bluuebunny/crossref_metadata_2025 huggingface dataset:
XXV.—Inversion Temperatures, and the Form of the Equation of State.
Authors: Peddie W.
Published: June 2016

1. RECENT experiments by Olszewski on hydrogen (Phil. Mag., May 1902), and on air and nitrogen (Phil. Mag., June 1907), have exhibited results which are not in accordance with theoretical deductions based upon Van der Waal's equation of state (Dewar, Proc. Roy. Soc, March 1904; Porter, Phil. Mag., April 1906; Hamilton Dickson, Phil. Mag., January 1908). An inversion temperature is not necessarily limited by the condition, which was satisfied in the porous-plug experiment of Joule and Kelvin, that the initial and final pressures should be nearly equal. In Olszewski's experiments that condition was widely departed from. Taking account of large differences of pressure, Dickson shows that Van der Waal's equation leads to the result that the inversion temperature must fall when the initial pressure increases, the final pressure being kept constant. Olszewski's experimental results are opposed to this conclusion; and Dickson suggests, as a possible cause of the discrepancy, an appreciable difference between the initial and final values of the kinetic energy. The following reasoning seems to indicate that such a difference would not alter the nature of the theoretical conclusion.
XXX.—On the Theory of the Leaking Microbarograph; and on some Observations made with a Triad of Dines-Shaw Instruments.
Authors: Chrystal
Published: June 2016

THE minor fluctuations of the atmospheric pressure are now engaging the close attention of meteorologists, and my own attention has been drawn to them on account of their connection with the oscillations of lake-surfaces generally known since Forel's investigations under the name of seiches.

As these fluctuations often do not exceed a millimetre or two of water, they are not shown by the ordinary self-registering apparatus. In order to record them we may use a specially sensitive form of barograph, such as the Richard statoscope, which is delicate enough to show these small fluctuations, and yet can be brought back to a momentary zero whenever the indicator threatens to go off the scale or beyond the limits of safety. There are, however, two objections to this method of measurement.
XXXII.—On the Effects on the Metabolism of Chloroform Administered by Different Channels.
Authors: Paton D. Noël
Published: June 2016

DEATH under the administration of chloroform as an anæsthetic is an accident which, although fortunately rare, is well known to all; but the occurrence of a late poisoning, sometimes manifesting itself several days after the administration of the drug, is less well recognised. This too is rare, but its occurrence indicates the very profound effect which such a drug may exercise upon living tissues.

A very large amount of work has been done upon the immediate influence of chloroform upon the nervous system and upon the circulatory and respiratory mechanisms, but few observations on its more lasting effects upon the general metabolism have been recorded.
II.—The Establishment of the Trichromatic Theory of Colour Vision
Authors: Peddie W.
Published: June 2016

The early years of the nineteenth century saw the final establishment, with regard to the ordinary phenomena of light, of the wave theory. And, in those years, the man, Thomas Young (1807), whose work had been mainly effective towards the final acceptance of that theory, put forward a tentative hypothesis regarding the actions and phenomena of colour vision. It stated essentially that these phenomena were explainable most simply on the assumption that all colour sensations that we can experience are due to the existence of three fundamental colour sensations which can be called into play in various proportions by the action of external luminous stimuli falling upon the retina.
V.—Solution in Multiple Series of a Type of Generalised Hypergeometric Equation
Authors: MacRobert T. M.
Published: June 2016

The differential equation

where θ denotes the operator xd/dx has p + 1 solutions valid for | x | < 1.

These may be denoted by

and

where r = 1, 2, …, p, and the asterisk signifies that the expression ρr − ρr + 1 is omitted.
VI.—Investigation of Visual Threshold Values
Authors: Beattie E. M.
Published: June 2016

The main object of the experiments was to obtain an indication of the manner in which fatigue of the eye by exposure to illumination of a given intensity, for various periods of time, affected the response of the eye to a rapidly intermittent illumination of constant strength. Expressed otherwise, the object may be stated to be that of determining the effect of fatigue upon the threshold values as made apparent in the flicker test.
XI.—The Relation between Mathematics and Physics
Authors: Dirac P. A. M.
Published: June 2016

The physicist, in his study of natural phenomena, has two methods of making progress: (1) the method of experiment and observation, and (2) the method of mathematical reasoning. The former is just the collection of selected data; the latter enables one to infer results about experiments that have not been performed. There is no logical reason why the second method should be possible at all, but one has found in practice that it does work and meets with remarkable success. This must be ascribed to some mathematical quality in Nature, a quality which the casual observer of Nature would not suspect, but which nevertheless plays an important rôle in Nature's scheme.
XIII.—Expressions for Generalised Hypergeometric Functions in Multiple Series
Authors: MacRobert T. M.
Published: June 2016

In a recent paper (Proc. Roy. Soc. Edin., vol. lix, 1939, pp. 49–54) expressions in multiple series with argument 1 – z were found for Generalised Hypergeometric Functions of the type

where p > 1. These formulæ are generalisations of known formulæ for the ordinary hypergeometric function F(α, β; ρ; z), and they are established by induction. The same method will be here employed to obtain generalisations of other known formulæ, these generalisations being in the form of multiple series.
XV.—On Non-Associative Combinations
Authors: Etherington I. M. H.
Published: June 2016

Numerous combinatory problems arise in connection with a set of elements subject to a non-associative process of composition—let us say of multiplication—commutative or non-commutative.

Non-associative products may be classified according to their shape. By the shape of a product I mean the manner of association of its factors without regard to their identity. Shapes will be called commutative or non-commutative according to the type of multiplication under consideration. Thus if multiplication is non-commutative, the products (AB.C)D and (BA.C)D are distinct but have the same shape, while D(AB.C) has a different shape. The three expressions, however, have the same commutative shape. I confine attention to products (like these) in which the factors are combined only two at a time.
IV.—Note on a Perforated Silica Plate for excluding Flame Gases from a Crucible during Ignition
Authors: Cumming Alexander Charles
Published: June 2016

The device shown in the accompanying sketch has been in use in the Chemistry Department of the University of Edinburgh for some time. It consists of a silica plate, 5 inches square, with a hole bored in it of such size as to admit a crucible to one-half of its depth. The silica plate is held in an inclined position by a clamp.

By this means the flame gases are excluded from the interior of the crucible during an ignition. With this device calcium carbonate in a platinum crucible is quickly reduced to oxide with a good bunsen burner, while with a Mecker burner the reduction is complete in a few minutes even when a porcelain crucible is used. The device is also useful for cases such as the ignition of nickel oxide, where there is a danger of reduction. For the estimation of sulphur in coal some such device is absolutely necessary to exclude the flame gases.
VII.—The Absorption of Light by Inorganic Salts. No. V.: Copper and the Alkali Metals
Authors: Houstoun R. A.
Published: June 2016

The research described in this article was undertaken with the double purpose of testing new apparatus and of making a rapid survey of the absorption of light by salts of the first periodic group.

The results described in the previous articles were obtained by three separate methods, viz. the thermopile in the infra-red, the spectrophotometer in the visible spectrum, and the photographic spectrophotometer in the ultra-violet. It would be a great simplification if the same apparatus could be used throughout the whole spectrum, and I therefore first of all devoted my attention to seeing if this were practicable.
XIV.—On General Dynamics:—I. Hamilton's Partial Differential Equations and the Determination of their Complete Integrals
Authors: Gray A.
Published: June 2016

The present paper contains the first part of a series of notes on general dynamics which, if it is found worth while, may be continued. In § 1 I have shown how the first Hamiltonian differential equation is led up to in a natural and elementary manner from the canonical equations of motion for the most general case, that in which the time t appears explicitly in the function usually denoted by H. The condition of constancy of energy is therefore not assumed. In § 2 it is proved that the partial derivatives of the complete integral of Hamilton's equation with respect to the constants which enter into the specification of that integral do not vary with the time, so that these derivatives equated to constants are the integral equations of motion of the system.*
XVII.—The Molecular Theory of Magnetism in Solids
Authors: Peddie W.
Published: June 2016

1. It is well known that the molar theory of magnetism, in which the magnetic medium is regarded as being continuous in its ultimate structure and properties, is of very limited applicability to the elucidation of magnetic phenomena. The fact of the impossibility of isolating one kind of magnetism from the other by any process based on inductive action makes evident the essentially molecular nature of magnetism. This was recognised even in the early development of the theory by Poisson, who presumed that the molecules only became magnetic under the action of an external field. Weber recognised the necessity for the ascription of permanence to the magnetic quality of the molecule in order to account for the phenomena of magnetic saturation; and his theory was modified by Maxwell so that it might also include in its range the phenomena of residual magnetisation. In Maxwell's discussion of Weber's theory, we have the first explicit statement of the distinctive feature of the modern theory of molecular magnetism.
XVIII.—On the Torsional Oscillations of Magnesium Wire
Authors: Seaman G. P.
Published: June 2016

It has been shown by numerous experiments (see Proc. Roy. Soc. Edin., 1911) that the equation yn(x + a) = b holds very accurately for wires of different materials, where y = range of oscillation, x = number of oscillations, n, a, and b, constants depending on the metal under the given conditions. In the following experiments a magnesium wire was subjected to various conditions, e.g. extensional strain, torsion, change of temperature, etc., and in each case the above law was tested. The method of procedure was as follows :— A magnesium wire of known dimensions and under ordinary physical conditions was fixed at its upper end to a clamp, and to its lower end was attached centrally a long horizontal heavy cylinder. To the cylinder a circular scale divided into millimetres was attached concentrically with the wire. When the upper end of the wire was turned round the cylinder was made to rotate round the wire as an axis, and the reading on the scale, when the maximum angular deflection was reached, was taken by means of a telescope. Similarly, consecutive maxima were read until the oscillations became small, when the zero was taken, and thus successive values of y were found.
XXI.—Transverse Induction Changes in Demagnetised and Partially Demagnetised Iron in relation to the Molecular Theory of Magnetism
Authors: Russell James
Published: June 2016

In a former communication the æolotropy of iron, demagnetised by the method of decreasing reversals, was shown. During the early stages of induction the permeability is greater to the re-application of a magnetising force in the same direction—whether positive or negative—as that used in the immediately preceding demagnetising process, than to a transverse force. The demagnetisation is complete in the sense that there is no external polarity, and also in the sense that perfect symmetry exists to the subsequent application of the same positive or negative directional field. This symmetry being uni-directional, æolotropy immediately appears if the subsequent magnetising force contains a transverse component.
XXVI.—Comparison of Mr Crawford's Measurements of the Deflection of a Clamped Square Plate with Ritz's Solution
Authors: Knott C. G.
Published: June 2016

When Mr Crawford's paper (see pp. 348–389) was passing through the press, Professor Love drew our attention to a paper by Walther Ritz, whose early death robbed the world of science of one whose brilliancy gave promise of a great future. This paper was published in Crelle's Journal in 1908 under the title, “Ueber eine neue Methode zur Lösung gewisser Variationsprobleme der mathematischen Physik.” In illustration of this new method Ritz showed how to solve, by a series of successive approximations, the problem of the clamped rectangular plate.
XXVIII.—Point Binomials and Multinomials in relation to Mendelian Distributions
Authors: Brownlee John
Published: June 2016

The subject of this paper is a consideration of the mathematics of some of the problems given by present-day developments of Mendelism. Breeding formulas are becoming more and more complex, and it seems probable that many others are yet more complex. Without a suitable mathematical analysis it will be nearly impossible to analyse some of these by direct experiment, while a suitable analysis must always render the method of experimental attack much less obscure. Some of the formulas in the present paper were calculated when I read my last paper* on this subject to this Society, but most of the developments seemed too remote from actual experimental work to render their publication useful. However, a paper published in the last number of the Journal of Genetics, by H. M. Leake, concerning the hybridisation of the cotton plant suggests that the time has come when they may prove of practical value.
XXIX.—On Novel Illustrations of Gyrostatic Action
Authors: Gray James G.
Published: June 2016

In this paper are described some new spinning-tops, gyrostatic apparatus, and illustrations of gyrostatic action devised by the author in the course of the last nine months. The apparatus has been built in the workshops of the Natural Philosophy Institute of the University of Glasgow, and has been employed in illustrating the lectures on rotational motion delivered in the Natural Philosophy classes in the course of the session just closed.

Fig. 1 shows a model aeroplane fitted with a small gyrostat in the position of the propeller. The gyrostat is therefore fixed on the front of the aeroplane with the plane of its flywheel at right angles to the length of the machine. The flywheel of the gyrostat, so fitted, represents exactly the rotor of the engine and the propeller of an actual aeroplane.
I.—Opening Address by the President
Authors: Geikie James
Published: June 2016

Gentlemen,—For the high honour you have done me in electing me to the Presidency of this, the premier scientific Society of Scotland, I offer you my grateful thanks. I am proud indeed that you should have deemed me not unworthy to succeed the eminent men who have heretofore occupied this chair. My complacency, however, is tempered, if not subdued, by the consciousness of my own limitations. But if I cannot, like my predecessors, add lustre to the office I hold, I can at least endeavour to devote all my energies to the performance of its duties.
III.—Note on a Siliceous Sponge of the Order Hexactinellida from South Shetland
Authors: Turner William
Published: June 2016

The specimen was presented to me by Mr G. Millen Coughtrey, who obtained it in Admiralty Bay, South Shetland, lat. 62° S., and long. 58° W., in 1912. It was procured in about 20 fathoms, and was brought to the surface when the ship's anchor was weighed. It consisted of white, delicate, thread-like spicules collected into two tufts or bundles. At the first glance the threads might easily have been mistaken for white hair, but they would not burn; neither were they calcareous, for they were not acted on by mineral acids. From their vitreous appearance they were obviously siliceous and indeed were not unlike spunglass. Their aspect and composition led me to regard them as belonging to a siliceous sponge, but the body of the sponge was wanting. In its absence one had to rely on the characters of the tufts and spicules in attempting to determine the genus of the sponge.
V.—The Theory of Bigradients from 1859 to 1880
Authors: Muir Thomas
Published: June 2016

My last communication in reference to the history of bigradients (Proc. Roy. Soc. Edin., XXX. pp. 396–406) brought the record up to the year 1859. The present paper continues it to the year 1880.
VII.—The Axial Inclination of Curves of Thermoelectric Force: a Case from the Thermoelectrics of Strained Wires
Authors: McWhan John
Published: June 2016

In a communication to the Royal Society of Edinburgh, Mr J. D. Hamilton Dickson has examined with great care the valuable results of Professors Dewar and Fleming on the thermoelectromotive forces of various couples, and has come to the conclusion that the curve representing the thermo E.M.F. is in every case a parabola whose axis is, not vertical as had always been assumed, but inclined a definite though very small angle to the E.M.F.-axis.

This remarkable result has led me to go back to some experiments which I made a few years ago on the thermoelectric properties of longitudinally strained metal wires, to see if by any chance the same phenomenon might be detected there, and in one instance (only) I have been able to establish its existence unmistakably. The experiments in question, which I have described elsewhere,† were made on couples consisting each entirely of one and the same pure metal; but one wire of the couple might be subjected to any desired longitudinal tension while the other remained unstrained. The temperatures of the junctions were the same in all the experiments, one junction being steam-heated, the other water-cooled.
XIV.—Notes on the Atmospheric Electrical Potential Gradient in the Industrial Districts around Leeds
Authors: Steuart W. , Jörgensen Ingvar
Published: June 2016

The general effect of products of combustion would be to cause a transformation of the small ions of the air into large ions, which, acting alone, would tend to decrease the air conductivity. Ionisation by flames, however, adds to the number of ions in the air, so that the size of the ions might be increased without the conductivity of the air diminishing. In the case of the fresh smoke direct from the forge or colliery chimneystalks or railway engines of our experiments, it is suggested that combustion in the furnaces would result in an ionisation producing more positive than negative ions. It is only where similar conditions obtain that we should expect such large increases in the positive potential Gradient, due to smoke, as we have recorded.
IV.—Studies in Clocks and Time-keeping: No. 6. The Arc Equation
Authors: Sampson R. A.
Published: June 2016

The isochronism of a pendulum is only true to a first approximation. If we make the arc large, the period increases, reaching infinity just before the pendulum makes complete circuits. Assuming the full value of the Circular Error, the actual calculation is given in No. 2 of this series (Proc. Roy. Soc. Edin., vol. xxxviii, 1918, p. 169) for the first few degrees, where it is seen that even with variations that may occur in practice, the change of daily rate may easily amount to several seconds. The defect was recognized before regulation of pressure and temperature were considered feasible, as early, for instance, as in 1673, when Huygens published his Horologium Oscillatorium. In fact Huygens invented the cycloid to prevent it, and gave an ingenious device to make the pendulum describe true cycloids—a device that has been given up for various reasons, among others, that it involves disturbance of the pendulum which it is very desirable to avoid.
V.—Microphthalmia and Other Eye-defects throughout Fourteen Generations of Albino Rats
Authors: Hain A. M.
Published: June 2016

The albino rats used in this study were obtained originally from the Wistar Institute of Philadelphia and belong to a strain in which microphthalmia was first observed by Dr Helen Dean King in the F4 generation extracted from a cross between an albino female of this stock and a wild grey Norway male. The defect occurred only in the “S” strain which formed a small proportion of the main stock. Its inheritance was observed by King (1931) through eleven generations, and 538 rats having either both or a single eye microphthalmic were obtained in a strain comprising 1884 individuals. The greater frequency of microphthalmia in the American stock is a marked feature, since only 154 rats with eye defects have been observed in the Edinburgh branch of Wistar rats in fourteen generations comprising over 5000 rats, and this total includes animals with eyes of normal size but possessing defects such as aniridia, cataract, etc., and also rare cases of anophthalmia and buthalmos. It is probable that 80 per cent, of the total affected were microphthalmics, and apparently the defect was generally more pronounced than in the parent stock, that is if the rat illustrated in King's monograph is to be taken as typical. According to King, the eye-defect could easily be detected at birth, “since a small eye did not protrude from the socket.” In the total given here no still-borns are included, as it was found that this method of diagnosis, as also the opacity of the lens in such rats immediately or soon after birth, were unreliable criteria of abnormality. We are in agreement that prenatal mortality did not play an important role in determining the ratio of normal to abnormal individuals, because litters containing affected were of the average litter size and generally contained some normals (Table I). However, where a large number of still-born rats occurred in litters containing defectives, it is possible that the abnormality involved proved lethal, since still-births are not of common occurrence in this stock (Table II).
X.—The Revised Complete System of a Quadratic Complex
Authors: Turnbull H. W.
Published: June 2016

This is a direct continuation of an earlier communication by the author, on “The Revised Prepared System of the Quadratic Complex,” which appeared in vol. lvi (1936) of the Society's Proceedings, pp. 38–49. It will be convenient to utilize the same notation and references to earlier works I, II and III as before, with IV to denote the 1936 paper. A complete system of concomitants for a quadratic complex is here worked out; omitting polar forms, it consists of 210 forms. The sign ≡ in a relation A ≡ B is here used to mean “may be replaced by”: thus A is equal to a non-zero numerical multiple of B plus reducible terms.
XIV.—The Genetical and Mechanical Properties of Sex Chromosomes. III. Man
Authors: Koller P. C.
Published: June 2016

In the male chromosome complement of man, Painter (1923) found that one chromosome pair is heteromorphic and forms an asymmetrical or unequal bivalent during meiotic metaphase, and consequently two kinds of gametes are produced. One member of this heteromorphic pair is about three times longer than the other and is designated the X, the other is described as the Y chromosome. Though the sex chromosomes of man were carefully studied and identified with certainty throughout the nuclear cycle of mitosis and meiosis by several investigators (cf. Shiwago and Andres, 1932), no further attempt was made to correlate the peculiar pairing properties of the heteromorphic chromosomes with their qualitative and structural differentiation.
XV.—Quantitative Evolution. II. Compositæ Dp-ages in Relation to Time
Authors: Small James
Published: June 2016

The ages of the various tribes and sub-tribes of Compositæ have been calculated in doubling periods, according to Yule's formulæ; these are known briefly as Dp-ages (Small and Johnston, 1937; Udny Yule, 1924). Yule advises caution in interpreting Dp-ages in terms of geological time, but if his conceptions are to be applied to realities there should be some method of comparing Dp-ages with actual ages. Further, in the case of Compositæ, an almost complete parallel seriation has been found for Dp-ages and order of origin of both tribes and sub-tribes (Small and Johnston, 1937). Since the order of origin has been provisionally correlated with geological time (Small, 1919) it is possible to compare the calculated Dp-ages with suggested points of origin in geological time. This has been done by Small and Johnston (1937, Tables, VI, VII).
XVI.—Quantitative Evolution. III. Dp-ages of Gramineæ
Authors: Small James
Published: June 2016

Applying Udny Yule's formulæ (1924) to the Compositæ, Small (1937) found that the average ages in doubling periods (Dp-ages) of the tribes of Compositæ, when plotted against a time-scale, gave points on an exponential curve called the BAT curve. If this curve is characteristic of average families of Angiosperms it should be possible to place the Dp-ages of tribes within other families on this curve as plotted against geological time, and thus obtain an order of geological origin which is quite independent of actual fossil records and which can be checked against any facts known concerning the evolutionary history of the family.
XVII.—Tests for Randomness in a Series of Numerical Observations
Authors: Kermack W. O. , McKendrick A. G.
Published: June 2016

It is often a matter of considerable importance to decide whether the fluctuations exhibited by a series of observations are random in character, or whether some factor operating according to a definite law must be assumed to exist. One general method of testing a statistical hypothesis is to work out results which would be expected theoretically, and then to compare these with the observations. A statistic such as the mean or standard deviation to be observed on a particular hypothesis may be calculated and compared with the actual mean or standard deviation as evaluated from the observed figures. Agreement does not necessarily imply that the hypothesis is a true one, or even that it is consistent with the observations, because it might be found that when another statistic was calculated, the agreement was no longer satisfactory. Obviously the greater the number of tests applied and found satisfactory, the greater the confidence which can be placed in the conclusions.
XVIII.—The Benthic Amphipoda of the North-Western North Sea and Adjacent Waters
Authors: Raitt D. S.
Published: June 2016

The order Amphipoda, of the Crustacea Malacostraca, which consists of the 3 sub-orders Hyperiidea, Gammaridea, and Caprellidea, is highly important in the economics of the sea as a source of fish food. Hyperiids figure prominently in the diet of species which feed pelagically. Hardy (1924), for example, found them amongst the principal items in the food of East Anglian herring. Gammarids are preyed upon by bottom feeders in general. Todd (1905, 1907) and Blegvad (1916) record them in varying percentages from the stomachs of adult cod, haddock, whiting, plaice, dabs, flounders, sole, and skate. Their chief importance, however, would seem to be in the diet of fishes in post-larval and adolescent stages. Todd (1907, 1914) found Gammarids the main support of cod under 15 cm. and of plaice and dabs under 10 cm. Blegvad (1930) states that in Danish waters, plaice in their first year feed almost exclusively upon them. Clark (1922) found that in the early stages of 4 species of skate, Amphipods occurred in from 50 to 84 per cent of the stomachs examined, and Steven (1930) found the food of young stages of R. clavata and R. maculata to consist chiefly of Gammaridea. Gammarid species, as recorded by Hunt (1924), are also eaten by a variety of bottom-dwelling invertebrates.
III.—The Invariant Theory of the Correlation
Authors: Turnbull H. W.
Published: June 2016

Beyond the ternary and quaternary cases considered by Clebsch (1891) and Weitzenböck (1910), there appears to be no writing on the bilinear form in cogredient variables—the correlation—from the point of view of the projective invariant theory. In the present work a complete system of concomitants is found for the single bilinear ground form. Incidentally it is shown that such a system belongs not to the single form but to the simultaneous system of two mutually conjugate forms. Symbolic methods are used, and the processes are analogous to those employed in the cases of two quadratic forms (Turnbull and Williamson, 1929), and also of one bilinear form (Turnbull, 1932) in contragredient variables. In contrast with these previous results it is remarkable that the present system involves no forms of weight greater than two (§ 3, § 6).
VIII.—Some Series and Integrals involving Associated Legendre Functions, regarded as Functions of their Degrees
Authors: MacRobert T. M.
Published: June 2016

§ 1. Introductory—In a former paper (Proc. Roy. Soc. Edin., vol. liv, 1934, pp. 135–144) the author discussed the evaluation of a number of integrals of Associated Legendre Functions, regarded as functions of their degrees. The methods employed depended mainly on contour integration, and most of the integrals were evaluated in terms of infinite series of Associated Legendre Functions. In the present paper the methods employed are of a more elementary character, depending mainly on the use of Dirichlet Integrals; the results obtained are more general; and the integrals and the corresponding series are evaluated in simpler forms. The same notation is employed as in the previous paper. The Mehler-Dirichlet Integral

where o < θ < π, μ > – ½, is used throughout.
XII.—The Experimental Analysis of the Growth of an Insect Population
Authors: MacLagan D. Stewart , Dunn Edward
Published: June 2016

Human populations have afforded favourite material for analysis by statisticians, and others, interested in mathematical theories of population-growth. Experimentally, however, human beings are not ideal biological material, so that other animals, such as protozoa, insects, and mammals, have been used. On account of their great reproductive capacity, rapid response to changes in their environment, and ease of handling in the laboratory, certain insects are very suitable for this type of work. The enormous reproductive capacity of insects has been the subject of comment by many biologists, but we are still comparatively ignorant of the exact rôle of the various factors involved in the limitation of their numbers.
I.—The Lunar Atmospheric Tide at Glasgow
Authors: Chapman S.
Published: June 2016

I. On seeing inNature(June 29, 1935) a summary of the paper “The Lunar Atmospheric Pressure Inequalities at Glasgow,” recently published in theseProceedingsby 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.
II.—The Effect of Present Trends in Fertility and Mortality upon the Future Population of Scotland and upon its Age Composition
Authors: Charles Enid
Published: June 2016

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.
III.—Studies in Clocks and Time-keeping: No. 5. The Suspended Chronometer
Authors: Sampson R. A.
Published: June 2016

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.
V.—The Revised Prepared System of the Quadratic Complex
Authors: Turnbull H. W.
Published: June 2016

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.
VII.—Fossil Pollen in Scottish Tertiary Coals
Authors: Simpson J. B.
Published: June 2016

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.
XIV.—Genetical and Cytological Studies of the Intergeneric Hybrid ofCairina moschataandAnas platyrhyncha platyrhyncha
Authors: Crew F. A. E. , Koller P. C.
Published: June 2016

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.
IV.—On Properties of Null Geodesics, and their Application to the Theory of Radiation
Authors: Kermack W. O. , McCrea W. H. , Whittaker E. T.
Published: June 2016

In a previous paper an expression was given by one of us for the Doppler effect in a de Sitter universe. In the present communication an attempt is made to obtain a more general expression for the Doppler effect, and for this purpose certain results have been derived relating to the properties of null geodesics in a general Riemannian space. In the paper referred to, the problem of defining spatial distance in general space was discussed and certain formulæ suggested which satisfy the essential conditions associated with the idea of spatial distance. This problem has now been approached from a different standpoint, and a new formula of more general form is now put forward. In the final section of the present paper a physical interpretation is given of the theorem relating to null geodesics which is proved in the first section. This involves a discussion of the concept of energy in general relativity, in order that a decision may be arrived at as to what law governs the transference of energy by radiation from one point to another. It appears that when the simplest and most natural assumptions are made for this purpose, then these are precisely the assumptions which are necessary to ensure the general consistency of relativity with the principles of quantum theory. This is illustrated by an application to a statical universe, and to the reddening of light in an expanding universe.
XIII.—The Formation of Rock Joints and the Cleat of Coal
Authors: Kendall P. F. , Briggs Henry
Published: June 2016

The occurrence in coal seams of planes of division, generally approximately at right angles to the stratification, has been known for centuries. Owing to the important part these planes play in the lay-out of workings, miners have found it necessary carefully to pay heed to their direction and character. They long ago observed, for example, that, in the majority of seams, there are main divisions or “cleats” and secondary divisions or “cross-cleats,” and that these systems intersect at an angle of generally 80 to 90 degrees. It was also seen that cleats are always best developed in the bright parts of bituminous coal, and that they are less distinct, more widely spaced, or even non-apparent in durain and in cannel. When the dull and bright parts are finely laminated, however, the cleat planes pass through the mass without interruption. Sparry inclusions (ankerites) are very common in the cleats of bright coal and equally rare in dull coal; occasionally the inclusions extend a little way into the roof, and then the existence of associated cleat in the roof is particularly easy to detect.
XIX.—The Diffusion Coefficients of Bromine-Argon, Bromine-Methane, Bromine-Hydrogen Chloride, Bromine-Nitrous Oxide
Authors: Mackenzie John E. , Melville Harry W.
Published: June 2016

In a previous communication (Proc. Roy. Soc. Edin., vol. lii, 1932, p. 337) a visual method of measuring the diffusion coefficients of Br2 : H2, Br2 : N2, Br2 : O2, and Br2 : CO2 was described. The investigation has been extended to include similar measurements for bromine diffusing into argon, nitrous oxide, methane, and hydrogen chloride. Preliminary experiments in which a photoelectric cell replaces the human eye have also been made and confirmatory results have been obtained.
XXI.—Geology and Petrology of the Dolerites of Spitsbergen
Authors: Tyrrell G. W. , Sandford K. S.
Published: June 2016

Within the group of islands which together comprise Spitsbergen outcrops of dolerite may be traced over an area of about 50,000 square miles. The area is doubled if the neighbouring dolerites and basalts of Franz Josef Land are included. Even so, this is but a part of a network widely spread over the north-western part of the Euro-Asiatic continental platform, and over adjoining circumpolar lands. The sill-swarms of Spitsbergen alone rival in extent any of approximately similar age in other parts of the world, such as those of South Africa, South America, India, Antarctica, or North Britain. They merit a great deal more attention than it has yet been possible for geologists to devote to them.
XXIII.—The Mathematical Representation of the Energy Levels of the Secondary Spectrum of Hydrogen
Authors: Sandeman Ian
Published: June 2016

I. Term Representation of Diatomic Spectra.

The mathematical symbolism now employed by the practical spectroscopist for the representation of the energy term F(J) of the diatomic molecule has recently been fixed with precision as a result of the labours of Mulliken and others. The formula employed to represent the rotational term is

where J is the quantum number and Be, De, … are constants. BeJ(J + 1) is the kinetic energy, expressed in wave-numbers, which the molecule would have if it were a rigid rotator; and the remaining small correction terms in powers of J(J + 1) correspond to the expansion of the rotator under centrifugal force.
II.—On Fitting Polynomials to Data with Weighted and Correlated Errors
Authors: Aitken A. C.
Published: June 2016

This paper concludes the study of fitting polynomials by Least Squares, treated in two previous papers. The problem being concerned with the minimum of a positive definite quadratic form, it makes for conciseness to use matrix notation. We shall therefore adopt the following conventions :—

The n values of the variable x, of the data u0, u1, …, un−1, of certain polynomials qr(x) entering into the solution, and so on, will be regarded compositely as vectors. They will be imagined as having their components or elements disposed in column array, but when written in full will be written horizontally, to save space, enclosed by curled brackets. Row vectors, when written out in full, will be enclosed by square brackets. In the shorter notation we shall write, for example, u, x for column vectors, u′, x′ for the row vectors obtained by transposition. The vectors occurring in the problem will be the following:—
VII.—Spermatogenesis inDrosophila pseudo-obscuraFrolowa. II. The Cytological Basis of Sterility in Hybrid Males of Races A and B
Authors: Koller P. Ch.
Published: June 2016

Two races or physiological species (A and B) were found inDrosophila pseudo-obscuraby Lancefield (1922), who described later (1925, 1929) the genetical behaviour of the interracial hybrids. The present writer (1931, 1932,a, b) has reported further investigations concerning the sterility of the male and the regional reduction of crossing-over in the female of the interracial hybrids. The results obtained suggested that there are genetic fertility factors, located in the sex chromosome complex, which are primarily responsible for the sterility of the F1males. A similar conclusion has been reached more recently by Dobzhansky (1933b) from his cytological studies of hybrid males.
XIII.—Some Integrals, with respect to their Degrees, of Associated Legendre Functions
Authors: MacRobert T. M.
Published: June 2016

Little is known regarding the integration of Legendre Functions with respect to their degrees. In this paper several such integrals are evaluated, three different methods being employed. In § 2 proofs are given of a number of formulae which are required later. In § 3 an example is given of the evaluation of an integral by contour integration. The following section contains the proof of a formula of the Fourier Integral type, a special case of which was given in a previous paper (Proc. Roy. Soc. Edin., vol. li, 1931, p. 123). In § 5 an integral is evaluated by employing Fourier's Integral Theorem; while in § 6 other integrals are evaluated by. means of expansions in series.
XV.—The Structure and Relationships of Lamellibranchs possessing a Cruciform Muscle
Authors: Graham Alastair
Published: June 2016

In the first decade of the present century Bloomer reported in a series of concise papers (for which see the list of references) the results of his investigations into the structure of the majority of the lamellibranchs which were then classified in the family Solenidæ. In addition to a general description of the external anatomy of these bivalves he paid especial attention to the details of the musculature, to the course of the alimentary canal and the structure of the stomach, while he gave rather generalised accounts of the nervous system and of the arrangement of the circulation, in which he almost entirely followed the previous work of Ménégaux (1890). Bloomer made little attempt to view as a whole the information which had been gathered together as a result of these years of work; the only papers which he published that can be regarded as dealing with his results from a general standpoint being a short one (1903b) on the classification of the British species of the genus Solen, and a second (1903c), equally brief, on the origin and function of the small fourth pallial aperture which is a marked feature of the anatomy of certain members of the family. This he proved to be a separated portion of the pedal gape, not homologous with the similar structure lying in a more posterior position in some of the Anatinacea and in Lutraria.
The Theory of Continuants in the Historical Order of Development up to 1880
Authors: Muir Thomas
Published: June 2016

The first of the writings dealt with in the present communication is of a considerably earlier date than the others: its proper place is immediately in front of Sylvester's paper of the same year. The account of it here given should therefore he found between pages 140 and 141 of this volume of the Proceedings.
A Report on the Medusæ found in the Firth of Clyde (1901–1902)
Authors: Browne Edward T.
Published: June 2016

Records relating to the occurrence of medusæ in the Firth of Clyde have not been numerous, though its waters have long been a noted resort for marine naturalists. Forbes, in his Monograph on the British Naked-eyed Medusæ, states that he paid special attention to the medusæ of the Clyde, and that those which he collected while on a yachting cruise in the autumn of 1839 were the foundation of his well-known monograph. Amongst those who have made additions to the list of species I may mention the names of Landsborough, Alder, Allman, Herdman, and two well-known foreigners, Claparède and Haeckel. In June 1902 Dr Clemens Hartlaub, of Heligoland, made a short stay at the Millport Biological Laboratory, solely for the purpose of collecting medusæ, but the complete results of his labours have not yet been published.
On the Action of Radium Bromide on the Electromotive Phenomena of the Eyeball of the Frog
Authors: M‘Kendrick John G. , Colquhoun Walter
Published: June 2016

It has been known for the last thirty-four years that when the fresh excised eyeball of a frog is connected by non-polarizable electrodes with a sensitive galvanometer, an electrical current (travelling through the eye from the retina to the cornea) may be detected, and that variations occur in this current, due solely to the action of light on the retina.

It is also well known that salts of radium are luminous in the dark, and that if a tube containing radium† is pressed against the closed lid of the eyeball, or even pressed against the temple, one has the consciousness of luminosity. This being so, it was of interest to ascertain whether this luminosity was due to the radium causing fluorescence of any of the structures of the eyeball, or whether it was due to the direct action of one or other of the emanations of radium on the retina itself.