The collected mathematical papers of Arthur Cayley.

409] OF EQUAL ROOTS OF A BINARY QUARTIC OR QUINTIC. 309
Fourth Table.
ft e3 d( cZ bW a3 d. 1234 c.1235 b.1236 b.1245 a.1246 a. 1345

a3ef
a2bdf
a2be2
a2C2f
a2cde
a2d3
ab2cf
ab2de
abc2e'
abed2
ac3d
b4f
b3ce
b3d2
b2c2d

+ +3 + 3 -114 -+4
-12 33 - 90 - 264 +6 -6 -4- 24
+ 21 - 195 - 990 +16 - 4 + 64
-16 + 10 + 468 - 4 -24 + 24
- 144 - 102 - 390 + 1320 - 16 + 24 + 24 - 208
- 216 + 1080 + 36 + 144
+50 + 155 + 360 + 900 + 4 - 22 + 6 +24
+ 30 + 135 - 1500 - 2700 + 16 - 6 -26 - 20 - 40
+240 + 100 + 900 + 900 -84 + 16 -96 + 60
+ 120 - 600 + 1800 - 600 - 152 - 24 +96 - 40
+ 480 + 1600 + 96 +64
-24 + 225 + 16
- 150 + 125 60 - 10 +90
- 150 - 1500 + 80 - 80
-300 - 1000 - 60 40

Fifth Table.

f13 e~ d) ca bR'

a~ e.1234 d.1235 c.1236 c.1245 b.1246 b.1345 a. 1256 a.2345 a. 1346

a3f2
a2bef
a2cdf.a2ce2
ab2df
ab2e2
abc2f
abcde
abd3
ac3e
ac2d2
b3cf
b3de
b2c2e
b2cd2

+ 3- 19 +1
+ 21 + 33- 114- 608 + 4 - 2 + 16
-144 + 10 - 90 + 537 -4 + 6 - 6 -16 + 20 -36
-102 - 195 - 245 - 16 +16 +16 - 80 -16
-216 - 390 + 1740 + 36 +24 +16 + 60 +36
+ 30 + 155 - 264 - 245 + 4 - 4 - 24 - 15 - 80 - 16
+135- 990 -1700 + 16 - 4 + 64 +240
+ 240 + 360 + 468 + 1740 -22 + 6 - 24 + 24 +60 + 36
+ 120 + 100 - 1500 + 1320 - 2000- 152 - 84 - 6 - 26 + 24 - 208 - 860 -20
- 600 + 1080 + 600 -24 + 144 +960
+480 + 900 + 600 + 96 +16 -96 + 960
+ 1600 + 1800 400 +64 +96 - 320
-150 + 225 + 900 + 16 +24
- 150 + 125 - 2700 + 80 +60 20 - 40
-300 + 900- 60 -10 +90 + 60
1000 -1500 - 600- 40 -80 40