The claims of Herbart on the attention of the teacher are at last being recognised in this country. Not merely is he deserving of study as one of the founders of modern psychology, not merely does he attract our interest as the central object of veneration of a rapidly increasing school in his native country and in the United States, but he also takes up a position apart from most philosophers, in that he actually devoted a large part of his life to the work of teaching, and deliberately applied his psychology to education. To the readers of this Gazette, the opinions of Herbart, who offers us this rare combination of the theorist of the first rank with the successful teacher of boys and men, will be of additional interest when it is realised that he plays somewhat the same rôle as the staunch advocate of Mathematics in the curriculum that Herbert Spencer does for Natural Science. He urges that “for six hours weekly” Mathematics should be “the beginning, middle, and end” of every system of instruction. And the fact that Mathematik is of wider connotation than we should now award to it will not deprive his remarks of much of their value. It will be as well, however, to bear in mind that he includes in this term all that is not comprised in Geschichte.

Edward Wright was probably born about 1560, and he died in 1615. He was a fellow of Caius College, Cambridge. The chief source of information about him, besides his own published works, is an obituary notice in a Latin paper preserved in the college library. He furnishes a notable instance of the conditions under which mathematical science was pursued in his time. The main object kept in view was to supply material needs of life, principally at this period in all matters connected with navigation, and the promoters and supporters of research in this direction were not the universities, but the trading and mercantile communities. Wright was appointed by the East India Company their Lecturer on Mathematics, at a salary of £50 a year. He was mechanical tutor to the eldest son of James I., Prince Henry, who died in 1612 at the age of nineteen. For his pupil’s instruction he designed and made a wonderful piece of mechanism, displaying all the movements of the heavenly bodies then known, and constructed to indicate these correctly for 17,100 years. It lasted, in fact, but a very few years. During the troubles of the civil war it was cast away as old rubbish, and in 1646 was found by Sir Jonas Moore, and deposited in its dilapidated state at his house in the Tower.

Let TP, TQ (Fig. i.) be tangents to a conic, C its centre, S, H its foci, 2a and 2b its axes. From S draw a perpendicular to TP and produce it to its image S′; then we know that S′T = ST, angle S′TP = PTS, and S′H = major-axis = 2a. Similarly with a perpendicular drawn from H to TQ and produced to its image H′. Thus the two triangles S′TH and STH′ are equal, and the angles S′TS, HTH′, and therefore the halves of these angles, are equal, that is, “the tangents from T are equally inclined to the focal distances of T.′