In the July number of the Gazette Mr. E. G. Phillips says: “Frequently it happens that students whose early training has been on the lines of many of the existing elementary text-books on the Differential Calculus come up to the University never even having heard of a differential! It would be of the greatest possible assistance to those responsible for the later teaching of the Calculus if the schoolmasters taught the subject from the differential standpoint right from the start”. I have the very greatest hesitation in subscribing to this latter statement.

Explanation of terms used. For “Bordered Squares” the term Heart is given to the core around which the border is to be arranged. The Heart can be one of several different kinds. In our case, the rows and columns do not sum to the same amount; but the Heart is Associated, that is, every pair of numbers equidistant from the centre of the Heart in a straight line sums to the same amount, here 50. The numbers which make up such a pair are Complementary Numbers. When the numbers of these pairs are subtracted one from the other, they give the Complementary Differences.

I do not know what proportion of the users of mathematical tables go beyond the use of proportional parts in interpolation work. But there are undoubtedly, on the one hand, some tables whose construction would be unnecessarily laborious and expensive were they to be at such an argument interval as to render linear interpolation feasible, and, on the other hand, there are those who find it necessary to use such tables. Given such a table, there are various methods of performing the interpolation. There is the use of the Taylor series, f (a + h) = f(a) + hf′(a) + ½h2f″ (a) + ..., which requires a knowledge of the derivatives of the function as well as the function itself. Then there is the use of the Lagrange formula of interpolation, fx = a0f0 + a1f1 + a2f2 + ..., involving a number of tabular values on both sides of the required value.

The next International Congress of Mathematicians is to be held at Zurich from 4th September to 12th September of this year. The complete programme of lectures and sectional meetings has not yet been received, but the list of those who have already promised to speak is so strong that an attractive week is certain.

Besides the scientific arrangements, there are plans for social functions and excursions ; for these Switzerland should prove an ideal setting.

1. The title of my paper is, perhaps, a little misleading. The word Elementary is intended to apply to the word Mathematics, not to the word School, and I will keep strictly to Elementary Mathematics.

The treatment of Geometry in feigned independence of numerical measurement was theoretically abandoned as soon as the supremacy of Euclid collapsed under the onslaught of Professor Perry in the year 1901, and gradually, largely through the efforts of a few outstanding educationists, the teaching of School Geometry in this country has undergone a very remarkable change.