I am not acquainted with any investigation of the problem of dissecting two given rectilineal figures of equal area, by straight lines, so that the parts of either will fit on the other, and the results given here are new to me. The problem is one which suggests a variety of interesting geometrical constructions. It is natural to consider first how, and in how many different ways, a dissection can be made so as to give the smallest possible number of parts ; but types of dissection which do not give the smallest possible number of parts may also be worth attention. I exclude cases of dissections depending on some accidental or unspecified coincidence of dimensions in the given figures.

The Note on Momentum and Kinetic Energy—432. [6. a. β.]—by Mr. W M. Roberts, is interesting in showing a return in the Royal Military Academy to the gravitation unit of force in Dynamics, as more tangible for application to practical gunnery and engineering than the absolute system, introduced into theoretical instruction about 40 years, and described in Maxwell's Matter and Motion.

Major Dixon has given in the Gazette for May an interesting representation, suggested, perhaps, by Hilbert's example of a non-desarguesian geometry, of a plane geometry, in which straight lines are represented by closed curves on a closed convex surface devoid of singularitles. Employing his theory of order and “collation,” he constructs this geometry so as to be desarguesian.

My first duty is to thank you for the honour you have conferred upon me in electing me as your President for the year. Once all mathematicians were astronomers and all astronomers were mathematicians. But now only some astronomers are mathematicians, and I fear that I can only claim to be one to a very limited extent. It was, however, my good fortune to be a member of a college where your ex-President was a lecturer, and to have learned there, from him and others of a very distinguished society, something of the pleasure to be obtained from the study of Mathematics.

It does not seem to be sufficiently realised that most of the theory usually classed under “Centre of Gravity” is purely geometrical in cliaracter ; and, on the other hand, such impossible terms as “centre of gravity of an area” still offend the eye. This paper suggests a presentation of the subject free from such defects ; but its main object is to establish a sounder transition from the treatment of discrete point-systems, which is the essential groundwork of the theory, to the much further reaching treatment of continuous point-systems. The fact that this transition remains in an unsatisfactory state is an instance of the reluctance to face the necessity for explicit recognition of certain fundamental ideas of the Infinitesimal Calculus, in elementary Mathematics. It is not long since the proper conception of tangent was admitted as suitable for an elementary course of Geometry. Still more recently the more abstruse conception of arc-length has been faced. From what follows it may appear that the conception of centroid awaits its turn.