Metzler was appointed to Syracuse University, New York, where he became a professor in 1895. He held this post until 1923 but during this period he also served as Dean of the Graduate School at Syracuse. In 1923 he moved to the New York State College of Teachers at Albany, New York, where he served as Professor of Mathematics and Dean for ten years until 1933. Erik Hemmingsen, writing about the Department of Mathematics at Syracuse University, mentions Metzler's contributions:-
In the early 1900's and up through the 1920's, the Liberal Arts Department of Mathematics had some real quality. William Henry Metzler, for instance, had found a proof of a conjecture about the relation between the coefficients of the characteristic polynomial of a square matrix and the determinants of some of its minors. Furthermore, he was the one who first pointed out that one could have the transcendental functions of a square matrix simply by substituting it into the appropriate Taylor series.We list a few of Metzler's papers: Homogeneous strains (1893); On certain aggregates of determinant minors (1901); On the rank of a matrix (1913); On the expression of certain minors of the lth compound of a determinant as a function of the elements of a single line of the mth compound (1913); Some relations between compound determinants (1925); On an expression of a minor of order two of the Mth compound of a determinant A in terms of minors of A of order higher than M (1925); On certain determinant relations (1926).
In June 1918 Metzler joined the Edinburgh Mathematical Society and remained a member of the Society throughout his career. He was elected to the Royal Society of Edinburgh on 3 March 1902, his proposers being D H Marshall, R M Wenley, John George Adami, James Douglas Hamilton Dickson.
An obituary, written by A C Aitken, appears in the Royal Society of Edinburgh Year Book 1946, page 34.
We give a version of this obituary at THIS LINK
He was awarded a D.Sc. by Syracuse University in 1931.
Article by: J J O'Connor and E F Robertson