Full text: The collected mathematical papers of Arthur Cayley, Sc.D., F.R.S., sadlerian professor of pure mathematics in the University of Cambridge (Vol. 6)

NOTES AND REFERENCES. 
599 
and my (3 + 22 + 1 =) 26 relations as follows: 
(1) a — a. 
(2) /=/'• 
(3) i =i. 
(4) a = n (n — 1) — 26 — 3c. 
(5) k! = 3 n (n — 2) — 65 — 8c. 
(6) 3' = \n (n — 2) (n 2 — 9) — &c. 
(A) (13) q — b- — b—2k — 2/— 87 — 6t. 
(B) (14) r = c 2 — c — 2h — 3/3. 
(C) (7) a (n — 2) = Z; — 5 + p + 2c7 + 3co. 
(D) (8) b (n — 2) = p + 2/3 + 37 + 3t. 
(E) (9) c (n — 2) = 2a- + 4/3 + 7 + # + <w. 
(F) (10) a (w- — 2)(n — 3) = 2 (8 — 0 — 3a>) + 3 (ac — 3cr — % — 3a)) + 2 (a6 — 2p — y ). 
(G) (11) b (n — 2)(n — 3) = 4>k + (ab-2p-j ) + S(bc -2/3-2 7 -f). 
(H) (12) c (r? — 2) (w — 3) = 6/1 + (ac — 3cr —^ — 3«) + 2 (6c — 3/3 — 27 — f), 
with the like reciprocal equations (4) to (14); 
(I) (26) 2{n — l)(w — 2){n — 3) — 12 (?i — 3)(6 -h c) + 6<? + 6r + 24i + 42/3 + 30 7 — 
= 2(n'— 1 )(n' - 2)(ri - 3) - 12 in' - 3)(6' +c') + 6q' + 6/ + 24i' + 42/3' + 30 7 ' - 
k + 3/+ St + SO' + 2. 
¿ + £ + 6*;' + 12Æ , + ¡7 + 40' +2 +2'. 
colc^» cofii
	        
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