Fifty years ago, when this Royal Society was a hundred years old, it fell to Lord Moncrieff, the President, to speak to the occasion. He sketched the history of the Society through its hundred years, and dwelt most on the days when it was born. He told how the Founders made their way one winter's night from homes in Lawnmarket or Canongate to the College Library (as Johnson and Boswell had lately done), with a few flickering oil-lamps to light the way and tallow-candles which dimly lit the room.

The object of the present investigation is to throw further light upon the differences between the disturbances in the chemical processes in the body in fever caused, on the one hand, by the mere rise of body temperature, and on the other by the action of the micro-organismal poisons on the tissues of the body.

The influence of such micro-organismal poisons has been already studied by several investigators-among others, by Noël Paton, Dunlop, and Macadam in the case of diphtheria (Journ. of Phys., vol. xxiv. p. 331,1899; see also chapter “Fever and Infection,” by Kraus, Von Noorden's Metabolism and Practical Medicine, vol. ii. p. 90); but so far few detailed studies of the metabolism in high temperature due to non-infectious processes have been recorded.

In January and February 1879 Mr J. Y. Buchanan communicated to this society two papers, on the distribution of temperature under the ice in Linlithgow Loch. In these papers he gives a most interesting and valuable series of temperature observations made by him, of the water, at different points, and at different depths, in the loch while it was covered with ice. He also gives the temperatures as taken by him under similar circumstances in Loch Lomond. These observations by Mr Buchanan disclose a somewhat unexpected thermal condition of the water.

A partial differential equation of physics may be defined as a linear second-order equation which is derivable from a Hamiltonian Principle by means of the methods of the Calculus of Variations. This principle states that the actual course of events in a physical problem is such that it gives to a certain integral a stationary value.

It has been pointed out by several experimenters, notably by Ewing, and Gray and Ross, that a specimen of steel freshly annealed is in a peculiar magnetic condition. Thus, if a specimen, thoroughly demagnetised, is annealed and then tested, a certain I–H curve is obtained. If it be then demagnetised, and tested again, a second I–H curve is obtained which lies definitely below the first; and any further tests after demagnetisation produce a repetition of the second curve, which is characteristic of the specimen. To obtain the first curve again, the specimen has to be annealed from the same temperature as before, and a test made before demagnetisation.

In this paper we consider equichordal curves in ℝn. We extend the notion of chordal area to all equichordal curves and introduce a notion of *-chordal area. We establish results connected with the length, *-chordal area and extended chordal area. Moreover, we give a Crofton-type integral formula for plane equichordal curves and derive an isoperimetric inequality for *-chordal area. The paper is based on the results of F. J. Craveiro de Carvalho and S. A. Robertson [2].

In this paper we study a class of 2-generator 2-relator groups G(m) and show that they are all finite. Moreover, two infinite subclasses are soluble of derived length 4.

We give an existence result and some qualitative remarks about the optimisation of the torsional rigidity of a beam.

I. The use of an excessive meat diet in rats induces a deterioration in the health of the animals. This deterioration is shown in (a) an imperfect physical development, (b) a loss of reproductive power, (c) defective lactation, and (d) a high mortality in early life in the second generation of meat-fed subjects.

II. The recuperative powers of these deteriorated animals, on a normal diet, is very striking.

III. In animals deprived of their ovaries, the minimum amount of proteid required is less than in normal females.

This investigation was carried out for the purpose of extending to other substances an inquiry into the effect of an electric current on Young's Modulus, which was carried out by Miss Noyes on a steel wire at Cornell University, and described in the Physical Review, No. 4, vol. ii. In the investigation of Miss !Noyes, the wire under examination was heated by a coil, the current being supplied by a storage battery. To vary the method of heating, the current was also sent through the wire with the expectation that the same effects would be obtained as when the wire was heated by the coil. This, however, was found not to be the case, and Professor Nichols, under whose superintendence the investigation was carried out, in his Laboratory Manual of Physics, vol. ii. p. 293, states that an extension of the inquiry to other materials than iron would be of interest.

Let P be a set of primes. A nilpotent space X is called “P-universal”, if its P-localization canbe obtained as a direct limit over a sequence of selfmaps of X. A nilpotent fibration is called “fibrewiseP-universal”, if its fibrewise P-localization can be obtained in a similar way as a direct limit of fibrewise maps. In this paper, the following results are proved. Let π:E → B be a nilpotent fibration of connected finite or cofinite spaces. If π is fibrewise P-universal for some proper subset P of the set of primes, then its minimal model (in the sense of D. Sullivan's rational homotopy theory) admits a certaintype of weight decomposition. But the existence of such a weight decomposition implies only that there exists a finite set of primes, such that IT is fibrewise P-universal for all P with . In the absolute case however, i.e.B is a point, the set P can be chosen as the empty set. Thus a result announced by R. Body and D. Sullivan is recovered.

In this paper, the existence of global smooth solutions and the formation of singularities of solutions for strictly hyperbolic systems with general eigenvalues are discussed for the Cauchy problem with essentially periodic small initial data or nonperiodic initial data. A result of Klainerman and Majda is thus extended to the general case.

A solution is given to an open question of Blyth and Varlet concerning bistable subvarieties of MS-algebras.

In October 1894 a pair of Cape hunting dogs were acquired by the Royal Zoological Society of Ireland and added to their collection in Phœnix Park. They were purchased from Hagen-beck, in Hamburg, and at the time they came to Dublin they were not quite full grown. Although still existing in considerable numbers over a very wide area in Africa, the Lycaon is by no means a common specimen in Zoological Gardens, and it is rare to meet with it on the lists that are periodically issued by dealers in wild animals.

Since the delivery of my presidential address (1) in July I have assembled an amount of supplementary information regarding “the Chemical Society instituted in the beginning of the Year 1785”. This, together with a brief description of some other chemical societies of the revolutionary period, forms the basis of the present paper.

First of all, it will be expedient to furnish a complete list of the dissertations read before the Society during 1785–86 and included in the first volume of its Proceedings, appending short comments with respect to the communicators or their topics when anything of special interest arises.

A sufficient condition on the angles of a bounded open subset Ω of ℝn is given for the best possible regularity of a solution to a class of parabolic problems with non-linear mixed boundary conditions.

Existence and uniqueness theorems are proved for the solution of a Dirichlet-Neumann-Third mixed boundary value problem for the Helmholtz equation in ℝ3. The proofs make use of an equivalent system of two integral equations of the second kind.

We study, in unbounded domains Ω⊂Rn, an elliptic semilinear problem with homogeneous boundary conditions. We assume that the nonlinear term f(x, u, Du) satisfies some condition of quadratic growth with respect to Du. We prove, in the framework of weighted Sobolev spaces, that, if and are respectively a subsolution and a supersolution of our problem, then there exists a least solution ū and a greatest solution û in the ordered interval and we obtain some multiplicity results.

An E-unitary inverse semigroup, S, has the property that, if x=S, and e2 = e=S, then (xe)2 = xe implies that x2 = x. As a consequence of this, we can see that S is an extension of its semilattice of idempotents, E, by its maximal group morphic image, G. Thus, following McAlister (1974), we attempt to describe S in terms of E and G. If we extend the semilattice E to a larger semilattice F, we are able to describe S in terms of a semi-direct product of F and G, giving a new interpretation to the approach of Schein (1975).

This paper gives sufficient conditions ensuring that a non-linear control system of the form

is controllable by means of control functions u(t), such that each ui(t) only takes two values, with a finite number of switches. It is assumed that the ‘unperturbed’ system ẋ = A(t)x + B(t)u is controllable in the usual sense, i.e. by measurable and bounded controls.