The absence of china clay from Scotland has been used as a weighty argument in favour of the pneumatolytic or deep-seated origin of the great china clay masses of Cornwall and Devonshire, of southern Sweden, and of some of those in Germany. Kaolin, which is often regarded—I think correctly—as a synonym of china clay, and kaolinite, have, however, been occasionally recorded as occurring in Scotland. A reported occurrence at Troon may be easily dismissed. Thus it is only recorded doubtfully, with the remark that its composition has not been determined, by J. Sommerville and G. R. Thompson, while John Smith describes it as a bed of finegrained volcanic dust deposited in water. Kaolinite has been recorded by Heddle from several Scottish localities; thus it is found in minute crystals in Shetland, and in a vein at the head of Glen Capel at Abington, Lanarkshire.

This paper is devoted to the study of the existence and uniqueness of almost-periodic solutions for elliptic and parabolic partial differential equations in unbounded domains. This kind of investigation had originally been motivated by the study of the so-called boundary layers, whose behaviour is crucial in the framework of periodic homogenization.

The question of the existence of true transition resistance at the surface of certain electrodes in given liquids has been in debate for many years, but has never yet been conclusively settled. It is admitted universally that in certain cases such resistance does occur, as, e.g., when a non-conducting oxide is formed on the surface of the metal; but the point in dispute is whether or not it occurs when no direct chemical action takes place between the metal and the products of electrolysis, or between it and substances dissolved in the liquid.

At long intervals notices of circular crystals have appeared before this Society. In 1853 Sir David Brewster read a paper on the subject, which followed one by Mr Fox Talbot in 1836, and which again had been preceded by one from Sir David Brewster about twenty years before. It is not easy to account for these long intervals, unless they may be attributed to difficulty and uncertainty in manipulation, for except in very few instances the crystals observed by Sir David Brewster are of microscopic size, and, he remarks, require the perfection of optical appliances for their observation, and naturally so when crystals of the 200th of an inch in diameter are looked upon as of respectable size.

The author commenced by stating that although these researches lead him to believe in the existence of two planets revolving in orbits external to that of Neptune, and although there was a great deal of evidence to show that he had actually determined the elements of the orbits, yet the latter point, being dependent on a coincidence of probabilities only, cannot be considered a certainty until the planets are observed.

The author accepts the theory of cometary orbits which supposes that these bodies, wandering through space, are attracted by the sun into the solar system so as to pursue parabolic orbits, and that some of these, in passing a planet, may have their velocity diminished, in which case they will afterwards describe an ellipse in a definite period.

Let B(ℤ)* be the Banach dual of the space of all bounded complex-valued functions on ℤ. For each n ε ℤ, let Ln be the translation operator on B(ℤ) and Tn be its adjoint operator on B(ℤ)*. This paper concerns itself with equations of the form

where (an)nεℤ is a sequence of complex numbers.

When, with head fixed, we allow the eyes to wander over a fixed scene before us, we find that the eyes do not move continuously, but by jerks, so that what we see is really a series of separate pictures, each of which is at rest, the jerk from one position to the next being so rapid that we practically see nothing during the change of picture. That this is so can be shown if we have a bright light—say, an incandescent electric lamp—in the field of vision. After allowing the eyes to wander over the scene before us, we find, on closing the eyes, that we see a series of separate sharp secondary images of the bright light. Even when we make an effort to move the eyes continuously we find, by means of the secondary images, that we have not succeeded in doing so.

This paper contains the substance of investigations made for the most part many years ago, but recalled to me during last summer by a question started by Sir W. Thomson, connected with Laplace's theory of the tides.

A comparison is instituted between the results of various processes employed to reduce the general linear differential equation of the second order to a non-linear equation of the first order. The relation between these equations seems to be most easily shown by the following obvious process, which I lit upon while seeking to integrate the reduced equation by finding how the arbitrary constant ought to be involved in its integral.

The Committee are of opinion that it is now time to submit a final Report to the Council. Nine Annual Reports have already been presented, extending altogether to about 400 pages, as printed in the Proceedings of the Society. The appointment of the Committee took place in April 1871, and the first Report was presented in April 1872, by which time a considerable number of answers were received to circulars sent by the Committee, first to the parochial clergy, and next to the parochial schoolmasters, asking for information.

Comparatively little attention has been given to the natural history of Lewis. Stray notices of the geology, botany, and zoology of the Outer Hebrides are to be met with, but, with one or two exceptions, these are not of much value. Martin's “Description of the Western Islands (1703),” is chiefly interesting for its full account of the industrial and moral condition of the people. Little, however, can be made of his incidental references to the natural history of the islands. Two volumes on the “Economical History of the Hebrides,” by Rev. Dr Walker, Professor of Natural History in the University of Edinburgh, were published in 1808, after Dr Walker's death. This work contains a good deal of information on indigenous plants, but almost none on zoology. Dr Maculloch's “Description of the Western Islands of Scotland (3 vols., 1819)” is in every way an abler and better work than either of the two now named. Its notices of the geology and mineralogy of the Outer Hebrides are even still valuable.

Those who have had experience of problems involving inbreeding or the correlation of relatives in a population with specified proportions of Mendelian genotypes will have realised what difficulties reside in the absence of a convenient notation. In the absence of such a notation difficulties arise more from the unwieldiness of the expressions obtained than the abstruseness of the problems encountered. The familiar chessboard diagrams of Mendelian hybridisation and the form of a contingency table for relatives alike suggest that a matrix notation might be generalised to take into account both sex-linked inheritance and the more usual type of transmission. A determinant form would meet some of the requirements of autosomal transmission; but is not adapted to the asymmetrical case, when the male sex cannot be heterozygous. In extending to more remote relationships a previous inquiry (3) into fraternal and filial correlations involving sex linkage, the writer has found it useful to employ a system of operations applicable to other types of inquiry. The former investigation is not yet complete. In the meantime it seemed possible that the method used might prove suggestive to other workers. A preliminary account of the fundamental operations is here given in so far as they are relevant to single gene substitutions.

In this method the liquid of which the latent heat is to be determined is contained in a glass vessel which is suspended by a fine wire from the hook of a balance, and the amount of electrical energy is measured which is required for the evaporation of an observed mass. The electrical energy is supplied by a large current passing through a small resistance in the liquid itself. In order to reduce heat losses as much as possible, the vessel carrying the liquid and the resistance is completely surrounded by a doublewalled shield, which is filled by the saturated vapour of the liquid itself. The estimation of the electrical energy supplied necessitates tne measurement of the current, C (amperes), the resistance R (ohms), of the heating coil, and the time in seconds, T, during which the current flows. It is expressed by C2RT joules, and if M be the mass evaporated in gms., the latent heat expressed in joules per gm. becomes C2RT/M.

Ever since the remarkable discovery by Graham in 1866 that palladium possesses the power of occluding hydrogen gas in large quantity, various views have from time to time been put forward to explain the true nature of the phenomenon. Whilst some observers regard hydrogenised palladium as an alloy or solid solution, others again consider it to be, or at least to contain, a definite chemical compound or hydride. Those who hold the latter opinion, however, are not agreed as to which compound or hydride is formed, as is proved by the fact that different formulae have been ascribed to it. Graham himself recognised the possibility that a definite chemical compound might be formed, for he says (Researches, 287) that in fully-charged palladium there exists one equivalent of palladium to 0·772 equivalent of hydrogen, or an approximation to single equivalents which would be represented by the formula PdH. His opinion was, nevertheless, opposed to the idea of such a definite chemical combination, one of his chief objections being that no visible change is occasioned to metallic palladium by its association with hydrogen. He regarded the product simply as an alloy of the volatile metal hydrogenium, in which the volatility of the one element is restrained by its union with the other, and which owes its metallic aspect equally to both constituents.

Considerations of a purely chemical character have up to the present time proved insufficient to decide which of these views is correct.

The author states that the results of the Trigonometrical Survey of Great Britain are nownearly ready for publication, and that he has deduced from them the most probable measures which they afford of the length of a meridian, and the figure of the earth.

After determining the most probable spheroid from all the astronomical and geodetical operations in Great Britain, it has been found that the plumb-line is sensibly deflected at several of the trigonometrical stations; but in almost every case the physical cause of such irregularity may be with probability inferred.

Exact solutions recently discovered for non-conservative three-wave resonance are here related to the ‘one-lump’ solutions obtained by Backlund transformation in conservative cases.

The state of knowledge of fast neutron polarisation due to elastic scattering is reviewed in relation to the optical model of the process. There is clearly a substantial lack of polarisation data at neutron energies and concerning nuclei appropriate to the optical model description. The situation for the extremes of small and of large angle scattering is also considered.

Let m(λ) denote the Titchmarsh–Weyl m-function associated with the differential equation

with Neumann boundary condition at 0. In the case q ∊ CM[0, ε) for some integer M and ε > 0 we prove the following result (Theorem 2.1): If for some integer ŋ ≧ 3 we know that Im {λ(ŋ + l)/2m0(λ)} = 0 on the ray λ = |λ| eiπ/ŋ, then q(v) (0) = 0 for all v in the set {0, 1, … M} for Which ≢ ŋ − 2 mod ŋ.

This paper is concerned with the problem of showing uniform stability and equiasymptotic stability of thezero solution of functional differential equations with either finite or infinite delay. The investigations are based on Liapunov's direct method and attention is focused on those equations whose right-hand sides are unbounded for bounded state variables.