1901—2.] Professor W. H. Metzler on Alternants. 243 
the product | a 0 b 1 c 2 D 2 eE 2 | - | 02457 | , and in no other product, 
therefore /x 7 = 0 . 
The term B 2 C 4 D 7 E 9 e c 2 b is contained in the product 
| a 0 b 1 c 2 D eE | • | 02468 | , and since p , /x 7 , and v 3 , the coeffi- 
cients of the only other products which could contain this term, 
vanish, it follows that X — 0 . 
Thus it is seen that the relation (C) does not exist, and it also 
appears why these identities cease with determinants of order five. 
It may be added here that the object for which Cayley desired 
these identities can be obtained in other ways.* 
* Of. Clebsch, Geometrie, i. ; Funfte Abtheilung, vii. Laeroix, Calcul 
diff. et int., 6th ed., Paris, 1862, p. 68. Bertrand, Calcul int ., pp. 578- 
583. Koenigsberger, Elliptische Functionen, ii. pp.1-17. Story, American 
Jour. Math., vol. vii. No. 4. Abel, “ Recherches sur les fonctions elliptiques,” 
Journal fur Mathematik, Bd. ii. Kronecker, Sitzungsberichte Der Akademie, 
Berlin, 1883, S. 717-729 ; 1883, S. 949-956 ; 1886, S. 701-780. 
{Issued separately August 14, 1902.) 
