1. In the Transactions of the South African Philosophical Society for January 1905, Dr Thomas Muir gives the most general continuant resolvable into factors by means of a given set of line-multipliers. He starts with the multipliers and determines the continuant resolvable by them. At the end of his paper he gives another continuant and its factors, but not the line-multipliers, which he says “is equally interesting in itself and equally full of promise as a base for investigation.” Throughout his paper Muir is dealing with one of the two determinant factors of order n into which every centro-symmetric continuant of order 2n can be broken up. Starting with the larger continuant of which Muir's is a factor, one of the objects of this paper is to determine a set of row and column multipliers that will cause the continuant to break up into quadratic factors and thence into linear factors. Other and more general types of continuants are given which these same multipliers reduce to quadratic factors. Another and more convenient way to determine the factors of these determinants is obtained in the form of reduction formulas It is also shown how, for the two parts of order n into which the larger continuant of order 2n breaks up, the linear factors come out by reduction.