543 
1898—99. ] Dr Muir on a Per symmetric Pliminant. 
Note on a Persymmetric Eliminant. 
By Thomas Muir, LL.D. 
(Read June 5, 1899.) 
1. The fact that the eliminant of the set of five equations 
S 0 = Pi + 1 > 2 » 
h = PlK + P2 X 2 » 
S 2 = Pl X i* P2 X 2 2 J 
s 3 = Pi\ s 4- P^2 J 
S 4 = yqAj 4 + P2 X 2^ > 
is, as shown by Professor Schoute,* the persymmetric determinant 
implies a linear relation connecting every three consecutive s’ s. 
As a matter of fact it is not difficult to see that we have 
s 0 • — s 1 (A. 1 + X 2 ) 4- s 2 
s i ’ ^1^2 “ ^2(^1 4 " A. 2 ) 4 " s 3 
s 2 • ^1^2 “ ^3(^1 4 “ ^2) 4 - s 4 
and from these, by elimination of A.^ , + A. 2 , we obtain the 
result just mentioned. 
2. Similarly, when each s is the sum of three terms, viz., 
^0 = Pi + P2 + P*9 
S 1 ~ .PlAl 4" P<2 X 2 4“ JP3A.3 5 
S 6 = JPlV + P2 X 2 6 4- P 3 X. 6 6 , 
* Schoute, P. H., “A Geometrical Interpretation of the Invariant II(a&) 2 
n+ 1 
of a binary form a 2n of even Degree.” Proceedings Roy. Acad. Amsterdam , 
I. pp. 313-321. 
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