106 ME. A. CAYLEY ON THE EQUATION OF DLFFEEENCES 
For the quintic equation («, h, c, d, e,f\v, 1)^=0, the equation of difFerences is. 
gio 
6'-' 
A 
6' 
A 
9' 
A 
0'^ 0’ 
A A 1 
100 «^x’ 
f 1 
50 «^x 
2500 a"x 
f ^ 
125 X 
( 1 
625 X 
( 1! 
2500 X 
i 
1 
i 
j 
1 
i 
: 
+ 1 
+ 1 a’e 
— 4 (^bd 
+ 78 c?c- 
— 150 ah~c 
+ 75 
+ 1 a^ce 
+ 1 aV* 
— 1 aWe 
— ] 0 a?hcd 
+ 32 aV 
+ 8 a?hH 
-81 «W 
+ 75 ah^c 
— 25 6" 
+ 16 a'^df 
— 19 aV 
— 48 a^bcf 
+ 72 a’bde 
+ 496 aVe 
+ 736 a^c(P 
+ 32 a*by 
— 980 a*b-ce 
— 880 
— 6400 a^bc'd 
+ 7600 a^c* 
+ 450 a^b*e 
+ 11600 a^b^cd 
— 20800 aW 
— 5000 a^b^d 
+ 22500 aW 
-12500 ab^c 
f 3125 b^ 
+ 1 O.Y- 
— 10 a’bef 
+ 64 a^cdf 
— 144 (fce^ 
+ 208 a^d^e 
— 44 a*b“df 
+ 169 c^6V 
— 192 a*b<rf 
— 416 a^bcde 
— 832 a^hd^ 
+ 1568 c^c^e 
+ 1888 a^(rd‘ 
+ 300 a^b^cf 
— 100 cdWde 
— 3600 aW<re 
+ 800 cdb"cd' 
— 17600 a^bc^d 
+ 1 0560 a®c“ 
— 120 aWf 
+ 3300 arb^ce 
— 300 a-b^d- 
+ 38400 bWc? 
— 26400 
— 1000 ab^e 
+ 33000 ab^cd 
+ 24000 aSV 
+ 10000 ¥d 
— 3750 6®e- 
-r 7 (^cf- 
— 19 (fdef 
+ 2 
— 13 a^bcef 
— 7 aWf- 
+ 71 a^bde^ 
+ 76 a^bd'f 
— 522 aVe* 
+ 96 a^irdf 
+ 1416 a^ctPe 
— 212 a'd' 
+ 32 cdPef 
+ 970 cdb'c^ \ 
— 394 cdbrcdf ' 
— 1890 a^b-dH 1 
— 288 cdb<?f ! 
— 4800 c?hede 
— 3120 c?bcd^ '■ 
+ 3880 aVe ’ 
+ 2080 (^c^dP \ 
+ 165 d'b^df 
— 525 crh^P 
+ 970 <r¥<rf : 
+ 8250 crb^cde ; 
+ 4600 bW® ' 
— 7600 a-lrc^e 
+ 17400 (fb-c"d‘ 
-28000 (rbc^d i 
+ 10000 
— 875 ab^cf 1 
— 2625 a¥de 
+ 4000 ab*<re 
-36000 a5"cd" i 
+ 50000 fliW 
— 18000 ab‘d 
+ 250 b‘f 
— 625 b^ce 
+ 13750 b^d‘ 
— 20000 
+ 7500 JV 
