The methods usually adopted for demonstrating the Lorentz Transformation are algebraic. Algebra is a powerful means of arriving at results, but does not in itself explain those results. In the present matter, the average reader is left with a sense of puzzledom, baffled by the paradoxes evolved by the algebra ; the results are demonstrated, but he is unsatisfied. The following paper is an attempt to treat the matter from first principles, avoiding algebra and getting down to the plain common sense. The results are obtained quite simply ; paradox is avoided. Some observations are hazarded at the end on the questions of simultaneity, “before” and “after,” in which the view taken differs somewhat radically from that ordinarily adopted.

Among the complicated rectilinear patterns employed in Saracenic art there is a group which may be described as “geometrical arabesques,” drawn by a curious method which may be of interest to mathematicians.

The function of the mathematical laboratory can best be understood in the light of the experience of many mathematical teachers. Anyone who has devoted even a comparatively short time to the mathematical training of workers in any branch of applied science must have had the experience that many past students return at frequent intervals for advice and consultation. The difficulties with which they are confronted appear invariably to be associated with the application in more or less concrete form of the mathematical principles and methods which they have learned. I find, as a matter of actual experience, that the complaint, when it is voiced, concerns itself not so much with the width of the mathematical field covered during training as the inability to know when to apply this or that mathematical method, how to attain the so-called solution, and how, when the mathematical solution has been obtained, to derive from it the desired information with reasonable expenditure of labour. It is partly this gap that the mathematical laboratory seeks to fill. An engineer confronted with a problem in heat conduction will not be satisfied should you provide him with an expression for the distribution in temperature in terms of a series of Bessel functions, unless he has at hand the means of immediately calculating to so many decimal places the values of these functions, either from a set of tables or by some direct mechanical process which he can apply. The form of solution provided may be to him more difficult to interpret than the original problem. It is partly because in the past mathematical teachers have been content to regard a problem as solved when, somehow or other, an analytical solution has been obtained, or to regard a problem as insoluble when such a solution cannot be obtained, that the failure exists on the part of the students of that training to utilise the mathematical weapons at their disposal, to modify them according to circumstances, and to interpret their results in actual cases.

I Think that everyone here will agree with me that we, who try to teach mathematics, have a heavily loaded curriculum and we are apt to become the slaves of public examinations. According to the age of our pupils, Intermediate or Matriculation hangs like the sword of Damocles above us, and we dare not be led far astray from the mark-gaining part of our work.