MR. A. CAYLEY’S RESEARCHES ON THE PARTITION OF NUMBERS. 
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P(2, 3)9 =^|29 + 5 
+ 3 (1,-1) pcr2, 
+ 4(1, — 1,0) pcr3,| 
P(2,3,4)9 =^{69^+549+107 
+ (189+81)(1,- l)pcr2, 
+32 (2,-l,-l)pcr3, 
+ 36 (1,-1, -1,1) per 4, 1 
P(2, 3, 4, 5)9 =y^{29^+429^+2679+497 
+ (459+315)(l,-l)pcr2, 
+ 160 (1, -1,0) per 3, 
+ 180 (1,0, -1,0) per 4, 
+288 (1,-1, 0,0,0) per5,j 
P(2, 3, 4, 5, 6)9=j^^|l09^+4009*+55509^+310009+56877 
+ (4509"+90009+39075)(1, -1) per 2, 
+32OO9 (1, — 1, 0) per 3, 
+ 1600 (21,— 19, —2) per 3, 
+ 10800 (1,0, -1,0) per 4, 
+6912 (4, -1, -1, -1, - 1) per 5, 
+4800 (1, - 1, -2, - 1, 1, 2) per 6, . 
P(l,2,3, 5)? =j^|4y>+66f+324j+451 
+45 (1,-1) per 2, 
+80 (1, —1,0) per 3, 
+ 144(1,0,0,0,-1) pcr5,j 
P(l, 2, 2, 3, 4)9=^|69^+1449^+11949^+39609+4267 
+ (549^+6489 + 1 70 1 )( 1 , - 1 ) per 2, 
+256 (2, — 1, — 1) per3y 
+ 432 (],0, — l,0)per4,j 
P(^)9 
+ 1 (1,-1) per 2, 
+2 (1,0, —1,0) per 4, 
+8(1, 0, 0, 0, — 1, 0, 0, 0) per 8, j 
MDCCCLVI. T 
