bluuebunny/crossref_metadata_2025 huggingface dataset:
Note on Some of the Magnetic Properties of Demagnetised and Annealed Iron
Authors: Russell James
Published: June 2016

In a paper laid before this Society in July 1902, the magnetic æolotropy of iron demagnetised by decreasing reversals of co-directional and transverse magnetising forces, and also of iron left transversely magnetised, was established. In later communications (July 1903 and July 1904) it has further been shown that iron and nickel demagnetised by decreasing reversals of a directional force, develop an induction component at right angles to the subsequent magnetising force, which tends to disappear as saturation values are reached, when the angle between these two forces is other than 0° and 90°. In annealed iron this property is absent.
Les Concrétions phosphatées de l'Agulhas Bank (Cape of Good Hope)
Authors: Collet Léon W. , Lee Gabriel W.
Published: June 2016

L'hiver passé je reçus une invitation de Sir John Murray à venir, en qualité d'assistant, au Challenger Office étudier sous sa direction une nombreuse collection de concrétions phosphatées et nodules provenant de dépôts dragués par les bateaux du “Department of Agriculture” du Cap de Bonne Espérance et envoyée par Dr J. D. F. Gilchrist, “Government Biologist of the Cape of Good Hope.”
A Comparative Study of the dominant Phanerogamic and Higher Cryptogamic Flora of Aquatic Habit, in Three Lake Areas of Scotland
Authors: West George
Published: June 2016

In this contribution an account is given of the dominant plants of aquatic and semi-aquatic habit existing in and about the lakes of the following districts of Scotland:—

1. The Loch Ness area.

2. The lakes in the Island of Lismore, Argyll.

3. Lakes situated between Nairn and the Culbin Sand Hills.
Note on a Problem of Elimination connected with Glissettes of an Ellipse or Hyperbola
Authors: Muir Thomas
Published: June 2016

The problem occurs in a paper of Professor Tait's (“Glissettes of an Ellipse and of a Hyperbola,” Proc. Roy. Soc. Edin., xvii. pp. 2–4). An ellipse whose semi-axes are a and b is considered as moving so as always to be in contact with both axes of coordinates, and the glissette in question is the curve traced out during this motion by a point whose coordinates with respect to the axes of the ellipse are p and q. Professor Tait states, and it is readily seen, that if the current coordinates of the point be x and y, and θ be the variable angle made by one of the axes of the ellipse with the axis of x, we have the equations

and that to obtain the x-and-y equation of the glissette it remains to eliminate θ between these two equations.
Note on Certain Remarkable Volume Effects of Magnetisation
Authors: Knott Cargill G. , Shand A.
Published: June 2016

In June of last year one of us gave before the Society a short account of certain preliminary experiments on the volume effects of magnetisation. These experiments had been made in Japan; and the results obtained evidently called for a more thorough investigation. The facilities of the Physical Laboratory of Edinburgh University were kindly placed at our disposal by Professor Tait. Five tubes of Swedish iron, all cut from the same original bar but made with different bores, were prepared for study in much the same manner as formerly. Many experimental difficulties encountered us; and only now have these been satisfactorily overcome. For it must be remembered that the effect to be observed is very minute, and can be measured only in one way, viz., by the motion of the meniscus along the narrow capillary tube which is in connection with the iron tube, the whole being filled with fluid. But such an arrangement is obviously a very delicate thermometer; and, as a matter of fact, we have seldom got the meniscus really steady. Generally it is moving at a rate which, though as inappreciable to the naked eye as the motion of an hour hand, is only too evident under the microscopic power necessary for the observation of the magnetic effect.
On the Eliminant of the Equations of the Ellipse-Glissette
Authors: M‘Laren Hon. Lord
Published: June 2016

The problem consists in the elimination of θ from two equations which (after expressing cos2θ in terms of sin2θ) may be written

As only two of the equations can be used, the elimination will be effected by means of (2) and (3), using the relation cos2θ + sin2θ = 1, where necessary, to suppress the term of cos2.
On a Crystalline Globulin occurring in Human Urine
Authors: Paton D. Noël
Published: June 2016

In October 1890, Dr Bramwell sent to the Laboratory a small quantity of urine, with a request that I should give him a report upon it. To him I am indebted for the opportunity of making the series of observations here recorded.

On examination, I found that the amount of proteid was enormous, and that it was made up almost entirely of a globulin :—

This condition of the urine persisted, with only slight changes, until the death of the patient.
Note on the Division of Space into Infinitesimal Cubes
Authors: Tait
Published: June 2016

The proposition that “the only series of surfaces which, together, divide space into cubes are planes and their electric images” presented itself to me twenty years ago, in the course of a quaternion investigation of a class of Orthogonal Isothermal Surfaces (Trans. R.S.E., Jan. 1872). I gave a second version of my investigation in vol. ix., p. 527, of our Proceedings. Prof. Cayley has since referred me to Note vi., appended by Liouville to his edition of Monge's Application de l'Analyse á, la Géométrie (1850), in which the proposition occurs, probably for the first time. The proof which is there given is very circuitous; occupying some eight quarto pages of small type, although the reader is referred to a Memoir by Lamé for the justification of some of the steps. But Liouville concludes by saying :—“l'analyse précédente qui établit ce fait important 'est pas indigne, ce me semble, de l'attention des géométres.” He had previously stated that he had obtained the result “en profitant d'une sorte de hasard.” As Liouville attached so much importance to the theorem, and specially to his proof of it, it may not be uninteresting if I give other modes of investigation.
On a Certain Locus
Authors: Schoute P. H.
Published: June 2016

If the two ends of a strip of paper are pasted on one another after having twisted one of them through 180°, we obtain a surface with only one side. On the last meeting of the British Association Professor A. Crum Brown showed a model of a mathematical surface closely connected with it. This surface, with the common name of “marrowbone,” is the locus of the line AB (fig. 1), cutting a given circle C orthogonally and moving under the condition ∠ AOD = 2 ∠ BAE.
Recent Innovations in Vector Theory
Authors: Knott C. G.
Published: June 2016

(1.) Of late years there has arisen a clique of vector analysts who refuse to admit the quaternion to the glorious company of vectors. Their high-priest is Professor Willard Gibbs. His reasons against the quaternion are given with tolerable fulness in Nature, April 2, 1891. His own vector analysis is presented in a pamphlet, “Elements of Vector Analysis, Arranged for the Use of Students in Physics—not Published” (1881–4). Mr Oliver Heaviside, in a series of papers published recently in the Electrician, and in an elaborate memoir in the Philosophical Transactions (1892), supports some of Gibbs's contentions, and cannot say hard enough things about the quaternion as a quantity which no physicist wants. Professor Macfarlane of Texas University sides with Heaviside in taking umbrage at a most fundamental principle of quaternions, and develops a pseudo-quaternionic system of vector algebra non-associative in its products.
Synthesis by Means of Electrolysis
Authors: Brown Crum , Walker James
Published: June 2016

Synthesis of Tetramethylsuccinic Acid.–Ethyl-potassium dimethylmalonate cannot be prepared from dimethylmalonic ether by following precisely the method which succeeded in all previous cases. When the ether is mixed, either at once or slowly, with the calculated quantity of caustic potash in alcoholic solution, half of the ether is completely saponified, while the other half is unacted on, only an insignificant fraction being half-saponified and converted into the ethyl-potassium salt. A good yield of the latter was, however, obtained by a modification of the process, the special points of which were great dilution with alcohol and low temperature
On the Particles in Fogs and Clouds
Authors: Aitken John
Published: June 2016

At the beginning of the paper some observations made on the water particles in clouds on the Rigi on the 21st of May last are described. Previous observations with the fog-particle counter had shown that there is a relation between the density of a cloud and the number of water particles observed. On the occasion above referred to the number was very much greater than corresponded with the density. It is pointed out that the number of dust particles in the air which become centres of condensation depends on the rate at which the condensation is taking place, quick condensation causing a large number of particles to become active, slow condensation causing a small number; and that after the condensation has ceased a process of differentiation takes place, the larger particles, robbing the smaller ones of their water, owing to the vapour-pressure at the surface of drops of large curvature being less than at the surface of drops of smaller curvature. The particles in a cloud are by this process reduced in number, those remaining becoming larger and falling quicker, the cloud thus tending to become thinner by the reduction of the number of particles and by the falling of some of them. It is shown that the exceptional readings above referred to, obtained on the Rigi, were owing to the observations then made being taken in a new and rapidly-formed cloud, due to the strong wind blowing at the time causing a quick ascent and rapid cooling and condensation, the result being the formation of a large number of very small water particles. Though the number was very great, the particles were so small they were only just visible with great care with the magnifying power used in the instrument. Previous observations on cloud particles had been made in slowly-formed or in old clouds after the process of differentiation had been in play for some time, and after the drops had been reduced in number and increased in size.
A new Solution of Sylvester's Problem of the Three Ternary Equations
Authors: M'Laren Hon. Lord
Published: June 2016

The solution is effected by the method of Symmetric Functions.

By a preliminary transformation * the equations of the original system are put into the form
I.—The Influence of an Excessive Meat Diet on the Osseous System
Authors: Watson Chalmers
Published: June 2016

In a communication given to this Society in December 1905, I described the clinical results obtained in an experimental investigation on the influence of an excessive meat diet on the growth and nutrition of rats. It was there shown that the progeny of meat-fed rats are usually poorly developed and show a high mortality in early life. The present record comprises an account of the naked-eye and microscopic appearances observed in the osseous system of these meat-fed subjects.
II.—The Effect of a Meat Diet on Fertility and Lactation
Authors: Waston B. P.
Published: June 2016

In a paper on “The Influence of Diet on Growth and Nutrition,” in the Journal of Physiology (vol. xxxiv., p. iii), Dr Chalmers Watson showed that in rats a diet of ox-flesh begun when the animals were weaned interfered with the development of pregnancy, none of the four flesh-fed animals having young, whereas the control animals from the same litter all became pregnant.
IV.—The Temperature of the Fresh-water Lochs of Scotland, with special reference to Loch Ness
Authors: Wedderburn E. M.
Published: June 2016

The communication of which this is an abstract has been published in the Society's Transactions (Vol. XLV. Part II. No. 16), with an appendix containing observations made in Loch Ness by members of the Scottish Lake Survey and of the Order of Saint Benedict at Fort Augustus.
X.—The Functions of the Rolandic Cortex in Monkeys
Authors: Jolly W.A. , Simpson Sutherland
Published: June 2016

The Rolandic cortex is discussed in the following paper, and an account is given of experiments on monkeys, performed with the object of mapping out this region more accurately and of delimiting in it the areas concerned with movements of different parts of the body. The method employed is a new one, and will be described in detail.
XII.—Heusler's Magnetic Alloy
Authors: Ross Alexander D.
Published: June 2016

Since the discovery by Heusler in 1903 of a magnetic alloy of copper, manganese, and aluminium, considerable interest has been aroused by the peculiarities of its properties and the difficulty of their explanation. In the summer of 1905 a preliminary investigation of a sample of the alloy was made in the Physical Laboratory of Glasgow University, and the results obtained have been published in a paper by Professor A. Gray.
XVIII.—The Physical Properties of Mixed Solutions of Independent Optically - Active Substances
Authors: Ranken Clerk , Taylor W. W.
Published: June 2016

The two systems containing one of a pair of optically-active stereoisomers and an independent optically-active substance present many points of interest and importance, but have not hitherto been investigated with any degree of completeness. What is known about them may fairly be said to consist of a series of isolated facts. The present communication also contributes a few more isolated observations, and is, in reality, a preliminary to a more systematic examination of the whole subject.
XX.—On the Partition of Heat Energy in the Molecules of Gases
Authors: Ehrenfest Paul
Published: June 2016

In a paper published some time since, Mr Peddie takes up the following question: Given a gas whose molecules contain atoms which are held together by purely elastic forces, do there exist, even in this simplest type of multiply-atomic molecules, cases in which, when there is equilibrium of heat, the average equipartition of kinetic energy demanded by the Boltzmann-Maxwell Law does not exist?
XXVIII.—A Preliminary Note on the Optical Rotations (throughout the Spectrum), the Electrical Conductivities, and the Densities of Mixtures of Sodium-Potassium-Tartarate and Ammonium-Molybdate in Aqueous Solution
Authors: Milne James Robert
Published: June 2016

It has long been known that the rotative power of certain optically active salts in aqueous solution is greatly, and in some cases enormously, changed by the addition of certain non-active salts. Of late years a good deal of work has been done on this subject, and a considerable amount of data has been collected; but, generally speaking, little explanation has been obtained of the precise causes of the observed phenomena. In some cases at least the reason for this no doubt lies in the fact that in such solutions there exist complicated molecular combinations, about which it may not be easy to obtain ordinary chemical evidence. This, however, only makes it the more important that we should utilise tothe fullest extent such means of investigation as are readily available, and of these none is so good as that of optical activity.
XXX.—Hydrachnidæ collected by the Lake Survey
Authors: Williamson Wm
Published: June 2016

The systematic study of the Hydrachnidæ, or water-mites, of Scotland appears to have been entirely neglected until within the last few years, and, so far as I am aware, the only communications dealing with Hydrachnids found in Scotland are two noted in the list of literature cited.

Of the life-history of Hydrachnids we have only a limited knowledge, and that may in time be modified as further information is acquired. At present the life-cycle appears to be in four definite stages—the egg, the larva, the nymph, and the imago. When an egg is hatched, a six-legged larva emerges, and apparently its main function is to find a suitable host to which it may attach itself.
XXXIII.—A Sketch of Japanese National Development, more especially with reference to Education
Authors: Kikuchi Baron
Published: June 2016

Fifty years ago, Japan was almost a mythical land to the Western world; what little was known of it was through the medium of the Dutch, who were allowed to trade in the single port of Nagasaki. What we Japanese knew of the outer world was also derived mostly from them, and from such books as were brought into the country by them. In 1853 came Commodore Perry, and demanded that we should open up our country to the commerce of the world; we were but ill prepared for such a course, but it was not in our power to resist the demand, and unwillingly enough the Shōgun's government was obliged, notwithstanding the strong opposition of the Imperial Court and of the conservative elements in the country, to contract a treaty of commerce with America, which was speedily followed by those with other nations.
XXXV.—On the Periods of the Elliptic Functions of Weierstrass
Authors: Innes R. T. A.
Published: June 2016

The elliptic functions introduced by Professor K. Weierstrass of Berlin are best known through the admirable pages of Professor H. A. Schwarz's Formeln und Lehrsätze zum Gebrauche der elliptischen Functionen, Göttingen, 1885. These pages have been translated literally into French by Dr Henri Padé, Paris, 1894. Halphen's well-known three-volumed treatise on elliptic functions is devoted almost entirely to the Weierstrassian forms. In the English language, the following references may be useful:—Whittaker, Modern Analysis; Greenhill, Elliptic Functions; Harkness and Morley, Theory of Functions; Forsyth, Theory of Functions.
II.—The Baleen Whales of the South Atlantic
Authors: Turner William
Published: June 2016

Whaling companies have for some years successfully conducted a whale fishery off the shores of the South Shetlands, Graham Land, South Orkneys, and South Georgia, where the waters of the Antarctic mingle with the South Atlantic Ocean.
IV.—Studies on Periodicity in Plant Growth. Part II: Correlation in Root and Shoot Growth
Authors: Crosse Rosalind
Published: June 2016

Part I of this work on Growth Periodicity (Proc. Roy. Soc. Edin., vol. xxxiii, Part I (No. 8), p. 85) dealt with the occurrence of a four-day periodicity in plant organs and with rhythm in roots. With reference to the latter, the following conclusions were deduced from various observations made up to that time:—

1. “Roots exhibit a periodicity under ordinary conditions of environment which differs from that of shoots.

2. “Owing to correlation, the root periodicity is affected by changes in the root rhythm, but to what extent has yet to be determined.”

Since then, numerous experiments have been performed to find out whether any correlation exists between the growth of the root and the shoot, and if so, the nature of such a correlation.
XVI.—On a Modification of Pelouze's Method for determining Nitrates
Authors: Letts E. A. , Rea Florence W.
Published: June 2016

Pelouze, as early as 1847, employed a method for determining nitrates in the commercial potassium and sodium salts, in which weighed quantities of the latter were boiled with ferrous chloride solution (obtained by treating a definite weight of iron wire with excess of hydrochloric acid), and afterwards the remainder of the ferrous salt was determined by titration of the diluted solution with potassium permanganate.
XIX.—On the Composition of Milk as affected by Increase of the Amount of Calcium Phosphate in the Rations of Cows
Authors: Lauder A. , Fagan T. W.
Published: June 2016

The various factors which are supposed to influence the composition of milk have already been the subject of numerous investigations. The general result of these has been to show that within very wide limits the composition of milk is very little affected by the nature of the food supplied. As regards the mineral constituents the results of some of the investigations are rather conflicting, and while there is a general consensus of opinion that the composition and amount of the mineral constituents are independent of the food-supply, certain investigators claim to have been able to increase both the calcium and phosphoric acid in the milk by slight amounts.
XX.—On a See-Saw of Barometric Pressure, Temperature, and Wind Velocity between the Weddell Sea and the Ross Sea
Authors: Mossman R. C.
Published: June 2016

In the course of a large inquiry on the inter-relations between the meteorological conditions in Antarctica and the Southern Ocean, on the one hand, and those prevailing in the southern continents, more especially South America, on the other, there has come to light an interesting see-saw between the barometric pressure, air temperature, and wind velocity in the Weddell and the Boss Seas. The above inquiry, which I hope to lay before this Society shortly, refers to the eight-year period 1902–09; and since the present paper deals with the years 1902, 1903, 1911, and 1912, I have thought it better to make it the subject of a separate communication. The positions of these stations and others where observations have been made are shown on the accompanying map, for which I am indebted to Dr H. R. Mill. The figures within the rings give the number of years covered by the records at the various places.
XXI.—The Magnetic Quality of Iron and Steel as affected by Transverse Pressure
Authors: Walker Wm. J.
Published: June 2016

It has been thought advisable to place the following qualitative results on record owing mainly to their general interest and to the unavoidable interruption of the experiments.

The experiments were carried out in order to determine the effect of transverse pressure on the magnetic induction in a piece of iron or steel.
XII.—Note on the Sublimation of Sugars
Authors: Ghosh Sudhamoy
Published: June 2016

The literature of the sugars would appear to show that no sugars have hitherto been observed to sublime with the exception of glycolose, CH2OH CHO, which is described as being “perceptibly volatile with water and alcohol vapour under diminished pressure, especially from a pure, concentrated solution” (Lippmann, Chemie der Zuckerarten, p. 4). This substance, being the first of the sugar series, might be expected to have properties somewhat different from the other members of the series, which are usually looked upon as non-volatile. Experiments with rhamnose and fructose appear to show that under diminished pressure they do sublime.
XV.—Preliminary Communication on the Effects of Thyroid-Feeding upon the Pancreas
Authors: Kojima M.
Published: June 2016

In the course of a systematic inquiry, conducted in the Physiology Department of Edinburgh University, into the morphological and physiological changes produced in animals by thyroidectomy and thyroid-feeding—especially in rats—certain striking morphogenetic changes in the pancreas have come under observation. The full results of the investigations of which these observations form a part will be published subsequently, but it has been thought well to bring the effects herein described before the notice of this Society without waiting for the completion of every part of the investigation.
XVI.–On the Theory of Continued-Fractions
Authors: Whittaker E. T.
Published: June 2016

The value of the continued-fraction, as a means of representing an analytic function f(x), is now fully recognised. Other representations, such as power-series or Fourier series or Dirichlet series or series of inverse factorials, converge in general only over limited regions of the x-plane, and fail to converge over the rest of the plane, whereas the representation of the function by a continued-fraction converges (in a large class of cases at any rate) over the whole x-plane, with the exception of certain singular curves.
XVIII.—The Trachytic and Allied Rocks of the Clyde Carboniferous Lava-Plateaus
Authors: Tyrrell G. W.
Published: June 2016

The lavas of the Scottish Carboniferous are predominantly basaltic. True andesites and rhyolites are conspicuous by their absence, whilst trachytes and allied rocks are present in quite subordinate quantity. This association of basalt and trachyte is in accordance with the fact that the basalts have a slight alkaline cast, which is evidenced by an alkali content greater than that of the average basalt, and by the occasional presence of nepheline and analcite amongst their constituents. The transition from basalts to more acid types is accomplished, not by way of the andesites, but through the mugearites, volcanic rocks with chemical affinities to the essexites. All transitions from the more felspathic types of basalts, the Jedburgh and Markle types, can be traced through mugearites to trachytes or allied rocks.
XIX.—On Systems of Partial Differential Equations and the Transformation of Spherical Harmonics
Authors: Bateman H.
Published: June 2016

§1. It is well known that Laplace's equation ∇2V = 0 possesses certain classes of solutions of the form V = F(X, Y) where F satisfies a partial differential equation with X and Y as independent variables and X and Y are real functions of x, y, and z. Such solutions have been called binary potentials. They are of some interest in the problem of finding cases in which the equations of motion of an electron in a steady magnetic field are readily integrable. There are also classes of solutions of the same type, except that X and Y are complex quantities and the coefficients in the partial differential equation for F may also be complex. In particular, there are solutions of the form V = Yƒ(X) where ƒ is an arbitrary function with continuous second derivative.
III.—Researches in Optical Activity. Part I: The Temperature-Rotation Curves for the Tartrates at Low Temperatures
Authors: Patterson T. S. , Moudgill K. L.
Published: June 2016

But a few years ago the diverse phenomena of optical activity, such as the changes of rotation which occur with alteration of temperature, of colour of light, of solvent, or of concentration in a solvent, appeared, in spite of the great accumulation of relative data, to be practically independent of each other, and gave very little hope of satisfactory generalisation. Quite recently, however, the possibility of bringing into one scheme all these different branches of the subject has become more than a mere aspiration, and the progress which has been made by several investigators reveals clearly the existence of a deep-seated and farreaching regularity underlying the remarkable sensitiveness to external conditions of the phenomena in question.
IV.—Note on the Determinant of the Primary Minors of a Special Set of (n–1)–by–n Arrays
Authors: Muir Thomas
Published: June 2016

(1) The main specialty in the construction of the arrays in question is that the elements of each row are the coefficients of the powers of x in the expansion of a product of the form

that is to say, the rows all belong to the type

The variables from which the elements of any row are formed are n − 1 consecutive members of a series of n(n − 1) members, the member considered to be consecutive to the last being the first member; for example, when n is 3 and the 3(3 − 1) independent variables are

a, b, c, d, e, f,

the rows of the arrays are

Further, these rows in order are taken to form all the first rows of the arrays, then all the second rows, and so on.
V.—Factors of Circulants
Authors: Metzler W. H.
Published: June 2016

1. Among the well-known theorems for the breaking up of a circulant into factors are the following:—

Theorem I.*—The circulant

where θ is one of the nth roots of unity.
VII.—The Origin of Anticyclones and Depressions
Authors: Logie John
Published: June 2016

I wish to preface this statement of my views with an acknowledgment of my indebtedness to the works of Major Gold, Mr W. H. Dines, Sir Napier Shaw, Captain Cave, and Mr Lempfert, and more especially to the suggestions of Captain G. W. Jones, R.A.F. Captain Jones was the first person to draw my attention to the fact that changes in the upper wind frequently precede changes in the lower wind. In addition, he has often expressed to me his conviction that the entire theory of the winds requires to be rewritten; that convection and surface friction are of much less importance than is generally supposed, and that we have no reason to regard the variations of the upper winds as less, either in magnitude or abruptness, than those of the lower winds.
XI.—On the Presence of Formic Acid in the Stinging Hairs of the Nettle
Authors: Dobbin Leonard
Published: June 2016

It is well known that when the stinging hairs of the common nettle (Urtica dioica or U. urens) are caused to discharge their contents upon blue litmus paper, intensely red spots are produced. On the subsequent exposure to the air of the paper thus spotted, the red colour gradually diminishes in intensity, and in a day or two is scarcely distinguishable, although it does not entirely disappear even after several weeks' exposure. This behaviour indicates that the reddening is due, in the main at least, to a volatile acid, and the range of acids probably present is thereby very strictly limited.
XVI.—A “Duplex” Form of Harmonic Synthetiser and its Mathematical Theory
Authors: Milne J. R.
Published: June 2016

The present paper is a continuation of one published thirteen years ago describing a new form of harmonic synthetiser. The object is to show that by a slight alteration the simple form of mechanism proposed by Lord Kelvin in 1881, but afterwards rejected by him on acount of “obliquity error,” can be made quite satisfactory.
XII.—A Survey of Clyde Plankton
Authors: Marshall Sheina M.
Published: June 2016

The tow-nettings on which this survey is based were taken mostly from Keppel Pier. The tide as a rule runs down the channel strongly for several hours after high water, and the current is sufficiently strong to hold out the tow-nets more or less horizontal. Owing to some peculiarity in the configuration of the sea-floor at Keppel, the downward current is much the stronger and often begins an hour or several hours before high water. The flood-tide is never strong enough nor constant enough to hold out a tow-net for any length of time, and so most of the observations are based on tow-nettings taken on the ebb. Tow-nettings were taken almost every day and the tow-nets were usually left out for an hour.
XXIII.—On the Cardinal Function of Interpolation-Theory
Authors: Ferrar W. L.
Published: June 2016

The function which is discussed in the greater part of this paper was introduced by Professor E. T. Whittaker in vol. xxxv (1915), pp. 181–194 of these Proceedings. A one-valued function, analytic in the finite part of the plane save possibly for poles, is taken and a table made of the values of f(x) for x = a, a + w, a — w, a + 2w, a — 2w, … The function

called the Cardinal Function, is then shown to be the simplest function satisfying the table of values so obtained, in that it is a function which, when analysed into its periodic constituents, has no rapid oscillations.
XXVII.—A Colour-Vision Spectrometer
Authors: Peddie W.
Published: June 2016

It is now a thoroughly well-established fact that a satisfactory match to any coloured light observable in nature can be made by a combination, in suitable proportions, of three standard lights suitably chosen from a spectrum. It is customary to choose for the standards a red, a green, and a blue light of definite average wave-length in each case. The greatest deviation from the average is made so slight that there is no visible difference in colour between the extreme components present in any one standard. A simple way (used by Maxwell) of obtaining these standards would be by means of an ordinary spectroscopic arrangement in which light is focussed on a slit, and is parallelised by a collimating lens, after which it passes through a prism and the object glass of a telescope, on whose focal plane a spectrum is thus formed.
XXVIII.—A Ball-and-Tube Flowmeter
Authors: Ewing J. Alfred
Published: June 2016

About 1876 the author had occasion to devise a method of indicating the rate of flow of a liquid through a pipe system, without interfering with the flow. For this purpose he used a ball, heavier than the liquid, in a slightly tapered glass tube, through which the liquid flowed from the narrower to the wider end. In the first instance the tube was set vertical, with the wider part above. The ball fitted more or less closely at the lower end: it was carried up by the current till the clearance round it became such as to suit the particular rate of flow. Its height was read off on a scale fixed alongside of the tube, and served to indicate the rate of the flow, once the relation of scale-reading to flow had been experimentally determined.
VII.—Graphical Classification of Carbonaceous Minerals: the Place of the Constituents of Common Coal
Authors: Briggs Henry
Published: June 2016

This communication extends the method of classifying carbonaceous minerals already introduced in order to include the three components of common coal. The existence of the three constituents has long been recognised, but their close study, and the nomenclature now generally accepted, date from 1919, when Dr M. C. Stopes described their salient characteristics in a paper to the Royal Society. In that paper she gave the name durain to the hard, lustreless constituent, that of vitrain to the lustrous part, and borrowed the French miner's name fusain for the charcoal-like material commonly found between the bands of a coal seam. A bright variety, called clarain by Dr Stopes, is now usually regarded as a blend rather than as a separate substance, and may be disregarded in a classification such as this.
IX.—Graphical Analysis of Internal Combustion Engine Indicator Diagrams
Authors: Horne Alex. R.
Published: June 2016

The analysis of the performance of an internal combustion engine, based upon the indicator diagram, for the purpose of investigating such matters as the cyclical changes of temperature and internal energy content of the charge, and the heat flow between the working agent and the cylinder walls, is of considerable importance.
XVII.—The Adrenal Gland of Xenopus laevis
Authors: Zwarenstein H. , Schrire I.
Published: June 2016

1. The adrenal gland of Xenopus is essentially similar in distribution and structure to the adrenal of Urodeles.

2. In addition, adrenal tissue occurs in the walls of the renal veins, inferior vena cava, aorta and renal arteries, a condition similar to that found in some Cyclostomes and Fishes.

We wish to thank Mr B. McManus for his assistance in the preparation of sections.
XVIII.—The Geodesics in Einstein's Unified Field Theory
Authors: Blackwell A.
Published: June 2016

§1. Einstein has shown that the gμv giving the metric, ds2 = gμvdxμdxv, for a unified field theory can be expressed in terms of the two tensors ahμahv by
XX.—The Diffusion Coefficients of Bromine-Hydrogen, Bromine-Nitrogen, Bromine-Oxygen, and Bromine-Carbon Dioxide
Authors: Mackenzie John E. , Melville Harry W.
Published: June 2016

A brief history of the measurement of diffusion of gases (excluding “effusion,” “transpiration,” and other processes from which data for the calculation of the diffusion coefficient may be obtained) is given.

A visual method of following the diffusion of a strongly coloured vapour (bromine) into colourless gases is described.

The diffusion coefficients calculated from the observed data are in good accordance with those obtained theoretically.

The authors desire to thank Miss Netta Macnaughton for valuable assistance in the experimental work.
XXIII.—Zeros and Turning Points of the Elliptic-cylinder Functions
Authors: Ince E. L.
Published: June 2016

In any discussion of the zeros and turning points of the elliptic-cylinder function it is not necessary to define them more precisely than as functions of period π or 2π which satisfy the Mathieu equation

for the corresponding characteristic values of a. To simplify the following discussion, it is convenient merely to impose the condition that y(0)>0 if y(x) is even, and y′(0)>0 if y(x) is odd.
II.—The Maximal Range of Error in Gross Reproduction Rates
Authors: Charles Enid
Published: June 2016

In the past two methods have been applied to the study of differential fertility. One may be called the absolute method, recently applied to Scottish data by the writer. The other may be called the comparative method, subsequently applied to the same statistics by Mr Barclay and Dr Kermack. Since the conclusions obtained by the two methods are not always consonant, it is important to evaluate the scope and reliability of each.
IV.—On the Independence of Linear and Quadratic Forms in Samples of Normally Distributed Variates
Authors: Aitken A. C.
Published: June 2016

It is well known, and fundamentally important in the justification of the current mode of deriving Student's t-distribution, that the mean m of n values xi all obeying the same normal law of probability, and the associated estimate of variance, namely

are statistically independent.
VIII.—Reciprocity. Part II : Scalar Wave Functions
Authors: Born Max , Fuchs Klaus
Published: June 2016

This paper contains an attempt to formulate more rigorously the postulate of reciprocity (Born, 1939) and to solve the problem of finding reciprocal wave functions. We have not yet completely succeeded in this task, though considerable progress has been made; but it turns out that the original discussion has to be modified in several important respects.
XIII.—Tests of Carcinogenic Substances in Relation to the Production of Mutations in Drosophila melanogaster
Authors: Auerbach Charlotte
Published: June 2016

The theory has often been put forward that cancer is a somatic mutation. The changes which differentiate the cancerous cell from the normal are reproduced in many or all of the cells derived from the original malignant cell, i.e. they show the properties by which we define a mutation. Thus, to a geneticist, the possibility which most readily suggests itself is (1) that of a mutation in the genetic material of the somatic cell. Other possible mechanisms that might simulate the results of (1) are (2a) the introduction into the cell of a malignant virus; (2b) the “activation” of some such virus pre-existing in the cell in an inactive state, a situation which would imply mutation in the virus since the change becomes reproduced; (3) the production of some autocatalytic substance other than gene or virus, inducing malignant changes in the cell which contains a certain amount of it.
XXIV.—Early Glacial Remains of Reindeer from the Glasgow District
Authors: Macgregor M. , Ritchie James
Published: June 2016

In the early part of 1937, during the course of excavations for a sewage extension tunnel at Queen's Park, on the south side of Glasgow, some pieces of bone were obtained by the workmen from a bed of gravel at a depth of 70 feet from the surface. Through the kindness of Mr T. Somers, Master of Works and City Engineer to the Corporation of Glasgow, these remains were loaned to the Geological Survey and, again with his sanction, submitted for examination to Professor James Ritchie of Edinburgh University, one of the collaborators in this note. Professor Ritchie reported that the fragments of bone fitted together to form the greater part of the right radius and ulna of a reindeer. At a later stage of the excavations a portion of an antler was disinterred from the same bed. It seems desirable to record these occurrences in some detail, and for convenience this communication has been divided into two parts. In the first of these the geological position and age of the fossiliferous deposit are briefly discussed, while the second part is devoted to a description of the remains themselves and to a comparison with similar remains elsewhere.
I.—Remarks on the Present Outlook on Descent
Authors: Bower F. O.
Published: June 2016

A rough periodicity may sometimes be seen in the progress of Science. After a stirring time of advance may come a period of lethargy, or even of negation, followed again by some fresh spurt of activity. At the present moment we seem to have reached a phase of negation in respect of the achievements of phyletic Morphology, and in conclusions as to Descent. This is suggested by the Presidential Address in Section K at the British Association at Liverpool. Already Professor Seward in the Hooker Lecture, 1922, had said, “It may be that we shall never piece together the links of the chain of life, not because the missing parts elude our search, but because the unfolding in all its phases cannot be compared to a single chain. Continuity in some degree there must have been, but it is conceivable that plant life viewed as a whole may best be represented by separate and independent lines of evolution, or disconnected chains which were never united, each being initiated by some revolution in the organic world.”
VII.—Studies in Clocks and Time-keeping: No. 3. Comparative Rates of Certain Clocks
Authors: Sampson R. A.
Published: June 2016

The following paper is one member of a series designed to elucidate the circumstances of correct time-keeping, the first two of which were published in 1918.

The problem has in the meantime gained appreciably in interest. It was known that time-determinations from night to night at the same observatory were liable to discrepancies, which were presumed to have an accidental character and would be eliminated by grouping. Now, comparisons by the aid of wireless telegraphy of determinations made at different observatories, and grouped with the intention of eliminating accidental error, exhibit like discrepancies, of a more systematic character, with a range certainly not less than 0s·3. The search for the cause of this fault is engaging the attention of astronomers. It is a larger fault than is found in any other region of their science; and as its source is obscure, additional value attaches to any collateral investigation bearing upon it.
XIV.—The Electrolysis of Mixtures of Acetates and Trichloracetates
Authors: Gibson Ralph Edward
Published: June 2016

When potassium acetate and trichloracetate are electrolysed together, mixed compounds are formed, but only to a very slight extent. A small quantity of trichlormethyl acetate is to be found among the reaction products. The presence of either salt affects the reactions of the other by diminishing the yields of the normal products and by promoting the production of substances like trichlormethyl alcohol and ethylene which result from the oxidation of single molecules of each acid. A short explanation of this phenomenon has been given. No methyl alcohol appears among the final products, but formaldehyde is found in considerable quantities. This oxidation is connected with the production of an oxidising agent such as chlorine at the anode. Hexachlorethane and methyl chloride are also produced during the electrolysis of this mixture.

The author desires to take this opportunity of thanking Professor Sir James Walker, F.R.S., upon whose suggestion this work was begun, for his helpful advice and criticism during its execution.
XVI.—On Mixed Determinants
Authors: Vaidyanathaswamy R.
Published: June 2016

It is well known that the value of a cubic (or odd-dimensional) determinant |aijk| (i, j, k = 1, 2, … n) will reduce identically to zero, if exactly similar rôles are assigned to all the suffixes in determining the signs of the terms. To escape this difficulty, the usual theory of determinants of higher dimensions assigns a special rôle to the first suffix i, and considers that the class of the permutation of the values of i in any term makes no contribution to the sign of the term. This is, in effect, to make the suffix i non-determinantal in character.
XXI.—The Law of Recurrences and Decay of After Images
Authors: Smith Winifred J.
Published: June 2016

1. The following work is based directly on the mathematical treatment of the phenomena of after images given in Colour Vision, a recent book on the subject, by Professor Peddie.

The aim is to prove that this treatment agrees with the results obtained from experiments in which one eye was exposed to light for a given period. The oscillating decay of the resulting after images may be represented by the combined effect of three exponentially decaying periodic curves representing, respectively, the sensations of red, of blue, and of green.
II.—Contribution to the Studies of the Origin of European Sheep
Authors: Kaczkowski B.
Published: June 2016

The problems of the evolution and ancestry of the numerous breeds of domestic animals have not yet been finally solved. In many cases craniological methods of investigation have been used, and the results obtained have formed the basis of far-reaching conclusions. Such data are, however, open to serious criticism because the influence of environmental agencies during the life of the individual may be responsible for great variability of characterisation of the plastic animal body. The difficulty is increased by innumerable migrations of the ancestral stocks, by extensive hybridisation between distinct though closely related types, and the subsequent mixing of the various types in the modern breeds.
V.—Reflex Postural Adjustments of Balance in the Duck
Authors: Paton D. Noël
Published: June 2016

A series of reflex adjustments of balance disturbed round the anteroposterior and horizontal axes are described in the domestic duck.
VI.—The Theory of Jacobians, from 1885 to 1919
Authors: Muir Thomas
Published: June 2016

The chapter on Jacobians and the chapter on Hessians were the only two for the period 1880–1900 that seemed to indicate that a slackening had begun in the interest taken in their subjects. We now find that, so far as Jacobians are concerned, any movement of the kind must have been temporary, the new period (1900–1920) showing the number of relevant writings listed for report to be almost if not quite double that of its predecessor.
XII.—An Analysis of Preferential Voting
Authors: Sommerville D. M. Y.
Published: June 2016

1. Many systems of preferential voting have been proposed, differing both in the way in which the preferences are expressed and the method of dealing with them in order to arrive at a result. A useful account and examination of the principal methods was given by E. J. Nanson. This paper also contains a description of the method commonly known under his name. We shall consider only those systems in which the electors express their preferences with regard to all the candidates, and in which all these preferences are taken into account.
XVI.—The Lattice Points of a Circle
Authors: Wilton J. R.
Published: June 2016

1. A great deal of interest has of late years centred round the arithmetical function r(n), defined as the number of integer solutions of the equation

p2 + q2 = n,

so that, for example, r(1) = 4, the four solutions being (0, ±1) and (±1, 0).
I.—Some Modern Aspects of Physical Research
Authors: Ewing Alfred
Published: June 2016

In this ancient and honourable Royal Society we have an association of persons with a common motive, namely to assist the advance of natural knowledge. The chief functions of such a Society are (1) to provide facilities for intercourse, personal and formal; (2) to provide a library—and we have a great library of ever-increasing value ; (3) to provide the means of publication. Records of scientific research are not a readily marketable commodity. They would fare badly if left to the mercy of the ordinary laws of supply and demand. So we meet the cost of publication, and they go out, after some winnowing of chaff from wheat, with our imprimatur. Looking back through the published volumes of our Proceedings and Transactions, you will find papers by Kelvin and other Fellows which may be said without exaggeration to mark epochs in the development of scientific thought.