1901-2.] A Continuant Resolvable into Rational Factors. 105 
A Continuant Resolvable into Rational Factors. 
By Thomas Muir, LL.D. 
(Read January 6, 1902.) 
(1) In a paper in the Proceedings of the London Mathematical 
Society , vol. xxxiii. p. 229, Professor Elliott has occasion to 
consider the equation 
x p 
- 1 X p - 1 
- P X 
which, it is stated, presents difficulties when a direct algebraical 
solution is attempted, but is seen indirectly to be 
(a: 2 + l 2 ) {x 2 + 3 2 ) (x 2 +p 2 ) = 0 , 
x(x 2 + 2 2 ) (x 2 + 4 2 ) {x 2 + p 2 ) = 0 , 
according as p is odd or even. 
As the determinant involved is one of a large family possessing 
the property of resolvability into quadratic factors, I have thought 
that it would be interesting to give a direct mode of effecting the 
resolution of it, and thus indicate how a generalisation may be 
arrived at. 
(2) Confining ourselves, merely for the purpose of convenience 
in writing, to the case of the 8th order, viz. 
x 7 
- 1 x' '6 
- 2 x 5 
- 3 x 4 
-4 x 
- 5 
2 . 
x 1 
7 x 
