May I be permitted to make some comments on the interesting paper by Dr. Robb in the July number of the Gazette? The point he raises is indeed interesting; though, without his having said so, I should have been surprised to find that it was not generally known; that the Time-Space Theory may, in a limiting instance, be incompatible with Euclid’s (I, 4). My comments must in a sense be critical, though I have nothing to say against his mathematics, so far as it is “pure,” or merely symbolic; for even though we might not, with Macaulay, say that it is well known to every schoolboy, or was even known to Macaulay himself, it would be obvious enough to every modern-side schoolboy who has got as far as “conic sections”; provided he was willing to take some of Dr. Robb’s technical terms in a more or less Pickwickian sense.

The customary school method of dealing with logarithms (i.e. the initial definition : if ax =N then …) has one great defect : it gives no lead whatever towards the higher theory of logarithms, nor even towards methods for calculating them. “How shall we introduce our sixth form girls to the theory?” a mistress recently asked; “it seems to come like a bolt from the blue.” Klein has some true and forcible things to say on the subject [Elementar Mathematik vom höheren Standpunkte aus, (3 ed. 1924) I, p. 155 et seq.] from among which a sentence or two may be quoted.

Gauss was the son of a bricklayer, and owed his education to the reigning duke. Ramanujan’s father was indeed accountant to a cloth merchant, but it may be doubted whether the position of an Indian accountant in the late nineteenth century was financially very much preferable to that of a German bricklayer in the late eighteenth. At any rate when Ramanujan, a married man of twenty-five, wrote his first letter to Professor Hardy enclosing statements of some of the results he had obtained in mathematics, he himself was employed as a clerk in the Accounts Department of the Port Trust Office of Madras and earning a salary of £20 a year. Ramanujan lived in a more democratic age than Gauss, so there was no reigning duke for him. Fortunate then that there were Indian and British mathematicians who were interested and impressed, and an able and sympathetic civil servant as chairman of the Madras Port authority.

Most mathematicians are aware of the unhappy controversy between Newton and Leibniz about the priority of the discovery of the Infinitesimal Calculus. This controversy lasted from 1707 to 1716, and, as Rouse Ball writes, “ it occupies a place in the scientific history of the early years of the eighteenth century quite disproportionate to its true importance”. It is, however, remarkable that this controversy is to a large extent responsible for the fact that even to-day much of the teaching of Elementary Calculus in this country is given in an unsatisfactory manner. The notation of differentials was invented by Leibniz in 1675, at about the same time as Newton invented his “ fluxions”. The bitterness of the aftermath of that unhappy controversy, however, resulted in the almost complete disappearance of the differential from English mathematics.

My recollections of W. J. Greenstreet date back half a century when we were both undergraduates at Cambridge, but we did not become personally acquainted till many years later. He had a slightly stooping figure and kind protective face which dissolved any feeling of awe produced by his great strength and height, penetrating eyes, and full-grown beard. He had two inseparable friends, E. F. J. Love and G. F. Stout. When in company together they drew the attention of every one who saw them. They looked more like three generations than contemporaries, Greenstreet being plainly the responsible head and Stout the cheerful but inscrutable infant, while Love appeared to be more normal and rather embarrassed by the strangeness of his companions.

“If pairs of common tangents be drawn to three circles, and if one triad of common tangents be concurrent, the other triad will also be concurrent.”

This is Casey’s enunciation * of a familiar theorem; Salmon † has the same unqualified assertion, and appends a footnote: “This principle is employed by Steiner in his solution of Malfatti’s problem…. [His] construction is: Inscribe circles in the triangles formed by each side of the triangle and the two adjacent bisectors of angles; these circles having three common tangents meeting in a point will have three other common tangents meeting in a point, and these are common tangents to the circles required.”

For more than twenty years W. J. Greenstreet was scientific correspondent of the evening Westminster Gazette, and he was one of the first to bring scientific developments regularly under the purview of a newspaper. His work consisted in writing articles on any discovery or research of special importance, contributing a regular fortnightly article on current science, and reviewing scientific books and periodicals. He read widely, English, American and foreign books and scientific records of all sorts, to equip himself for this work, and, whenever possible, gave it a practical application.