It is well known that Euclidean metric geometry is a special case of projective geometry, inasmuch as it refers to transformations which leave the line at infinity and the circular points invariant. Every projective theorem will thus have one or more Euclidean counterparts according to which line and which points on it are taken to be the line at infinity and the circular points. It is, on the other hand, also possible to translate any theorem into projective language by removing every trace of metrical properties. A theorem of projective geometry is thus obtained of which the original theorem is a special case. This principle will be illustrated by applying it to the following elementary

Many members of the Association know the Gazette only in its hampered and restricted war-time form. The time is therefore opportune for some remarks on the pre-war Gazette and on what may reasonably be expected from the post-war Gazette. The history of the Gazette, however, cannot be fully understood without some reference to the history of the Association; such reference need be only brief, since a full account is available in the admirable Presidential Address by Mr. A. W Siddons (XX, No. 237, February, 1936).

This note is intended to supplement Note 1754 and the article on pages 77 to 79 of Gazette XXVII. There is some danger that the reader of that note or article may get the impression that the writers are trying to prove some absolute truth about the signs when they are really only concerned with consequences of the definitions and conventions. There is not much difference between a definition and a convention. Often a convention is little more a an instruction about how a definition is to be interpreted. Neither a nition nor a convention can be right or wrong: it can be appropriate or appropriate.

Most of us have asked this question at some time or another; generally we have received some such answer as: “It’s a gyroscopic effect, of course” Further details are not easy to obtain, and the majority of books on Mechanics do not mention the subject.

If BPC, DPE are circular sections of the cone vertex A, a sphere can be drawn containing these two sections, and the cone will touch the sphere at the points P, P1 where the line of intersection of the two planes meets the sphere. Thus AP2 = AD AB. Taking BPC as the base of the cone, if AC is the least and AB the greatest of the generating lines drawn from A to the base, ABC will be a principal section of the cone and the planes of circular ection of the cone are perpendicular to the plane ABC. If AF is perpendicular to DE and AH perpendicular to BC,

That is, AP2 is the product of the perpendiculars drawn from P to the planes hrough the vertex A parallel to the planes of circular section, divided by in B sin C.

This paper, while it does not merit the attention of workers in the field of summability, may be of some interest to readers of the Gazette who are using Bromwich's classical work on infinite series as a textbook. Its main purpose is to show that Bromwich's proof of the Hardy-Landau converse of Cauchy's limit theorem can be made to yield, without any modification of the underlying idea (due to A. E. Jolliffe), all the familiar converse theorems on Rieszian summability of the first order. The paper also shows that after having obtained these theorems, one can pass on, by a natural transition suggested by Szász, to the corresponding results in the theory of summability by Dirichlet's series

Universities have taught in England for about seven centuries, and mathematics has always been one of the subjects taught; but in the earlier centuries it was not part of the undergraduate course. This consisted of three years’ study of Latin grammar, logic, and rhetoric, forming what was called the trivium. Mathematics was part of the M.A. course, consisting of arithmetic, geometry, music and astronomy, forming the quadrivium; but this postgraduate status meant less than might seem, because the undergraduates had the position of schoolboys today, and became Bachelors of Arts at ages from fourteen to seventeen. The B.A.s of those days corresponded to the undergraduates of our time.