I. On seeing in Nature (June 29, 1935) a summary of the paper “The Lunar Atmospheric Pressure Inequalities at Glasgow,” recently published in these Proceedings by Robb and Tannahill (1935), I wrote to Mr Robb (with whom I had had correspondence and discussion on the same subject in 1926) to point out that a certain “convex effect” discovered by Bartels was probably the main cause of their results. It was fortunately not too late for the authors to refer to this point by adding two sentences at the end of their paper. But despite this addition I fear that their paper will produce a wrong impression on almost all its readers, particularly since no reference was given to Bartels' paper. It seems, therefore, desirable to state that the inequalities described in their paper are not lunar in any real sense. This is strictly true for the major (diurnal) component of the inequalities, and substantially true for the semidiurnal component. It is of some interest and importance to demonstrate this to the many readers of the paper who will not have previous acquaintance with the subject or ready access to its literature.

In a previous paper (“The Effect of Present Trends in Fertility and Mortality upon the Future Population of England and Wales and upon its Age Composition,” London and Cambridge Economic Service Memorandum No. 40, 1935) the author prepared estimates of the future population of England and Wales on the basis of present trends in fertility and mortality. The present contribution gives estimates of the future population of Scotland based on similar considerations. For a full description of the significance of the methods employed, the reader is referred to the previous memorandum.

In his Popular Lectures and Addresses, vol. ii, 1894, p. 360, Lord Kelvin published a paper which he had read before the Institution of Engineers in Scotland in 1867, on “The Rate of a Clock or Chronometer as influenced by the Mode of Suspension.” The effect has long been known. Almost two centuries ago, Ellicott observed the marked beats exchanged by two similar regulators when their cases were connected, which is due to the same effect (Phil. Trans., vol. xli, 1744, p. 126). The fact has crystallised into the rule that the cock that holds the pendulum ought to be as firmly fixed as possible; but as the question is not familiar, and as the observations of Lord Kelvin are given in general terms, and his description—though remarkably correct—contains some oversights, I thought it worth while to repeat the theory and the experiment.

The present investigation of the discharge of water from one vessel or reservoir to another with free surfaces, through capillary tubes of various ratios of outside to inside diameters between 1.59 and 4.31 and of various ratios between 28.8(7) and 155.2, indicates that the behaviour as a whole is represented by

provided the ends of the tubes are sharp and the conditions within the range of values of R exhibited in fig. 2.

The losses of energy are reduced by grinding the ends to a bell-mouth shape, although the effect becomes very small with the longest tubes.

The author is indebted to Professor A. H. Gibson, D.Sc, LL.D., for the facilities placed at his disposal in the Whitworth Engineering Laboratory of Manchester University, and to Mr R. Butt, M.Sc, for assistance in both the experimental work and the calculation of results.

The following is a sequel to two earlier papers by Dr J. Williamson and the author, on “The Invariant Theory of the Quaternary Quadratic Complex,” which appeared in the Proceedings in 1928. As a result of further study of two quadratics in n variables it appeared that the list of forms which constituted the starting-point of the former investigation was incomplete. The present work gives the prepared system on the basis of the revised data, and thus rectifies the earlier of the 1928 papers. It will be convenient to refer to these three papers as I, II, and III, their full title and reference being given at the end of this investigation.

In this paper the canonical form of matrix pencils will be discussed which are based on a pair of direct product matrices (Zehfuss matrices), compound matrices, or Schläflian matrices derived from given pencils whose canonical forms are known.

When all pencils concerned are non-singular (i.e. when their determinants do not vanish identically), the problem is equivalent to finding the elementary divisors of the pencil. This has been solved by Aitken (1935), Littlewood (1935), and Roth (1934). In the singular case, however, the so-called minimal indices or Kronecker Invariants have to be determined in addition to the elementary divisors (Turnbull and Aitken, 1932, chap. ix). The solution of this problem is the subject of the following investigation.

Associated with the volcanic rocks of Tertiary age that bulk so largely in the Mull, Morvern, and Ardnamurchan districts of Argyllshire, western Scotland, are occasional sedimentary deposits of insignificant proportions. The sediments, for the most part, consist of sandstones and conglomerates, but there may also be shaly bands and thin, impersistent seams of lignites (Mull Memoir, 1924, Chap. III). These lignites have been found to possess an abundant pollen-content of great interest and considerable variety, and this paper is a preliminary account of some of the forms isolated. It has not yet been possible to make a detailed examination of each seam throughout its entire thickness and thus get a complete picture of its pollen-aspect—but it is hoped to attempt this interesting task in the near future.

The results of the interaction of any two genes cannot yet be foretold with any degree of accuracy. This is another way of saying that our knowledge concerning the problem of the gene and development is still very meagre even in its grosser details. The work of Schultz (1935) and others has shed much light on the reasons for such phenomena as the disproportionate modification of vermilion by purple (Bridges and Morgan, 1919), and for many other observed effects following the combination of eye-colour mutants, but explanations for similar phenomena in other parts of the body, for instance, the non-additive action of bristle modifiers found by Plunkett (1926), and the interaction of the wing and bristle mutants of Lebedeff (1935), are of a somewhat more speculative nature. The accumulating data on these problems do not yet allow the empirical method to be dispensed with in seeking the answer to the question: What will happen when these two mutants are put together? From another point of view, the interaction of two genes, when it can be observed, is a useful method of approach in the investigation of genetic control in development, and has been used by various workers such as Csik (1934), Goldschmidt (1935), Dunn and Coyne (1935).

A System of intrusions of the type now known as cone-sheets was first definitely recognized and mapped by Harker in the Cuillin district of Skye, and was described by him in the Geological Survey memoir issued in 1904. The members of the complex were simply designated “inclined sheets,” but they incline inwards towards a common centre from north, west, south, and south-east. When the Scottish Survey undertook the mapping of Mull, in the years preceding the war, two further series of centrally inclined intrusions were soon recognized. Owing to the number of these sheets, and consequent liability to confusion, individual members can seldom be traced very far, or shown to have arcuate curvature. But the systems as a whole sweep round centres in continuous curves. In one case the curve was originally closed, though it has been somewhat interrupted by later intrusions. In the other case the main body of sheets only forms a horse-shoe. Nevertheless the term cone-sheets, which was here applied to these intrusions by Professor Bailey, is extremely appropriate.

Dr Anderson's paper (Proc. Roy. Soc. Edin., vol. Ivi, 1936, pp. 128–157) is of considerable interest as a contribution both to geology and to the theory of elasticity. One of his assumptions about fracture, however, has little support, and I am inclined to think that some difficulties that he mentions towards the end would be lessened if it were removed. This assumption is that the complete form of a fracture surface can be inferred directly from the distribution of stress before fracture, intersecting the surfaces of principal stress at some constant angle. It is often to be found in both geological and mechanical literature; but it rests on no theoretical grounds and is, I think, untrue.

Braier (1931) showed that hypophysectomised dogs on a complete diet excrete 24 per cent. less urinary creatinine than the controls, and 35 to 40 per cent. less when fasting. Schrire and Zwarenstein (1933, 1934) found that injection of anterior lobe extracts increased the urinary creatinine in rabbits.

These results afford evidence of an endocrine relationship between the anterior lobe of the pituitary and urinary creatinine. In view of the well-established relationship between urinary creatinine and muscle creatine the present authors decided to investigate the relationship of the anterior lobe to muscle creatine. An effect on phosphocreatine of muscle was reported by Marenzi (1933), who obtained a decrease of 33 per cent, following removal of the anterior lobe of the pituitary. The effect of hypophysectomy and of injections of anterior lobe extracts on muscle creatine has not been previously investigated.

About the year 1695 Martin Martin visited the Hebrides, and of the Island of North Uist he writes, “There is such a number of fresh water lakes here as can hardly be believed. … They are generally well stocked with trout and eels and some of them with salmon, and, which is yet more strange, cod, ling, mackerel, etc., are taken in these lakes into which they are brought by the spring tides.” This old reference suggested that the brackish-water fauna of the Hebrides might be of considerable interest and extent. Consequently I spent part of the summers of 1933 and 1935 in North Uist in order to study the fauna of the lochs and the conditions under which the animals were living.

The grey squirrel (Sciurus carolinensis leucotus Gapper), which is a native of the North American continent, was introduced into England and Scotland quite recently and soon became of great economic importance in these countries. In his very excellent monograph, Middleton (1930) states that both sexes of the grey squirrel show diminished activity during the winter and while they do not hibernate in the true sense of the word, they probably sleep if the weather is severe. The breeding habits of the female were studied by Deanesly and Parkes (1933), who ascertained that the female definitely has a period of anœstrus during which the reproductive organs are atrophic. In the male, however, fully functional testes were found throughout the year (Allanson, 1933), and there were no histological changes which would indicate a regular period of quiescence.

It is recognised that infecundity and infertility are among the major problems which confront the breeder of livestock, and in this country, as elsewhere, investigation into their causes, prevention, and cure is actively encouraged. A number of pathological and nutritional factors have been shown to lie at the root of these conditions, and it has become abundantly clear that in many instances genetic factors are undoubtedly responsible for the inability on the part of the individual to elaborate functional gametes and/or of these gametes in their union to give rise to fully viable zygotes. These factors may be discovered in intergeneric crosses.