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

268 HISTORY OF THE THEORY OF DETERMINANTS

where the symbol on the left stands for the determinant whose
elements are 11, 12,..., 21, 22,... and the peculiarity of skewness is understood but not expressed. Had the specialisation
of the elements of the diagonal been as before, the development
would clearly have been
1
+ (45 )2+ (35)2 +(34)2 +(25)2 +(24)2 +(23)2 +(15)2 + (14)2 + (13)2 + (12)2
+ (2345)2 +(1345)2 + (1245)2 +(1235)2 + (1234)2,
which, if the order be reversed, agrees exactly with the result of
putting n=5 in the identity towards the end of the paper of
1846. By way of explanation Cayley adds the sentence "Les
expressions 12, 1234, etc., a droite sont ici des Pfaffiens," which
is noteworthy as being the first intimation that he desired "les
fonctions de M. Jacobi," as he had formerly called them, to be
known by the name of the mathematician whose integrationmethod had led Jacobi to the discovery of them. The change is
easily accounted for by the fact that it was more appropriate to
attach Jacobi's name to another class of determinants which
were of greater importance and to which Jacobi had given far
more attention.
Immediately following this there comes the announcement:" J'ai trouve recemment une formule analogue pour le developpement
d'un cdtelrminant gauche borde, tel que
a1234 | 1234 = alp al a2 a3 a4
1/3 11 12 13 14
2/3 21 22 23 24
3/3 31 32 33 34
4/B 41 42 43 44
Cette formule est:
a1234 / 1234 = ca/ 11.22.33.44
+a/3.12.12.33. 44
+a/3 13.13.22 44
+a/3 14.14 22.33
+a/. 23.23.11 44
+a3 242424 11 33
+a.34 34 11 22