Full text: The collected mathematical papers of Arthur Cayley, Sc.D., F.R.S., late sadlerian professor of pure mathematics in the University of Cambridge (Vol. 10)

693] 
A TENTH MEMOIR ON QUANTICS, 
373 
Table No. 98 (continued). 
L divided and (as to first six coefficients) segregate is 
-f- 3 -f- 3 
l + l 
abd — 3 
a 2 £ - 4 
«V - 13 
a s n — 3 
a 4 m - 1 
a 3 bde — 7 
a 4 b* - 2 
a°b 2 c - 7 
+ 1 
a 2 6 3 — 5 
a 2 bl - 45 
a 3 b 2 d + 13 
a 2 b 3 f - 7 
,,bd 2 + 3 
„ c/t + 7 
a°cl- 21 
„ bh - 5 
„ ck — 20 
» cj + 3 
„ b 2 ce +14 
a 3 b 2 cd +10 
„<# + 10 
abci — 10 
a 2 b 3 c - 13 
,,d?f+ 12 
,,de 2 + 2 
abed + 30 
a°c 2 l + 105 
„ bch + 29 
abedf + 23 
aW +13 
a°b 2 c 2 + 105 
,,c 2 g - 16 
„ c 2 de — 24 
+ 4 
,,ch -105 
abc 2 d — 3 
a°b 2 cf+ 25 
,, bee 2 — 2 
a°b 2 c 3 — 21 
„ bc 3 e - 55 
,,c 2 d 2 -15 
„ c 3 h + 21 
,,c 3 l - 3 
a&c 3 e? — 28 
,,c 2 fh+ 2 
» edef — 7 
,,ce 2 f- 7 
«W -19 
,, bc 2 ef- 10 
,,c 4 /i - 1 
„ cV + 5 
5.7 6.10 7.13 8.16 9.19 10.22 11.25 12.28 
where the fractional coefficients are = 
a?b 3 — 6 
a 2 6 2 e - 1 
,,d 2 + 3 
abdf + 39 
abed +26 
„ ede — 22 
a°b 2 c 2 + 31 
a°6 2 c/+ 16 
,,bef + 7 
„ bc 2 e — 4 
„ c 2 h - 7 
,,c 2 l + 19 
„ ce 2 - 1 
CO 
1 
,,fl -11 
,,eY + 1 
the last two coefficients have not been reduced to the segregate form. 
M divided and segregate is 
J7= a 8 ( 
m + 1 
6£- 1 
1 
p -1 
ac?<7 + 
1 
1 
yf- 
7.5 
6.2 
8.8
	        
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