The absence of English names from the first part of the record has often been remarked upon and deplored. The whole story and its lessons are given in Mr Rouse Ball’s well-known History of Mathematics at Cambridge. We may point with pride however to the later achievements of our countrymen, most of them more or less connected with this University. Some features, specially characteristic, which we may claim as of English origin have been already indicated, the search for definite geometrical images of physical relations, and especially the cultivation of graphical methods. I may in particular mention the instructive diagrams which are appended to Maxwell’s treatise, and which have been so great an assistance to the imagination of his readers, and so valuable as an example to later writers. The period we have been surveying had I think a fairly definite beginning, and an almost equally definite close. From the mathematical [Pg 47] point of view its most striking achievement is the wide-embracing scheme of relations, which can be applied to so many diverse subjects, with hardly more than a change in the names of the various concepts. In their purely abstract form, in the rarefied atmosphere of Vector Fields, Triple Tensors, and so on, these relations might almost be developed in an hour, though they could hardly be understood or appreciated without reference to their physical aspects, to which they owe all their value. That such generality should have been attained is an instance of the constant endeavour of Mathematics to reduce to simple laws the infinite variety of nature. With a wider view than was possible to Fourier, we may echo his Newtonian quotation: Quod tam paucis tam multa praestet geometria gloriatur. CAMBRIDGE: PRINTED BY W. LEWIS AT THE UNIVERSITY PRESS