The theory of relativity leads to a relation between matter and radiant energy such that a mass m is equivalent to a quantity of energy E given by

in which c is the velocity of light. According to the quantum theory a photon of wavelength λ has energy E given by

Dr. W. G. Bickley : In the first place some explanation may be looked for as to why one so apparently unsuitable should be entrusted with the task of opening this discussion. It is years since I was associated with school teaching; at present drawing is difficult, and proper instruction of pupils, and criticism of their work, would be almost impossible. Admittedly I was rash enough to try to help the programme secretary by proposing this subject for discussion, and then the Council would not let me escape the punishment for my temerity.

ABC is a triangle; BX, CX′ are equal arcs of the circumcircle taken in opposite senses from B and C. AX, AX′ are then said to be isogonally conjugate with respect to AB and AC. (The usual textbook definition is to say that the angles BAX, CAX′ are equal. The definition by equal arcs is used throughout this paper both because it has practical advantages and because it leads easily to theoretical development.)

I Feel it a great honour to be permitted to address you to-day There have been some schoolmaster Presidents in the history of the Association. R. B. Hayward was President from 1878 to 1888 while a master at Harrow; Canon J. M. Wilson, a pioneer of Science teaching at Rugby, and one of the earliest to work actively for geometrical reform, became our President long after his retirement, and then there have been three in recent times, with all of whom I have been closely associated, and to whom I should wish to pay tribute.

The general problem may be stated as : Given a plane polygon A1A2 … An, to find the polygon inside A1 … An which minimises the perimeter S of , subject to a condition

Mr. I. R. Vesselo: The problem of selecting a suitable programme of films and film strips for this meeting was not a very difficult one; the choice is very limited. Like the evening-class system, which grew out of a desire, as much to make use of empty classrooms as to educate, the educational film grew partly out of a desire to make wider use of films whose first function was to fill out the normal entertainment programme. An audience would tolerate a little education whilst waiting for the “big picture”

In a comparatively short paper, no complete survey of the range of agricultural problems whose solution involves statistical methods can be given. I have therefore chosen to confine myself to one particular theme, the development of the modern field experiment, even though this has meant that I must present a rather unbalanced picture on account of the omission of other important topics such as the use of sampling methods. During six years in the Statistical Department of the Rothamsted Experimental Station, I spent much time in the planning and analysis of a large annual programme of field experiments, and I have illustrated my paper with examples drawn from the work of this Station, at which many of the new ideas in field-experimentation were first tried. I have not attempted to discuss mathematical details at all fully, for the pure mathematics of statistics is a large subject in itself; my present concern is to show some of the practical applications of the theory.

The method of solving linear differential equations with constant coefficients by using the operator D, which is given in elementary textbooks, was introduced in 1841 by Boole. In spite of the developments summarised below it remains the best method available for certain types of problem. As usually presented it is a tentative process, justified only by substitution in the original equation of the result produced. It is used only to obtain particular integrals, although it can be adapted to deal with complementary functions. This is not done in practice, however, since these can usually be written down directly.