A popular gibe against the branch of the teaching profession to which most of you belong is that the qualifications on which an appointment is made are not always related very closely to the duties of the post which is being filled. It is athletic prowess, we are told, that really matters. If only a man has a blue, all that is expected of him in the way of learning is sufficient intelligence to keep a clear week ahead of his class, in whatever subject he is engaged to teach. I am not going to ask whether there is or ever has been any truth in this aspersion, but I can properly point out to you this afternoon that you have no right to resent it. The accidents and aptitudes that may bring a man to the Chair of your Association are many and diverse, but one consideration is certainly never raised.

There are two main roots to the tree of modern statistical method : the longer one takes us back to the mathematical investigations into games of chance of the seventeenth and eighteenth century mathematicians, the other starts with the statistical researches of Quetelet and Galton.

Of the former we are told by Poisson “that a problem, relative to games of chance, proposed to an austere Jansenist by a man of the world, was the origin of the calculus of probabilities”.

Students find partial differential equations difficult not only on account of the inherent difficulties of the subject, but because of confusion, omissions, and, frequently, errors in the textbooks. To take an illustration, Piaggio (p. 147, new edition), begins with the statement that the equations

1

2

are equivalent because they represent the same surfaces.

The following treatment is perhaps easier than, and is in son respects an expansion of, that given by Professor H. F. Baker in h Principles of Geometry, vol. ii, pp. 58-60.

1. A,B,C,O are four given points ; AO meets BG in D, BO meet CA in E, CO meets AB in F. Then DEF is the diagonal point triangle of the quadrangle ABCO. Take this as triangle of reference for areal coordinates and let O be (u, v, w). Then A is (-u, v, w) B is (u, - v, w) and C is (u, v, -w).

In the Gazette of October, 1928 (Vol. XIV, p. 233), Professor H. G. Forder gives a simple inductive proof of the theorem on the Euler Numbers :

He remarks, however, that his method is not successful in proving completely the allied theorem for the coefficients of the tangent series