The theory of determinants in the historical order of development, by Sir Thomas Muir.

158 HISTORY OF THE THEORY OF DETERMINANTS
pound determinant equal to I aOb'c'2d I I a0blc2d3 j, and therefore
answered by Bazin in 1854 (Hist., ii. p. 207).
All that Ferrers gives is the easily reached result *
4 J ab 1c2d3e6 -6 a0b'c2d4e = a0bc c3e4 b)2
SALMON, G. (1876).
[... MODERN HIGHER ALGEBRA. 3'"' edition. xx+318 pp.
Dublin.]
A note by Cayley (pp. 290-292) deals with determinants of the
form.
) (y).I, W AMY)
to which, oddly enough, the name 'rational functional determinants' is given, because V, r... are taken to be rational integral
functions. A method of Jacobi's (Hist., i. p. 341) is illustrated by
showing that
WI 0 a Cy (aI(C, b,, b, C (ak, bC~b- b b = ~ (a, b, c) (a, b, c) (a, b, c) P (a, b,c)B2
ca CP Cy (a, b, c)v (a, b, c)y, c)
KOSTKA, C. (1876).
[Ueber Borchardt's Function. Crelle's Journ;., lxxxii. pp. 212-229.]
The main interest here is connected with the generating function
of 1855 t: but as the investigation of this involves the frequent
use of determinants of the form
ChL C/, C1
Cl/,- 8 CIO - 8, C1 - 8,
Cli - 8, Ck. - S., C1 - 8.
where Cr is defined by the identitv
(X - t1) ( - t2)... (X - tn) Xn-Cl~- n- I +C2Xc 1 -2 -* Cambri dge Univ. Exam. Papers, iv. (1875), p. 220.
t In the list above (p. 150), bearing on this subject, should be inserted
1860. METER, F. Sur une nouvelle fonction gen6ratriee des fonctions symn5
triques. Bull de l'Acad.... de Belgique (2) x. pp. 608-631..