Interest for mathematicians in general rather than concern with problems intelligible to small groups was the characteristic of most of the papers in mathematics at the centenary meeting of the British Association. The Department had a full programme for four mornings, and Prof. A. R. Forsyth occupied the chair throughout.

It is well known that a curve has only one equation in Cartesian co-ordinates When referred to a given pair of lines as axes, but it does not appear to be so well known that a curve can have many equations in polar co-ordinates, all referred to the same pole and initial line. This fact, although of considerable importance in the study of curves by means of their polar equations, appears to be consistently ignored by most text-books.

Mr. Fletcher begins his article in the January number of the Gazette by giving two reasons why a logarithm ought not to be defined as the index of the power of the base which is equal to the number. But are these reasons well-founded? One is that it does not afford a basis for the more advanced parts of the theory of logarithms. That statement would require a proof that might be very difficult or perhaps impossible to produce.

The advent of the modern calculating machine has reduced the labour of computation in an extraordinary degree; continued products, long division, and so on, offer no terrors to anyone who has access to any of the latest excellent machines; even the extraction of a square root can be performed to ten digits in a minute or two. Under these conditions the numerical solution of algebraic equations, a process stigmatised in the seventeenth century as intolerably laborious, can even be in danger of becoming a vice : the present note owes its origin to a mild indulgence.

Most of the following theorems regarding the hyperbola of Apollonius and the parabola of Chasles are classical, but not all of them are as well known as they deserve to be, and it is hoped that this purely geometrical treatment may be of interest.