1888-89.] Dr T. Muir on the Theory of Determinants. 41 7 
where S is “une fonction alternee de l’ordre n formee avec les 
quantity que renferme le tableau, 
in which 
o 
o 
<1 
-A-0,1 
• • • -h-Q,n- 2 
Ao,n-l 
^0.1 
Am 
• • • ^l.n-2 
-A-l.n-2 * 
• • • •h-n—2,n—2 
A n— 2 f n — ] 
' -^0,71-1 
K,n-1 • 
• . . h- n -2,n-l 
A 
A o,l 
+ 
II 
— b 0 a l+1 , 
— b ± a l+1 + A 0(?+1 , 
■h-2,1 
— a 2^l+l 
— b 2 a l+1 + A v+1 . 
In connection with this, however, no reference is made to Jacobi’s 
paper of 1835. 
The fourth method, which occupies much the largest space 
(pp. 397-422), is not a determinant method. 
SYLVESTER (January 1841). 
[Examples of the dialytic method of elimination as applied to 
ternary systems of equations. Cambridge Math. Journ ., ii. 
pp. 232-236.] 
In returning to extend the method, here and generally afterwards 
called “ dialytic,” Sylvester takes occasion to say that “ the principle 
of the rule will be found correctly stated by Professor Eichelot of 
Konigsberg in a late number of C retie’ s Journal .” It may be 
noted, too, that he now for the first time uses the word determinant. 
Only the first and last of the four examples need be given, as the 
subject strictly belongs to the application rather than the theory of 
determinants. Even these, however, will suffice to show the 
masterly grip which Sylvester had of his own method. 
“To eliminate x, y, z between the three homogeneous 
equations 
VOL. xvi. 16/11/89 2 D 
