In Dr Muir's Paper on a Peculiar Set of Linear Equations (communicated December 3, 1900) there occur two Determinants of the nth order, the expansions of which are given by Dr Muir, As the paper in question has so much to do with Symmetric Functions, the following simple method of obtaining their expansions may not prove uninteresting, based, as it is, upon the elementary theory of Symmetric Functions and the so-called Principle of Indeterminate Coefficients.