The Edinburgh Mathematical Colloquium 1914

The successful Colloquium which was held in Edinburgh last August was described in the October number of the Gazette, and the suggestion was there made that a Colloquium should be held in the same city in the present year, in conjunction with the Napier Tercentenary Celebrations.
This suggestion has been adopted by the Edinburgh Mathematical Society, who have now resolved to hold an open Colloquium on July 28th to 31st inclusive, immediately following the Napier celebrations on July 24th to 27th.
The following short courses of lectures have been arranged:
 Two lectures by M d'Ocagne (Professor at the École Polytechnique and the École Nationale des Ponts et Chaussées, Paris, and Past President of the Société Mathématique de France), on NOMOGRAPHY.
It is now generally recognised that for most purposes the nomographic methods are superior to the older graphical methods of calculation. The introduction of some nomographic teaching in British Universities (and schools, for much of it is not too hard for schoolboys) is much to be desired.
 Four lectures by H W Richmond, M.A., F.R.S. (Fellow and Lecturer of King's College, Cambridge, and University Lecturer in Mathematics), on INFINITY IN GEOMETRY.
The "line at infinity," the "cyclic points," and the "circle at infinity" are familiar conceptions, and may serve to indicate the class of questions to be discussed in these lectures.
 Four lectures by E Cunningham, M.A. (Fellow and Lecturer of St John's College, Cambridge), on CRITICAL STUDIES OF THE MODERN ELECTRIC THEORIES.
Of recent years most things in Physics have been explained in terms of electrons: and electric theories of the constitution of matter, gravitation, spectroscopy, etc., have been freely produced. Some of these theories will be described, and the points at which they are theoretically incomplete will be indicated.
 Two lectures by E T Whittaker, Sc.D., F.R.S. (Professor of Mathematics in the University of Edinburgh), on THE SOLUTION OF ALGEBRAIC AND TRANSCENDENTAL EQUATIONS IN THE MATHEMATICAL LABORATORY.
The methods described will be chiefly arithmetical, and the lectures will therefore be supplementary to the lectures of Professor d'Ocagne on nomographic methods.
The fee for the whole Colloquium is 15s., and should be sent to the Honorary Secretary of the Edinburgh Mathematical Society (P Comrie, M.A., B.Sc., 19 Craighouse Terrace, Edinburgh). Those who wish also to become ordinary members of the Napier Tercentenary Celebrations may send the fee for this (5s.) at the same time, making a total of £1. An additional fee will be charged to late entries.
In connection with the Napier Celebrations, an Exhibition of Calculating Apparatus of all kinds, from Napiers Bones to the present time, is being organised, and a descriptive handbook will be issued.

The colloquium held under the auspices of the Edinburgh Mathematical Society opened its meetings yesterday in the University Buildings, Edinburgh under the presidency of Dr Sommerville, St Andrew University. The large turn out of members from all parts or the country has justified the action of the Society in promoting another meeting of this kind. Mr Richmond, F.R.S., King's College, Cambridge, lectured on points and lines at infinity, the theory of which now forms a very important part in modern geometrical principles. The lecturer developed his ideas from analytical considerations, but passed on to their application to the geometry of the conic. Be showed the connection between the circular lines and the focus, and applied it to a few special cases.
Professor d'Ocage, Paris, speaking in French, introduced his audience to the principles of nomography, of which be himself is practically the originator. This method bids fair to displace in practical application the older method of graphical solution equations, as it can very readily be applied to equations in any number of variables.
Mr E Cunningham, St John's College, Cambridge, in his lecture, dealt with the ideal theory of the electrical constitution of matter. It is assumed that every part of matter consists of electric charges in motion, according to laws which are a generalised form of those of Maxwell's famous theory. In addition to these, certain other hypotheses are made: one, which has arisen out of the results of experiment, is that electricity exists only in separate and indivisible atoms called electrons; another, which has also been justified experimentally, is that what we have always thought of as a characteristic property of matter, its inertia, is to be attributed to the electric charges which constitute it.

At the second day's proceedings of the colloquium yesterday under the auspices of the Edinburgh Mathematical Society, Professor d'Ocagne, Paris, continued his exposition of the nomographic principle, and discussed its application to spherical trigonometry. He showed the necessity for using three general nomograms to solve all possible cases, and showed the method of constructing them. In the second lecture of the series, Mr Cunningham reviewed the results of recent experiments which had for their aim the discovery of the detailed structure of matter. He discussed the Zeeman effect, and showed how, along with the results of recent experiment on the spectra of various elements, it yielded information regarding the constitution of the atom. Mr Richmond, lecturing in the afternoon, applied the principles he developed on Tuesday to curves of higher degree than the second, and considered certain wellknown, groups of curves, chiefly of the fourth degree, which past through the circular points at infinity and have singularities at these points. The lecturer examined from this point of view the Cardioid, Limaçon, Cartesian Oval etc.

At the third day's proceedings of the Edinburgh Mathematical Colloquium yesterday, Mr Richmond commenced his lecture by criticising Cayley's statement with reference to the distinction between projective and metrical geometry. He showed that the length of a straight line and the magnitude of an angle can be expressed in terms of a property which is unaltered by projection  e.g., crossratio. In this way the sine of the angle between two lines can be expressed in terms of the crossratio of the pencil formed by the arms of the angle and the circular lines through the vester. He next showed how all special elements  i.e., those at infinity, are reduced to uniformity by introducing a special line or a special plane. Two types of geometry were indicated  viz., projective geometry, in which incidence is the fundamental property, and affinitive geometry, in which parallelism is retained after any transformation. Mr Cunningham's third lecture began with a short reference to the famous quantum hypothesis, and suggested one or two difficulties in reference to it. It then passed on to a discussion of the way in which mechanical quantities, force, momentum, and energy, may be defined in terms of electrical quantities. A suggestion was then made as to the possibility of a moving aether, in which the laws of conservation of energy and momentum are retained, and which is consistent with the principle of relativity. Professor Whittaker delivered the first of his two lectures on the solution of equations. He divided the known methods into iterative and noniterative. He dealt in yesterday's lecture with the first of these, the best known of which is Newton's rule, or the rule of tangents. After showing the geometrical principle on which they were based, he applied them to a special case.

JOC/EFR February 2008
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