In this paper some properties of the functions J[n](x, λ), P[n](x, λ), Q[n](x, λ) will be investigated. These functions are generalised forms of Bessel's and Legendre's Functions.

Consider a sequence of elements p1, p2, p3,.......... then (mr) will denote the sum of the first mr elements of the sequence. The simplest connection between the terms of the sequence is equality.

In a recent paper published in these Transactions I gave an account of certain experiments upon the change of electric resistance of nickel due to magnetization at different temperature up to 100·C.

In a recent paper published in these Transactions I gave an account of certain experiments upon the change of electric resistance of nickel due to magnetization at different temperature up to 100·C.

The area embraced in this paper consists of that part of Pembrokeshire which lies to the north and north-east of St Bride's Bay. Bounded on the west by St George's Channel and on the north by Cardigan Bay, it extends to the north-east as far as the mouth of the river Teifi, near Cardigan.

That part of the country which lies in the immediate neighbourhood of St David's has, through the laborious researches of the late Dr Hicks and others, become well-known to geologists, and may now be regarded as classic ground. The solid geology of this promontory has given rise to much discussion, and has, perhaps, attracted more attention than that of any other part of the Principality. The reason for this great interest is to be sought in the facts that the rocks of this area are of a very great antiquity, and that the sedimentary series contain the remains of some of the earliest organic forms yet found in the earth's crust, whilst the igneous rocks are also displayed in great abundance and variety, and present us, in the words of Sir Archibald Geikie, with “the oldest well-preserved record of volcanic action in Britain.”

The causes of the peculiarities of the solar rotation exhibited by the superficial layers of the sun's body must still be considered unknown, notwithstanding recent interesting attempts at explanation. This is no doubt partly due to the difficulties of the hydrodynamical problem placed before the mathematician in an investigation of such complexity as the movements of particles in a rotating fluid subject to energetic convection. But it must also be conceded that the observational data available for a basis of mathematical, or even speculative, research are still so scanty, that for this reason alone we may perhaps not feel surprised at the failure so far of theoretical attempts.

In this paper, theorems which are extensions of the following, are discussed:—

We define J[n] (λ, x) as

In this expression

My main purpose in the following short paper is to publish figures illustrating some of the more important facts of the early development of myotomes and motor nerves in Lepidosiren. The bearing of some of the observations of nerve development upon current theories renders it particularly desirable that they should be illustrated by untouched photographs of the sections. A few photographs illustrating the more important stages in the development of the motor nerve trunks are given on Plate I. For the preparation of the photographs here published, as well as several others, I am indebted to the skill of my friend Dr T. H. Bryce, and of Mr Fingland, our University photographer.

The following paper contains a purely analytical discussion of the problem of the deformation of an isotropic elastic plate under given forces. The problem is an unusually interesting one. It was the first to be attacked (by Lamé and Clapeyron in 1828) after the establishment of the general equations by Navier. The solution of the problem of normal traction given by these authors, when reduced to its simplest form, involves double integrals of simple harmonic functions of the coordinates. The integrals are of complicated form, and practically impossible to interpret, a fact which, without doubt, has had much to do with the neglect of the problem in later times, and the almost complete absence of attempts to establish the approximate theory on the basis of an exact solution. An even more serious defect of Lamé and Clapeyron's solution is that the integrals, as they stand, do not converge. A flaw of this sort has often been treated lightly by physical writers, the non-convergence of an integral being regarded as due to the inclusion of an infinite but unimportant constant. In the present case, however, the infinite terms are not constant, but functions of the coordinates, and the modifications necessary to secure convergence, so far from being unimportant, lead directly to the most significant terms of the solution.