By rational mechanics is meant the development of the subject of Mechanics according to a strict logical scheme, proceeding, like Geometry, from certain hypotheses or axioms established (or indicated) by experiment, from which particular theorems or applications are deduced. Every branch of theoretical physics aims at such a complete rational treatment, but whereas in Geometry the axioms have long ago been classified and isolated, and the bulk of the science consists of the deductions from them, in Physics we are still largely occupied with the discovery of the laws and axioms.

Let A B C be three travellers going along a straight road, each at constant speed. Let the following three events happen in succession, the passing of C by A at O (Fig. 1), the passing of B by A at V, and the passing of B by C at W. At the meeting of A and C let A set his watch by C’s, and at the meeting of A and B let B set his watch by A’s. Our question is whether the watches of B and C will agree when they meet at W.

Readers of the article in the October Magazine on “Systems of Conics satisfying four conditions” would notice the important part played by degenerate conics. A little more explanation of these degenerate conics may not be out of place.

Now that the Infinitesimal Calculus is becoming part of regular school courses in Mathematics, the question of how the subject should be introduced takes on correspondingly increased importance. And the question is really of fundamental importance; for it is only when the average person, as distinguished from those of special aptitude for a subject, has to be considered, that we are driven back upon the necessity for a sound common-sense basis of theory. Recent articles in the Gazette are evidence of the growing interest in this question—discussion of the perennial issue of e being only a part of this wider inquiry.

Analysis Situs, or Topology, is the investigation of those properties of surfaces and spaces which are unaltered by deformation, that is, by bending and stretching without tearing. For example, a circular disc with a hole in it can be stretched so that its boundary circuits have any of a great variety of forms, but the number of circuits (two) remains unaltered—it is a topological invariant. The fundamental problem of topology (at present unsolved) is to determine necessary and sufficient conditions that a given surface or space A should be deformable into a given surface or space B.

A 16-Page pamphlet which has been prepared at Burnley Grammar School and published there at the price of 6d. under the title Guide to the Eclipse of June 29th, 1927, fits into the gap between the instructions of the professional astronomer and the advice of the professional journalist. Of the five sections—the cause, what to look for, hints to photographers, the eclipse in history, an expedition which “failed”—perhaps it is the third which is the most important; the last section, a quotation from Piazzi Smyth’s account of the terrestrial effects of totality when the sun itself is clouded, is a valuable antidote when meteorological friends have operated with their usual depression and we feel that the chance of a fine morning would hardly justify us in getting up early even if we lived on the central line.

The object of this paper is to exhibit the application of the Stieltjes integral to harmonic analysis.

The following solution is suggested of Mr. J. Katz’s problem, “How is e to be introduced into our teaching?” published in the December number of the Gazette.

In spite of the great increase in the last fifteen years in the use of the Calculus in the higher forms of schools, and of its introduction into the Intermediate Examinations of many universities, it has not yet been used as much as it could be in the teaching of elementary Applied Mathematics.

It has, of course, long been realised that in the kinematics of the motion of a particle in a straight line we have some of the best examples of the ideas that are the basis of the Calculus, and the notation and machinery of the Calculus is now extensively used in dealing with this part of the subject.

In the preface to his Principles of Geometry, Professor Baker states that the “Foundations” volume “assumes only those relations of position, for points, lines and planes, which, furnished with a pencil, some rods and some string, a student may learn by drawing diagrams and making models.” When the beginner attempts to make these diagrams, it is not unusual for one or more points to go off the page. To illustrate how, in an important set of cases, it is possible to get all of the diagram on the page at the first trial is the purpose of this note.