April 8, 1922] 



NATURE 



451 



the last three years of his life, and ended it, to the 

 enforced system of rationing during the latter part of 

 the war. 



While thoroughly familiar with all branches of pure 

 mathematics, Mathews' main interests were in the 

 theory of numbers and projective geometry. The 

 theory of numbers which, in its widest sense, is the 

 t heory of discrete as opposed to continuous magnitude, 

 has passed through four well-defined stages of develop- 

 ment. First there came the Diophantine analysis 

 proper, of which the greatest exponents, after Dio- 

 phantos among the ancient Greeks, were Fermat and 

 Euler. In this the general problem is to determine 

 all the solutions in rational numbers of a system of 

 m (Z.«) algebraic equations. 



Ri(xi, Xj, , . . x,i) = o, z = i, 2, . . . w. 



Next came the discovery of the law of quadratic 

 reciprocity which rendered possible a discussion of 

 quadratic arithmetical forms, so ably expounded by 

 Gauss in the " Disquisitiones Arithmeticae." ' Such 

 writers as Lejeune-Dirichlet, Eisenstein, and Stephen 

 Smith added much to what Gauss had done, and a 

 scholarly introduction to the whole theory was given 

 by Mathews in his "Theory of Numbers" of 1892. 

 A problem which arises in the theory of quadratic 

 forms (the determination of the class-number) was 

 the forerunner of the analytical theory which is in- 

 timately bound up with certain transcendental functions 

 of a complex variable. It had little attraction for 

 Mathews (though his book contains an introduction 

 to it), but has recently received much attention from 

 Prof. E. Landau, Prof. G. H. Hardy, and the late 

 S. Ramanujan. The fourth stage was marked by 

 Dedekind's discovery of his theory of ideal numbers, 

 which restore completely to a system of algebraic 

 numbers certain factorisation properties of ordinary 

 integers that appear at first to be lost. Taking 

 numbers of the type a + h^J - 5, where a, h are ordinary 

 integers, a threefold factorisation of 21 is possible, viz. : 

 2i=3X7 = (4 + \/-5) (4- \/-5) 

 = (1 + 2^-5) (i-2\/-5), 

 whereas none of the factors 3, 4 -t- -y/ - 5, etc., is de- 

 composable into two factors (a + ^\/~5) ('^ + ^'v/~5)- 



Mathews' was probably the first mind in England 

 to realise the far-reaching effect of Dedekind's dis- 

 covery, two papers by him on the subject appearing 

 in the London Mathematical Society's Proceedings of 

 1892. The tract " Algebraic Equations " on a kindred 

 topic, written fifteen years later, contains a masterly 

 exposition of Galois' theory, completed by Jordan 

 and others, showing how the different types of irration- 

 ality which can be defined by an algebraic equation 

 are associated with different types of group. 



Written in collaboration with Prof. Andrew Gray, 

 the " Treatise on Bessel Functions," concerned mainly 

 with physical applications, is still a standard work. 

 The " Projective Geometry " (1914), inspired by 

 Henrici's lectures in London many years before, 

 contains two unusual features : first, an exposition 

 of the logical groundwork of the .subject, and secondly, 

 an account of Staudt's theory of complex elements 

 (whereby a real involution defines a complex point or 

 line). He also brought out a new edition of R. F. 

 Scott's " Determinants " (1904), and contributed 

 articles on Number and Universal Algebra to the 1910 

 edition of the " Encyclopaedia Britannica." 



NO. 2736, VOL. 109] 



Most of Mathews' mathematical papers appeared 

 in the London Mathematical Society's Proceedings 

 or in the " Messenger of Mathematics." A few of them 

 are geometrical, and nearly all the rest have an arith- 

 metical bearing. Pride of place, perhaps, should be 

 given to a four-page note of 1897, in which he explained 

 a method of reducing multiple partitions to a single 

 partition. Several papers were written on the complex 

 multiplication of elliptic functions, a subject which 

 had a singular fascination for Mathews. The publica- 

 tion of a manuscript on the lemniscate functions has 

 been delayed by the war and his subsequent illness. 



Ever since the mid-eighties Nature has published 

 frequent reviews and articles from Mathews' pen. 

 These articles, most of which appeared over the 

 initials " G. B. M.," were always written in a careful 

 and scholarly style ; they contained his considered 

 opinion on the book or point concerned. In conversa- 

 tion with the present writer he once expressed the 

 opinion that some of his best work had appeared in 

 Nature reviews. 



A man of simple tastes and naturally retiring by 

 disposition, Mathews expressed sound judgment on both 

 men and affairs. Some of his views, perhaps, were 

 those of an idealist, and hardly feasible in the domain 

 of practical politics. His capacity for maturely 

 grasping everything with which his mind came into 

 contact made him unique in the experience of his 

 friends. Only one or two sides of so versatile a man's 

 brilliant intellect really appealed to most people. 

 When he was appointed professor of mathematics at 

 Bangor, at the age of twenty-three, it was manifest 

 that he could equally well fill four or more chairs in 

 the college. During recent years he spent much time 

 in reading and translating Arabic : he was also a 

 competent musician. W. E. H. B. 



Dr. J. T. Merz. 



Dr. John Theodore Merz, whose death on March 

 21, in his eighty-second year, was announced last 

 week, was a son of Dr. Philip Merz, headmaster 

 of the Chorlton High School, one of the pioneer 

 institutions of higher education in Manchester. 

 He was an acknowledged authority upon indus- 

 trial chemistry and took a leading part in the 

 industrial development of electricity supply, being one 

 of the founders of the Newcastle-upon-Tyne Electric 

 Supply Company. By the use of his great scientific 

 and practical knowledge, he rendered invaluable 

 service to the industrial community of Tyneside and 

 the counties of Northumberland and Duiham. 



Dr. Merz will, however, be most widely remembered 

 on account of literary activities, which go so far back 

 as 1864, when he wrote a paper, which was published 

 in Germany, on Francis Bacon, and another on Kant. 

 For a long time the work by which he was best known 

 was a small but much appreciated volume on Leibniz, 

 contributed in 1884 to Blackwood's " Philosophical 

 Classics for English Readers." A German translation 

 of this appeared in 1886. These publications, how- 

 ever, were mere preliminaries to that which he had 

 planned as the great work of his life, " The History 

 of European Thought in the Nineteenth Century." 

 The first volume of this was published in 1896, the 

 fourth and last at the end of 1914. From the first 



