25480 
. 34944 
24052 
7072 
12 
9 
312 
3822 
22932 
76440 
148512 
167076 
100776 
25194 
13 
10 
420 
6300 
47040 
199920 
514080 
813960 
775200 
396800 
90440 
14 
11 
550 
9900 
89760 
476240 
1534996 
3197700 
4263600 
3517470 
1634380 
326876 
15 
12 
704 
14960 
161568 
1023264 
4093056 
10744272 
18759840 
18573816 
15690048 
6547520 
1188640 
•2 
4. These functions, U and V, are particular values satisfying the equation 
(r, 
V 3 y +V 4 f + ...) = (U 1 + U 2 y + U z y 2 + U 4 f + ...y ; 
that this is so will appear from the following general investigation. 
5. Taking x, y as independent variables, denoting by X an arbitrary function 
of x, and using accents to denote differentiations in regard to x, we require the 
following identity: