If four rigid rods are smoothly pivoted together at their ends to form a closed quadrilateral the system is said to form a four-link chain. Under certain conditions, five in number, it is found that the quadrilateral is freely deformable and the system is then regarded as a mechanism. Isolated systems, satisfying the necessary conditions and hence admitting deformation, have been known for some time, namely,

• (a) the case in which the rods are coplanar and all the hinges are perpendicular to this plane;

• (b) the general “spheric or conic-chain” in which the lines of the four hinges are concurrent;

• (c) the case of the “Skew-isogram” discovered by Dr. G. T. Bennett.

Modern engineering employs the use of the cathode-ray oscillograph as a means to solve some of its problems. A Lissajou figure produced on the cathode-ray tube provides a convenient method of determining the phase difference between two sinusoidal variations of the same frequency. The figure is, in general, an ellipse and this note gives the mathematical basis of the method of determining the phase angle in terms of the axes of the ellipse and of the sides of the principal circumscribing rectangle (whose sides are parallel to the injection axes).

A Meeting was held on 4th August. The principal business was connected with the main-school mathematical syllabus, and in particular the new alternative scheme of the Cambridge Local Syndicate. The following points were made:

A fixed sequence is to be deprecated even if it facilitates the task of the examiner; but it was urged against this that the selection of theorems in the Cambridge syllabus, and their arrangement, actually made things easier for the pupil and only restricted the teacher in the area group. It was important to decide whether a formal exposition of geometrical arguments was desirable or not. If it was, it could be practised and tested by a small number of key-theorems such as those suggested by the Syndicate.

A Well-Known method of integrating the simple differential equation of the second order

y″ + k2y = 0 .....1.1

consists in multiplying by an integrating factor 2y′ and integrating directly, when we obtain

y′2 + k2y2 = k2a2, .....1.2

where a is an arbitrary constant.

By a curious chronological coincidence, the tercentenary of Newton’s birth in 1642 is succeeded by the centenary of another outstanding event in the history of mathematics; the discovery of Quaternions in 1843 by Sir W. R. Hamilton. It seems a suitable occasion for drawing attention to the extent to which conceptions due to Irish mathematicians of that epoch are interwoven into the technique employed in recent developments in mathematical physics.

A girl is about to leave school and is not intending to go to a university. She has always been interested in mathematics and has done quite well in that subject while at school. Are there any jobs available in which she will find her knowledge of mathematics an advantage?

Members of the Association must frequently have been asked this question, and while war-time conditions have perhaps decreased its importance, when the war is over we shall again be expected to provide an answer. The Executive Committee would be most grateful for any relevant information, and members who can make suggestions are urged to write to Mrs. E. M. Williams, 17 Belgrave Square, Nottingham. It is hoped that in this way a list of ideas can be compiled for publication in the Gazette.

Mathematics has for so long had an honoured place in the curriculum that teachers have expanded the essentials of elementary algebra, and have brought in excessive manipulation, without considering its value or whether it is needed. They have lost sight of the objects of their teaching and have allowed manipulation, of a type comparable to a difficult cross-word puzzle, to creep in. This may satisfy the puzzle instinct of a few of the more intelligent pupils but certainly causes much heart-burning to the average pupil with little distinctive mathematical ability. We should, then, from time to time review the objects of our teaching, and not only our methods, and then examine the contents of the curriculum and discard those parts which are unnecessary, and replace by mathematics which is more value.