This method of division is related to several methods which have been published from time to time. The advantage of the method given below is the advantage that iteration has, of substituting a repetition of a number of easy operations for a more difficult one, and the fact that at each operation the work starts at the beginning so that errors (except in the last operation) are automatically corrected.

As his presidential lecture the President of the Edinburgh Mathematical Society read, on November 4, 1938, the opening paper of a debate on School Algebra of the First Year The algebra of the Mathematical Association 1933 Report and the 1937 British Association Colloquium was for short referred to as 1933-1937 algebra or as N-D-S algebra (Nunn-Durell-Siddons), and was taken as an authoritative map of the present position in first year algebra.

Attention has been recently drawn to the rapid mathematisation of science during the past half-century and the contributions to educational technique which are being made by teachers of mathematics in technical colleges.

The kind of mathematics with which they deal may be called “Applied” Mathematics, although it is far different from what is ordinarily termed applied mathematics. It may be said to include certain portions of pure mathematics, practical mathematics, theoretical mechanics and, in rare cases, such practical mechanics as is considered necessary to illustrate the theory—whereas, in fact, it should cover all applications of mathematics to the various fields of knowledge.

Triangles with integral sides and circumradius.

A general formula giving such triangles was stated by Gauss, we propose to find a general formula giving prime solutions—that is, a formula giving integral sides and circumradius, a, b, c, R, which have highest common factor unity

If α β γ are the angles of an integral triangle, then sin α, sin β, sin δ and cos α, cos β, cos γ are rational.

A little to the north of the Yenching University near Peking stand the ruins of the famous Yuan Ming Yuan. It was a palace built during the reign of Emperor K’ang Hsi of the Ch’ing Dynasty, about 200 years ago, and was given to and repaired and enlarged by Yung Cheng, his son. The Chinese unit of length at the time of building may have been different from the modern unit, and it is therefore interesting, mathematically and archaeologically, to determine the old unit by a mathematical method. Additional interest arises from the fact that the cut stones remaining belong to a section of the palace designed in Western style by Jesuit Fathers who came as missionaries to China. Did they use Chinese or French units in their plans?

Introduction. Impulses occur not only in technical work but in everyday existence. There is hammering and door banging which may cause annoyance, handclapping which denotes enthusiasm and enjoyment, motoring on rough roads which causes discomfort (especially after a good meal!), speech, electrical communication in the Morse code, and so on ad infinitum. Impulses have been treated by applied mathematicians with reference to various technical problems, e.g. Heaviside in his work on electromagnetic theory. Moreover, the subject is one which merits attention, so in what follows a brief outline will be given of recent work based upon a particular case of the Mellin inversion theorem.

A man has three vessels, whose capacities are 3, 5 and 8 pints respectively. The largest is full of water. He desires to divide this water into two equal parts by using these vessels only What are the simplest ways of doing this?

Graphical solution.

Call the vessels X, Y and Z respectively, and the amounts of water they contain x, y and z respectively.