bluuebunny/crossref_metadata_2025 huggingface dataset:
VIII.—On the Theory of Graduation
Authors: Whittaker E. T.
Published: June 2016

The mathematical theory of graduation or adjustment, which hitherto has been developed chiefly in connection with the needs of actuarial science, centres round the following problem: A set of numbers u1, u2, u3, … un is supposed to have been obtained from observations or statistics of some kind. These numbers would represent the values of a variable ux corresponding to the values 1, 2, … n of its argument x, were it not that they are affected by accidental irregularities due to errors of observation, or to the imperfections of statistics. It is desired to construct a set of numbers , which represent the most probable true values of the variable ux corresponding to these values of x, so that the “graduated” numbers differ as little as possible from the “ungraduated” numbers u1, u2, … un, but are freed from the accidental irregularities, and thus form a “smooth” sequence, i.e. a sequence from which a regular difference-table can be formed for use in various calculations.
X.—Investigation of the Banded Structure of a Fifeshire Coal Seam
Authors: Cooper James
Published: June 2016

It has long been known that a bituminous coal seam is not a homogeneous bed, but is made up of a number of parallel bands. For example, Karsten in 1826 observed and described three banded constituents of such a seam, viz. Faserkohle, Matt Coal, and Glanz Coal, corresponding respectively to mineral charcoal, dull coal, and bright coal, and he gave some chemical details of their composition. Bowman, 1841, stated “there is a peculiarity in the texture of coal which has not received the attention it deserves. If it be clearly examined it will be found to consist of a series of parallel horizontal layers varying in thickness, these laminæ being best observed in the cross fracture, and often exhibit considerable difference in compactness and lustre. This structure, though in coal seams indistinct, is so general that it seems to point to some law which the chemical geologist might advantageously investigate.” Again, Wethered in 1884 observed that a coal seam is separated by partings into many beds differing in quality as in structure while in 1885 he pointed out the advisability of studying the different bands of a seam, and of recording details of its dull and bright portions.
XI.—The Theory of the Mechanical Analysis of Sediments by means of the Automatic Balance
Authors: Fisher R. A. , Odén Sven
Published: June 2016

In 1916, in a paper on the size of the particles in deep-sea deposits, Odén showed that the distribution by mass of a suspension into classes of particles of different size could be inferred from a study of the course of sedimentation of such a suspension from a state of uniform dispersion in water. The experimental data required constitute the “sedimentation curve ” of the suspension, showing the total weight deposited, at a fixed depth, at the end of any assigned length of time.
XIII.—The Cathode Fall of Potential in a High Voltage Discharge
Authors: Thomson G. P.
Published: June 2016

Most of the work which has been done directly on the cathode fall of potential refers to discharges where the potential difference applied was less than 1000 volts. In view of the large amount of work which has been done with discharge tubes worked from an induction coil at voltages of the order of 30,000, it seems of interest to consider how far the results obtained at the lower voltages can be applied to this case.
XV.—An Investigation into the Structure and Life-History of the Sulphur Bacteria (I)
Authors: Ellis David
Published: June 2016

The sulphur bacteria are found in shallow waters, both marine and fresh, and play an active part in the decomposition of animal and vegetable matter. They require for their full development an abundant supply of oxygen and of sulphuretted hydrogen. They do not thrive unless the water is periodically renewed, or else is so shallow that oxygen is obtainable to a fairly large extent from the atmosphere. When the oxygen is used up their development rapidly comes to an end, and in some cases, as is described below, the organisms disappear completely. They derive their supply of sulphuretted hydrogen from the decomposition of the protein molecule of vegetable and animal matter. Usually a growth of sulphur bacteria is visible to the naked eye as a greyish or reddish mantle covering the surface of a mass of decomposing organic matter. If, for some reason or other, the supply of oxygen is not plentiful at the bottom of the pool, the mass of growth leaves the surface of the decomposing matter and moves nearer the surface of the water.
VIII.—The Invariant Theory of the Quaternary Quadratic Complex. I. The Prepared System
Authors: Turnbull H. W.
Published: June 2016

Projective and differential geometry are in close touch at two places, once because of the fundamental rôle played by a quaternary quadratic form in each,

and again through the quadratic in six associated variables,

where
XV.—The Invariant Theory of the Quaternary Quadratic Complex. II. The Complete System
Authors: Turnbull H. W. , Williamson J.
Published: June 2016

This paper is a direct continuation of the paper entitled “ The Invariant Theory of the Quaternary Quadratic Complex ” published in the Proceedings of the Royal Society of Edinburgh, Session 1927–28, 48, pp. 70–91. In that paper a prepared system for the quadratic complex has been obtained and tabulated there in § 13. We here deduce from that prepared system the complete system of concomitants. The notation throughout this paper is the same as that suggested in § 13 (loc. cit.), except that, for convenience, the symbol α has been used instead of the symbol 1.
VI.—On the Theory of Graduation
Authors: Aitken A. C.
Published: June 2016

The present paper is intended to be a supplement to two previous papers on the same subject by Professor E. T. Whittaker. For information regarding the meaning of the term “graduation” and the new standpoint from which Professor Whittaker views the subject we need only refer to the papers themselves. Our concern here is with the practical solution of the problem, for which we suggest an alternative method.
XIV.—The Distribution of Electric Force in High Voltage Discharges
Authors: Geddes A. E. M.
Published: June 2016

Within comparatively recent times a large amount of work has been done on the cathode fall of potential. As a result it is now regarded by many investigators that no sudden fall of potential occurs close to the cathode, at least in the case of low voltage discharges. A comprehensive treatment of recent work on this subject is to be found in a paper by Stücklen. Further, F. W. Aston, in his investigations on the cathode fall, came to the conclusion that practically the whole fall occurred in the dark space between the cathode and the negative glow, and that if there were any force in the negative glow it was negligible compared with that in the dark space. The potentials used by Aston across his discharge tubes were comparatively small, however, never exceeding 1000 volts. With voltages of this order he showed further that the electric force in the dark space was very nearly in linear relation with the distance from the negative glow.
XV.—A Chapter in the Calculus of Variations: Maxima and Minima, for Weak Variations, of Integrals involving Ordinary Derivatives of the Second Order
Authors: Forsyth A. R.
Published: June 2016

The present memoir is devoted to the determination of criteria for the possession of maxima and minima by an integral which involves one independent variable, one dependent variable, and the first and second derivatives of the latter. All the variations, leading to tests for the existence of maxima and minima, are of the class called “weak”; not only are the variations themselves small, but their derivatives of all orders are small also.
XVI.—On Triple Systems of Surfaces and Non-Orthogonal Curvilinear Coordinates
Authors: Weatherburn C. E.
Published: June 2016

The properties of “triply orthogonal” systems of surfaces have been examined by various writers and in considerable detail; but those of triple systems generally have not hitherto received the same attention. It is the purpose of this paper to discuss non-orthogonal systems, and to investigate formulæ in terms of the “oblique” curvilinear coordinates u, v, w which such a system determines.
XI.—Further Tests upon Dewar Flasks intended to hold Liquid Air
Authors: Briggs Henry , Mallinson John
Published: June 2016

This communication describes a series of experiments carried out at the Heriot-Watt College, Edinburgh, on behalf of the Oxygen Research Committee, Scientific and Industrial Research Department. The experiments may be regarded as continuing a line of inquiry introduced by a paper read before the Society in 1921; their aim was to obtain data in regard to the rate of decay of the vacua (i.e. the rate of increase of the pressure in the vacuum envelope) of metallic Dewar vessels.
II.—Observations on the Relative Rate of Growth of the Nails of the Right and Left Hands respectively: on Seasonal Variations in the Rate, and on the Influence of Nerve-section upon it
Authors: Sharpey-Schafer E.
Published: June 2016

The growth of the finger nails has been investigated, and the rate on the right side as compared with the left, and in summer as compared with winter, determined for each finger. In nearly every case the rate is faster in summer than in winter.

In nearly every case also the rate is faster on the right hand than on the left. A notable exception is presented by the thumb nails, which have grown faster on the left hand than on the right both in summer and winter. The slowest rate of growth occurred in the nail of the little finger of the left side. The cutaneous nerves (ulnar) of this finger had been severed, and, with the exception of those which subserve pain, had not shown functional recovery. It is therefore probable that a trophic influence is exercised through the nerves upon the growth of the nail; the probability being supported by the fact that the little-finger nail on the left or de-nervated side not only exhibits a slower rate of growth but is distinguished from the corresponding nail on the normal side by being more flattened in form, rougher on the surface, and more brittle in texture.
III.—On some Problems involving the Persymmetric Determinants
Authors: Geronimus J.
Published: June 2016

Consider a system of “orthogonal polynomials”

P0, P1 (x), P2(x), …

possessing the property

x1, x2, …, xr being real given numbers, and p (x) a given “weight” function.
XIV.—Male Haploidy and Female Diploidy in Sirex cyaneus F. (Hymen.)
Authors: Peacock A. D. , Gresson R. A. R.
Published: June 2016

1. From the above it is therefore justifiable to conclude that Sirex cyaneus is typically hymenopterous, in that:

(a) the ripe male reproductive tissue is haploid (8 chromosomes), while the female oogonia are diploid (16 chromosomes);

(b) the abortive character of the first spermatocyte division is evidence that chromosome reduction does not occur during the maturation of the male gametes.

2. Support is thus afforded to the hypothesis commonly held, that the male hymenopteron is a haploid organism and is the product of an unfertilised (haploid) egg, while the female is a diploid organism arising from a fertilised egg.

3. Feulgen's “Nuclealreaktion” holds for the chromatin involved in the abortive division and for the chromosomes of the second spermatocyte; but the large chromatoid body and cytoplasmic granules seen in these same stages by the iron hæmatoxylin technique did not give the chromatin reaction. The nature of these chromatoid bodies remains to be discovered.
XIX.—Photochemical Measurements of Light Intensity in Two Common Vegetation Types in Tropical Africa, by Means of the Improved Eder-Hecht Photometer
Authors: Phillips John , Scott J. D. , Moggridge J. Y.
Published: June 2016

(1) A year's measurement of the light-intensity in an exposed site (“mbuga”) and in a Berlinia woodland community, Kikori (4° 21' S.), Tanganyika, by means of the Eder-Hecht Graukeilphotometer is described.

(2) The Bunsen-Roscoe units per second are shown to be very high, even under canopy of the Berlinia; they are very much greater than measurements recorded by Dorno for Assuan and Rio de Janeiro.

(3) While there is a positive correlation between the B.-R. values and the hours of direct sunshine, it is also clear that during cloudy periods (less than 50 per cent, of possible sunshine is experienced at Kikori and on the Central Plateau of East Africa generally) the B.-R. values are also very high.

(4) There is a positive correlation between the values of the Eder-Hecht photometer (in terms of blue-violet-ultraviolet rays), and the readings of the Livingston radio-atmometer measuring the total light-intensity of the same stations in terms of cubic centimetres of water.

(5) In virtue of the peculiar effects of the light of Tropical Africa upon the European nervous system, it is urged that quantitative and qualitative studies of the light in those regions should be investigated.

(6) Field biologists should make greater use of this efficient, cheap, simple, and portable instrument.
XXI.—Studies in the Scottish Marine Fauna. — The Crustacea of the Sandy and Muddy Areas of the Tidal Zone
Authors: Elmhirst R.
Published: June 2016

1. An attempt is made to indicate the quantitative distribution of the Crustaceans inhabiting certain Scottish intertidal areas.

2. Certain areas in the Clyde, notably Cumbrae, show a rich Amphipodan fauna which exhibits zoning by species.

3. Bathyporeia guilliarnsoniana is the dominant amphipod on the Tellina-Nephthys grounds (clean sand) and Corophium volutator is indicative of a muddy to brackish environment.
XXII.—An Operational Method for the Solution of Linear Partial Differential Equations
Authors: Kermack W. O. , McCrea W. H.
Published: June 2016

1. A general method for the solution of differential equations by definite integrals has recently been given by Professor E. T. Whittaker. It is briefly that, if a contact transformation from variables (q, p) to (Q, P) be given by Q = Q(q, p), P = P(q, p), and if this transforms an expression G(Q, P) into F(q, p), then the solutions of the differential equations

are connected by a relation of the form
I.—The Relation of Science to Industries and Education. Opening Address
Authors: Horne John
Published: June 2016

At the opening of another session it seems to me not inappropriate to refer to the question of the relation of science to industries and to education. Not much that is new can be said on this theme. The neglect of science by the Government and the people and the persistent indifference to scientific training and methods have been exposed by prominent scientists for many years. Repeated appeals and warnings have had little or no effect. But this world war has, at last, aroused the Government and the practical Briton to realise that success in war and prosperity in peace under modern conditions depend upon the application of scientific methods, and the development of research in relation to the industries.
VII.—On the Adelphic Integral of the Differential Equations of Dynamics
Authors: Whittaker E. T.
Published: June 2016

§ 1. Ordinary and singular periodic solutions of a dynamical system. — The present paper is concerned with the motion of dynamical systems which possess an integral of energy. To fix ideas, we shall suppose that the system has two degrees of freedom, so that the equations of motion in generalised co-ordinates may be written in Hamilton's form

where (q1q2) are the generalised co-ordinates, (p1, p2) are the generalised momenta, and where H is a function of (q1, q2, p1, p2) which represents the sum of the kinetic and potential energies.
XIV.—On some Nuclei of Cloudy Condensation. Part III
Authors: Aitken John
Published: June 2016

In communications to this Society in 1893 and in 1912, and in other papers, I have shown that some of the nuclei in the atmosphere have a power of condensing water vapour even when the air is unsaturated, owing to the material of which they are composed having an affinity for water. All kinds of nuclei have an affinity for water vapour, and by their surface action condense some water at all degrees of humidity, so causing increase in their size and hazing effect; but the particles having an affinity for water condense very much more and cause fogs in. unsaturated air. In the present communication I intend to deal with the more common form of nuclei—that is, those which have little or no chemical affinity for water—and with those nuclei which require supersaturation to cause condensation; the reason for this investigation being some statements which have appeared in scientific journals in this country and abroad regarding the nuclei counted by the condensation method. It has been definitely stated that the greater number of the nuclei counted are not dust particles but only ions, or aggregations of them. It therefore seemed desirable that further investigation should be made into the subject to see if there was anything to support this ionic theory of the condensation nuclei in the air, and at the same time to inquire into their origin.
XVI.—Experiments and Observations on Crustacea: Part V. A Functional Interpretation of certain Structural Features in the Pleon of Macrurous Decapods
Authors: Tait John
Published: June 2016

In the last paper of the present series it was pointed out that the articulations between the thoracic somites of Glyptonotus are so designed as to minimise change of internal volume during flexion and extension of the body. The pleon of the long-tailed Decapoda forms a system comparable to the series of thoracic somites of Glyptonotus; and as the macrurous decapods execute very rapid strokes of the pleon, one might expect that change of volume during movement is slight, for otherwise there would be waste of energy owing to inertia. It was decided to examine the matter experimentally.
II.—On the Phenomenon of the “Radiant Spectrum” observed by Sir David Brewster
Authors: Raman C. V.
Published: June 2016

In a paper on “The Scattering of Light in the Refractive Media of the Eye” published in the Philosophical Magazíne, for November 1919 (p. 568), I discussed the explanation of the luminous effects observed when a small brilliant source of light is viewed directly by the eye against a dark background, and especially of the marked difference between the cases in which the source emits white light and highly monochromatic light respectively. In both cases the source appears to be surrounded by a diffraction-halo: but the structure of the halo is markedly different in appearance.
IV.—Results obtained at the Physical Test Station, Edinburgh
Authors: Briggs Henry
Published: June 2016

It became evident during the War that some men who are organically sound are nevertheless incapable of supporting heavy exertion; and among the older groups that were called to the Colours in 1918 the proportion of such individuals was considerably more. The effect of forcing these men to carry out the duties falling to the lot of an “A” recruit was in many cases harmful to them, and in extreme instances resulted in permanent disability and sometimes in death. The Army Medical Department therefore sought to obtain a method of physical examination, which would supplement the ordinary medical examination of a recruit, and which could be applied to men who proved to be unserviceable material in the hands of the drill sergeant—a test which would, in fact, enable the malingerers to be distinguished from those who were truly incapable of sustained labour.
VII.—A New Method of investigating Colour Blindness, with a Description of Twenty-three Cases
Authors: Houstoum R. A.
Published: June 2016

During the past four years I have been conducting surveys of the colour vision of students in the University of Glasgow. The first survey was made by a colour-perception spectrometer very similar to Dr Edridge-Green's instrument, and embraced 79 observers. The second survey was made by Dr Edridge-Green's bead test, and embraced 100 observers. The third survey, carried out in collaboration with Miss Margaret A. Dunlop, was made by an original method, called here for short the microscope test, and embraced 1000 observers. At present there are two other surveys under progress. The object of these surveys is to find a numerical method of specifying goodness of colour vision; to see, by the application of statistical methods, whether the colour blind fall naturally into groups or are merely outliers of a homogeneous population; to find whether colour blindness is a Mendelian characteristic for men and merely an extreme case of normal variation for women; and to throw light on the subject of colour vision generally. Consequently, the normal have been investigated with as much care as the colour blind. But in the course of the four years I have made the acquaintance of many trained observers with abnormal colour vision, and have been possessed with an ever-growing desire to know exactly, irrespective of all theory, what was the matter with their colour vision. In spite of the vast literature on the subject, the tests generally have been of a very superficial nature, and unsatisfactory to the man with mathematical instincts. As these abnormal cases were beginning to leave the University, I addressed myself last spring to the problem of finding a method of testing which would describe their condition independent of theory, and, indeed, independent of words. This paper describes how the problem was solved, and gives data for twenty-three cases of colour blindness, four of normal colour vision, and one case of exceptionally good colour vision.
XII.—The Concomitants (including Differential Invariants) of Quadratic Differential Forms in Four Variables
Authors: Forsyth A. R.
Published: June 2016

The characteristic properties of quadratic differential forms, involving two or more independent variables, have been investigated from the days of Gauss onwards. Initially, the discussion arose for the case of two variables; and, in its most general trend, it was concerned with a form

associated with surfaces, E, F, G being integral functions of p and q. But the relation does not, by itself, define a surface completely. When a surface is deformed in any manner, without stretching and without tearing, the quantity ds2 preserves its measure unchanged; the measure is of fundamental importance. Consequently, the measure must remain unchanged whatever changes of the variables are admitted. Further, changes of the variables, of any kind, allow the existence of covariant concomitants which therefore persist through these changes. In particular, there is one function, of E, F, G and of their derivatives up to the second order inclusive, which persists unaltered; it is the Gauss measure of the curvature of the surface.
XIV.—Note on Professor Whittaker's Quantum Mechanism in the Atom
Authors: Houstoun R. A.
Published: June 2016

It seems desirable to check Professor Whittaker's model numerically; algebraical expressions when evaluated sometimes have the wrong order of magnitude.

Let us suppose that initially the magnet system is at rest, and that the electron starts from the origin with velocity u.
XVI.—On the Faraday-Tube Theory of Electro-Magnetism
Authors: Brown William Gordon
Published: June 2016

The method of describing a field of force by means of lines or tubes of induction, which originated with Faraday, was given a quantitative form by Sir J. J. Thomson, and further discussed by N. Campbell in his book Modern Electrical Theory. Since Maxwell himself looked on his work as a mathematical theory of Faraday's lines of force, one is tempted to examine the original physical theory for hints as to the modification of the Maxwellian theory to suit certain modern requirements.
Some Electrical Measurements on Metals
Authors: Fawsitt Charles E. , Brown A. Crum
Published: June 2016

There are many isolated records of facts showing that the physical properties of (pure) metals alter when the metals are subjected to hammering, rolling, heat-treatment, and other processes.

Somewhat recently Beilby has shown* that the differences in all the various states of metals are explained by the fact that solids exhibit two distinct phases: these are the amorphous or vitreous, and the crystalline. The properties of a metal in any given state are due to the metal being made up either of one or other of these phases, or both.
The Tarpan and its Relationship with Wild and Domestic Horses
Authors: Ewart J. C.
Published: June 2016

In December 1902,1 communicated to the Society a preliminary note “On a New Horse from the Western Islands,” and six months later submitted the results of experiments made with a view to ascertaining whether Prejvalsky's horse is a true wild species, or, as suggested by Flower and others, a chance hybrid between a kyang and an escaped Mongol pony.

The new horse (now commonly known as the Celtic Pony) described in the first paper is characterised by a small head, large prominent eyes, short ears, and narrow nostrils; by a long tail, mane, and forelock, and, during winter, by a thick, light yellow-dun woolly undercoat and a remarkable tail-lock (PL II. 7); by having, like Prejvalsky's horse, only 23 dorso-lumbar vertebræ, and also by the complete absence of callosities from the inner aspect of the hocks and from the region of the fetlocks—i.e. by the absence of the hind warts or chestnuts, and of the four ergots invariably present in typical specimens of the common horse. In speed and staying power, intelligence and docility, the Celtic pony takes after high-caste, fine-tempered Arabs.
Bathydraco Scotiæ, Poisson abyssal nouveau recueilli par l'Expédition Antarctique Nationale Ecossaise
Authors: Dollo Louis , Traquair M. R. H.
Published: June 2016

L'Expédition Antarctique Nationale Ecossaise, sous le commandement de M. W. S. Bruce, a recueilli une importance collection de Poissons au cours de son exploration de l'Atlantique austral et de la Mer de Weddell (1902–1904).

A la suite de la publication de mon mémoire sur les Poissons de la Belgica,* M. Bruce m'ayant fait l'honneur de me prier d'étudier les matériaux ichthyologiqucs qu'il avait rapportés, je me propose de soumettre à la Société Royale d'Edimbourg, si elle veut bien me le permettre, les résultats de mes recherches, au fur et à mesure de leurs progrèss, afin d'assurer à la Scotia la priorité de ses découvertes, en attendant que je sois assez avancé pour faire paraître mon travail définitif.
On Vibrating Systems which are not subject to the Boltzmann-Maxwell Law
Authors: Peddie W.
Published: June 2016

It is well known that the Boltzmann-Maxwell Law, which asserts average equi-partition of kinetic energy amongst the various motional freedoms, finite or infinite in number, of suitably conditioned systems, meets with apparently insuperable difficulties in its application to actual gases. Even in the case of gases showing complicated spectra, and therefore possessing numerous vibrational freedoms, the actual values of the ratio of the specific heats never deviate much from values which should, according to the law, be limited to very simple systems. Possible modes of evading this result, such as that supplied by J. J. Thomson's suggestion (Arch. Néerlandaises, 1900, Ser. II. t. v.) that individual molecules may not be concerned in radiation, are too problematical to give much relief.
On the Methods of Standardising Suprarenal Preparations
Authors: Cameron I. D.
Published: June 2016

For the standardisation of adrenalin preparations.

(a) The colorimetric method is not reliable with weak or impure solutions.

(b) The effect on the pupil of the frog's eye gives uncertain results.

(c) The determination of the minimum effective dose on the arterioles of the perfused frog is tedious and uncertain; on an average 0·1 per million produces an effect.

(d) The determination of the minimum effective dose in causing a rise on the blood pressure of the atropinised rabbit yields fairly satisfactory results.

(e) Adrenalin, suprarenalin, and hemisine all give a precisely similar result, 0·0003 mg. per kilo of body weight, or 0·006 per million, of the rabbit's blood causing a distinct rise in the blood pressure in the rabbit, and 0·012 mg. per kilo of body weight, or 0·24 per million, of the blood causing a rise in the cat.

(f) The most satisfactory method is the determination of the dose just sufficient to antagonise 0·6 mg. of nitroglycerin (Parke, Davis & Co.). Of adrenalin, 0·0075 mg. is sufficient.

I wish to express my indebtedness to Dr Noël Paton for much help in the preparation of this paper.

The expenses of this research were defrayed from a grant made to the Laboratory by Mr J. Francis Mason for investigations on the physiology of the ductless glands.
The Theory of Alternants in the Historical Order of Development up to 1860
Authors: Muir Thomas
Published: June 2016

My last communication in reference to the history of alternants dealt with the period 1795–1841 (Proc. Boy. Soc. Edin., xxiii. pp. 93–132). The present paper continues the history up to the year 1860, but in addition contains an account of three writings belonging to the previous period, namely, by Murphy (1832), Binet (1837), and Haedenkamp (1841).
On an Exception to a Certain Theorem in Optics, with an Application to the Polarimeter
Authors: Milne James Robert
Published: June 2016

There is a well-known law in geometrical optics, that the “intrinsic luminosity” of the image formed by any lens system whatever is the same as the intrinsic luminosity of the object. An exception, however, which seems not to have been pointed out before, exists in the case of polarised light, based on the fact that by the agency of a double-image prism two light rays polarised in directions mutually perpendicular may be combined into one ray, which carries the total energy of both. In this way an intrinsic luminosity of image can be attained which is twice as great as that of the object.
IV.—The Electrolysis of Salts of Alkyloxyacids
Authors: Fairweather David A.
Published: June 2016

Four compounds have been electrolysed and the nature of the resulting compounds investigated. These are:—

(a) Potassium ethyl ethoxymalonate, which gave ethyl diethoxyacetate, the alcoholate of ethyl glyoxylate, a little ethyl diethoxysuccinate, ethyl alcohol, oxalic acid, formaldehyde, and acetaldehyde.

(b) Potassium ethyl diethoxysuccinate, which gave ethyl formylethoxyacetate, oxalic acid, ethyl oxalate, ethyl alcohol, formaldehyde, and formic acid.

(c) Potassium ethoxyacetate, which gave formaldehyde, alcohol, and formaldehyde diethylacetal.

(d) Sodium amyloxyacetate, which gave amyl amyloxyacetate, formaldehyde diamylacetal, formaldehyde, and iso-valeric aldehyde.

The author wishes to acknowledge his indebtedness to Professor Sir James Walker, F.R.S., for his helpful suggestions and advice in the course of this research.
X.—The Action of Salts with Multivalent Cations on Colloidal Solutions of Gold and Gum Benzoin
Authors: Kermack William Ogilvy , Voge Cecil Innes Bothwell
Published: June 2016

It has been pointed out in a previous paper (Wright and Kermack, 1923), that whereas the precipitation of colloidal gum benzoin by salts containing a uni- or bi-valent cation commences at a given concentration and continues to take place with increasing concentration, in the case of ferric chloride, there occurs with continuously increasing concentrations of this salt, first non-precipitation, second precipitation, then a range of concentrations where no precipitation occurs, and lastly precipitation again. Such a series of changes has been observed with other sols under the action of tervalent ions (cf. Burton, 1916).
III.—The Place in Nature of the Tasmanian Aboriginal as deduced from a Study of his Calvarium.—Part I. His Relations to the Anthropoid Apes, Pithecanthropus, Homo primigenius, Homo fossilis, and Homo sapiens
Authors: Berry Richard J. A. , Robertson A. W. D.
Published: June 2016

IN our communication to the Royal Society of Victoria of the 11th March, 1909 (1), describing our recent discovery of forty-two Tasmanian crania hitherto quite unknown to the world of science, we stated that “one of the earliest purposes to which it is proposed to utilise the present material is the determination of the relationship of the Tasmanian to the anthropoids and primitive man on the one hand, and to the Australian aboriginal on the other hand. Schwalbe's study of Pithecanthropus erectus (2) may serve as a basis for the former purpose, and Klaatsch's recent work (3) for the latter, though it must be remembered that innumerable authors have contributed to both subjects.” The present work is the fulfilment of the first part of this undertaking, namely, the determination of the relationship of the Tasmanian to the anthropoids and primitive man.
XVIII.—The Less Common Special Forms of Determinants up to 1860
Authors: Muir Thomas
Published: June 2016

There now only remain for consideration those special forms which, prior to 1860, had not received any noteworthy attention. These will be found to include: (α) permanents, which are touched on by three authors; (β) determinants with the typical element ars + brsi, which are referred to in four memoirs; (γ) two other forms, which are each dealt with in two papers; and (δ) nine others, which make their appearance only once.
XIX.—A Study of Artificial Pyrexia produced by Tetra-hydro-β-Naphthylamine Hydrochloride
Authors: Black Adam
Published: June 2016

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

The influence of such micro-organismal poisons has been already studied by several investigators-among others, by Noël Paton, Dunlop, and Macadam in the case of diphtheria (Journ. of Phys., vol. xxiv. p. 331,1899; see also chapter “Fever and Infection,” by Kraus, Von Noorden's Metabolism and Practical Medicine, vol. ii. p. 90); but so far few detailed studies of the metabolism in high temperature due to non-infectious processes have been recorded.
XXIX.—Boole's Unisignant
Authors: Muir Thomas
Published: June 2016

1. In two memoirs on the “Theory of Probabilities,” Boole was led to the consideration of a peculiarly interesting form of determinant which has only positive terms in its final form of development, and which in the case of the fourth order may be written

V standing therein for

In the first of the two memoirs the determinant is not explicitly referred to, but in the second it receives considerable attention, Boole, indeed, there saying that the memoir “involves discussions relating to the properties of a certain functional determinant, and to the possible solutions of a system of algebraical equations of peculiar form, discussions which will, I trust, be thought to possess a value as contributions to mathematical analysis, independent of their present application.”
On the Influence of Temperature upon the Magnetic Properties of a Graded Series of Carbon Steels
Authors: Moir Margaret B.
Published: June 2016

1. Experiments of Hopkinson, Curie, and D. K. Morris.

2. Precautions necessary in magnetic testing. If the temperature of a test-specimen is changed, the specimen must be rendered neutral at the new temperature previous to carrying out the test.

3. The effect of increasing the temperature of a specimen of cast iron from 15° C. to 190° C. is to improve its magnetic quality for moderate values of the magnetising force; from 190° C. to 260° C. the magnetic quality falls off, after which there is a further improvement. Finally the specimen becomes non-magnetic at the critical temperature. These results indicate the presence of a transformation point for carbon alloys of iron in the neighbourhood of 200° C.

4. Steel containing 1·64 per cent, of carbon resembles cast iron in its behaviour. The set-back in magnetic quality takes place at much the same temperature as that which occurs in cast iron, the magnitude of the set-back being much the same for both.

5. Steel containing 0·8 per cent, of carbon exhibits the transformation point, but in a less marked degree. The first maximum point in the susceptibility curve occurs at 180° C, and the first minimum point at 220° C.

6. Low carbon steel containing 0·3 per cent, of carbon shows the transformation point; it is, however, very much less marked than in the case of the steels containing the higher percentages of carbon.

7. The susceptibility-temperature curve of a specimen of soft iron containing 0·06 per cent, of carbon exhibits no turning points in the neighbourhood of 200° C. for fields lying between 2 and 15 c.g.s. units.
XXXV.—The Vapour Pressure of Dry Calomel
Authors: Smith Alexander , Menzies Alan W. C.
Published: June 2016

We have shown that calomel vapour contains no measurable amount of Hg2Cl2 or of HgCl, and consists wholly of the dissociation products, mercury and mercuric chloride. According to chemical theory, therefore, when, by the removal of all moisture, the dissociation is prevented, the vapour pressure of the dry substance should be equal only to the partial pressure of the undissociated molecules of the undried vapour; that is to say, it should be negligibly small. Brereton Baker, however, was able to measure the vapour density of such dry calomel, finding it to be almost double the ordinary density. Since the measurement was made by the V. Meyer method, at 445°, it follows that this dry calomel must have possessed a vapour pressure approximating, if not exceeding, one atmosphere.
XXXVI.—The Absorption of Light by Inorganic Salts. No. I.: Aqueous Solutions of Cobalt Salts in the Infra-Red
Authors: Houstoun R. A.
Published: June 2016

The present article is intended to be the first of a series on the absorption of light by solutions of inorganic salts of different elements. With a few scattered exceptions all the work hitherto done on the absorption spectra of inorganic salts has been merely qualitative and has been confined to the visible spectrum. Kayser in his Spectroscopie, vol. iii. p. 45, states that in this field there is work for years and for numerous observers. E. C. C. Baly states in his Spectroscopy, p. 407, that not much is known about the absorption of light in inorganic salts. Merely for its own sake, then, an accurate determination of the molecular extinction coefficient for as many salts under as many different conditions of temperature and concentration, and for as many wave-lengths as possible, would be very valuable.
XLVI.—On Photometric Paddle-Wheels
Authors: Milne James Robert
Published: June 2016

This paper describes a new form of rotating photometric “sector,” capable of very accurate adjustment to any desired light-transmission value while running, and possessed of the great advantage of having its rotating part in one piece only.

A mathematical discussion of this new type of apparatus follows, in which are deduced formulæ for the intensities of the light transmitted under different conditions, and for the greatest width of the beam of light that can be employed; and a graphical tabulation of the values of these formulae in different cases is provided.

The mounting and details of an actual instrument are described; together with an additional mechanism for the purpose of automatically recording the photometric measurements obtained.
VIII.—The Rôle of Inbreeding in the Development of the Clydesdale Breed of Horses
Authors: Calder A.
Published: June 2016

Coefficients of inbreeding have been calculated for 676 stallions and mares, with the object of studying the part played by inbreeding in the development of the Clydesdale breed of horses. Wright's coefficient of inbreeding was used in this study.

It is found that during the early history of the breed very little inbreeding had been practised, and it is suggested that this may be due to the fact that the foundation stock contained many recessive factors for undesirable characters. The first marked rise in the average percentage of inbreeding for the breed occurs during the period 1880–1890, and from that time onwards there is a gradual but constant increase in the breed average, reaching its highest level at 6.25 per cent. for the period 1920–1925.

A method is outlined by which a measure can be obtained of the contribution of any particular sire to the graph of the average percentage of inbreeding for the breed. It also measures the degree of concentration of his blood in animals inbred to him and the rate at which his blood is diffused through the breed.
XII.—Magnetisation and Temperature in Crystals
Authors: Peddie W.
Published: June 2016

In previous papers (Proc. R. S. Edin., 1905, 1907, 1912) on the subject of crystalline magnetic quality, all questions of temperature were left aside. Molecular heat motions were regarded as non-existent, and the magnetic atoms or molecules were considered as representable by small ideal magnets centred upon a geometrical space lattice. No other mode of representation is possible until explicit notions regarding the origin and seat of molecular magnetic quality become definitely possible; and the general nature of magnetic actions and properties indicate that the general nature of the conclusions thus arrived at will not be fundamentally altered by particular assumptions regarding the nature of the magnetic molecules themselves. The crystalline quality of the magnetisation is due to the geometrical spacing of the atoms or molecules, and is manifested under the control afforded by the magnetic fields originating in surrounding molecules. This is essentially, when freed from the restriction to crystals, the statement of the modern Theory of Molecular Magnetism, which was definitely put forward by Weber in 1852, in all its features, and was recognised by Maxwell, who, in the state of experimental knowledge at the time, contented himself with an addition to Weber's representation of the law of force by postulation instead of by direct deduction. The first explicit applications to crystalline, or randomly crystalline, solid materials were made by Ewing, who obtained approximate quantitative results, relatively to ordinary magnetic materials such as iron, by neglecting the effect of all but closely neighbouring molecules, a condition which, though only strictly justifiable under the postulate of small pole clearance, is sufficient to give a good-elucidation of the effects. The action of his models was not so narrowly restricted.
XVIII.—On the Consistency of Cardinal Function Interpolation. Parts I, II
Authors: Ferrar W. L.
Published: June 2016

In a previous paper on the Cardinal Function it was proved that, calling

the cardinal function of the table of values αr at the point α + rw], “the cardinal function of the table of values [C(rw′) at the point rw′] is a function C1(x) which coincides with C(x) provided that 0<w′<w, and Σ | αn/n |, Σ |α−n/n| are convergent.”
XXII.—Researches into the Characteristic Numbers of the Mathieu Equation—(Third Paper)
Authors: Ince E. L.
Published: June 2016

The importance in Mathematical Physics of the Bessel functions, whose order is half an odd integer, suggests that the corresponding Mathieu functions may be worthy of a closer attention than they have yet received. At the very least it is expedient to pave the way for their computation. In the second paper bearing the above title, asymptotic developments of the characteristic numbers which correspond to these functions were given; it is here proposed, in the first place, to take the more direct line of approach.
I.—The Theory of Bigradients from 1861 to 1919
Authors: Muir Thomas
Published: June 2016

The number of writings dealt with here is very slightly in excess of the number under the same heading for the period 1880–1900, and there is also little alteration in the general character of them. The bigradient which still receives most attention is that resulting from Sylvester's dialytic method of elimination, and others are close relatives of it.
V.—The General Expression for Boundary Conditions and the Limits of Correlation
Authors: Thompson J. Ridley
Published: June 2016

The attempt to extract information from correlation coefficients concerning possible common factors among measured variables presents serious difficulties, since common factors are not determinate functions of the original variables. It is indeed possible, by the assumption of specific, group (common to some), and general (common to all) factors, to construct various hypothetical correlated variables which will produce correlations of a given magnitude. If it is required, for instance, to construct three variables to produce three given positive correlations, we may choose among various ways to produce the correlations by means of a triple factor (common to three variables) or dual factors (common to two), or both in co-operation. We are faced by a certain restriction, however, for whereas correlations of any magnitude can be produced by using a triple factor with or without dual factors, yet with dual factors unaided by a triple factor certain magnitudes are unattainable. The condition expressing this restriction is known as a “boundary condition.”
XV.—The Stability of Suspensions. III. The Velocities of Sedimentation and of Cataphoresis of Suspensions in a Viscous Fluid
Authors: Kermack William Ogilvy , McKendrick Anderson Gray , Ponder Eric
Published: June 2016

1. When a suspension of a large number of small rigid spheres in a viscous fluid is allowed to sediment under the action of gravity the rate of fall of any of the particles in the body of the suspension is

U = U0(1 – κΦ), where U0is the rate of fall of an isolated single particle calculated according to Stokes' law, where α is the radius of the particle, η the viscosity of the fluid, ρ the density of the particle, σ the density of the fluid, andgthe constant of gravity. Φ is the volume of suspended material per unit volume of the suspension, and κ is a constant whose value according to theory is 5·5 +c, wherecis probably in the neighbourhood of 1·6.
XVIII.—Quanta in Biology
Authors: Przibram Hans
Published: June 2016

The elaborate system of molecules, atoms, ions, and electrons modern chemistry and physics have constructed to meet their needs invites the biologist to inquire into the problem of material particles as bearers of life. Leaving aside all questions of finality in the organism touching the vexed problem of purpose in our world, which science has also not been able to solve in lifeless matter (1), we may try to get glimpses of the construction of living material by different methods of attack.
XIX.—Colour Sensitivity
Authors: Hunter G. N.
Published: June 2016

In his investigations on colour blindness, Dr. Houstoun produced two identical patches of colour on a screen; one of these patches was gradually altered until a difference in tint could just be observed. These two patches were at a distance of 8 mms. apart on the screen, and Dr. Houstoun suggested that if these patches were juxtaposed the observer's colour sensitivity might be improved. The following communication records the results of investigations carried out under that suggested condition.
XXII.—The Theory of Skew Determinants and Pfaffians from 1891 to 1919
Authors: Muir Thomas
Published: June 2016

The subject of this chapter, unlike Jacobians and Hessians, increases without halt in popularity, the number of relevant writings coming up for report in the new period being a half more than in the period immediately preceding, where the rate of increase had been still higher. A notable feature, too, is the exceptional attention given to Pfaffians, and along with it the growing tendency to view them as entities apart from determinants. Of less importance perhaps but interesting is the first appearance (in 1894) of determinants that are “block” skew.