bluuebunny/crossref_metadata_2025 huggingface dataset:
II.—Prenatal Death in the Pig and its Effect upon the Sex-Ratio
Authors: Crew F. A. E.
Published: June 2016

The cytological evidence concerning the pig is that the sex of the future individual is determined at the time of fertilisation, and that in respect of the elements of the sex-chromosome sex-determining mechanism the male is digametic. If this is so, if the two sorts of sperm are produced in equal numbers, if each kind is equally viable and functional, and if fertilisation is at random, then a primary sex-ratio (that which obtains at the time of conception) of equality must follow. If male and female zygotes are equally viable, then the secondary sex-ratio (that which obtains at the time of gestation) will also be equality. A secondary sex-ratio other than equality must be the reflection of an unequal primary sex-ratio, the result of a differential production of the two sorts of gametes elaborated by the digametic sex, of a selective fertilisation by these, or of a sexually selective mortality among the embryos or/and fœtuses. A secondary sex-ratio of equality can follow a pronounced inequality in the primary sex-ratio if a sexually selective mortality operates prenatally.
VII.—The Theory of Continuants from 1900 to 1920
Authors: Muir Thomas
Published: June 2016

The number of writings on continuants belonging to the twenty-year period now reached is 44, being 15 more than for the immediately preceding period 1880–1900. The period bears also three other marks which serve to give it some little additional distinction, (1) the exceptionally full consideration given to the subject of factorisation (factorisation of continuants), (2) the first appearance of an entirely fresh form for special study, the “block continuant” of Simandl, (3) the fact that one of the said 44 writings is a text-book of very considerable extent devoted exclusively to continuants and continued fractions.
IX.—The Slow Oxidation of Phosphorus Trioxide. Part I. The Action of Water-Vapour on Phosphorus Trioxide
Authors: Miller Christina Cruickshank
Published: June 2016

1. During spectroscopic investigations of the phosphorus trioxide glow a method was found for maintaining a stationary glow for twelve to twenty-four hours.

2. Experiments were performed illustrating the necessity of water-vapour for the glow phenomena.

3. The effect of water-vapour on phosphorus trioxide in evacuated bulbs was systematically studied at 25°. Pressures of water-vapour ranging from 1–23 mm. were maintained by the use of certain salt hydrate mixtures, and of water.

4. In every case pressure increased owing to the production of phosphine.

5. When the pressure of water-vapour was 2·5 or 5 mm. a liquid, in addition to gas, was produced in sufficient quantity, after the elapse of several hours, to cause a rapid pressure rise to a maximum. Its vapour-pressure at different temperatures showed that it was liquid phosphorus hydride. A rapid pressure fall from the maximum was observed, and was due to the interaction of hydrides of phosphorus and phosphorus trioxide.

This investigation was proposed by Sir James Walker, F.R.S., to whom the author is deeply indebted for many valuable suggestions, as well as for his constant interest and kindly criticism. She has also to express her thanks to Messrs Brunner, Mond & Co., Ltd., for a grant which defrayed the cost of a Cenco Hyvac Pump and other apparatus.
XII.—On the Adjustment of Sir J. J. Thomson's Theory of Light to the Classical Electromagnetic Theory
Authors: Whittaker E. T.
Published: June 2016

In many recent publications Sir J. J. Thomson has suggested a “corpuscular” theory of light; that is, a theory which supposes that the energy of the light is done up into parcels or quanta which retain their energy undiminished as they travel out into space without the unlimited spreading which takes place with ordinary diverging waves. A corpuscular theory of light in this sense has indeed been advocated by Einstein and by many other writers: it is in fact evident that the wave-theory of optics, in its classical form, must be modified in some way in order to be capable of explaining the relations between light and electricity which have been discovered in the last thirty years. Thus, if cathode rays fall on a metallic plate and generate X-rays, which fall on a second metallic plate, electrons are ejected from the second plate whose energy is of the same order as that of the electrons in the primary cathode rays and is independent of the distance of the plates. This seems to indicate that the energy of the X-rays is retained in a compact parcel during the transmission between the plates.
XIII.—Partial Differential Equations and the Calculus of Variations
Authors: Copson E. T.
Published: June 2016

A partial differential equation of physics may be defined as a linear second-order equation which is derivable from a Hamiltonian Principle by means of the methods of the Calculus of Variations. This principle states that the actual course of events in a physical problem is such that it gives to a certain integral a stationary value.
XXI.—The Slow Oxidation of Phosphorus Trioxide. Part II. The Production of Phosphorus Tetroxide by Direct Oxidation of Phosphorus Trioxide
Authors: Miller Christina Cruickshank
Published: June 2016

At 25°, in oxygen at 600 mm. pressure, and in presence of water-vapour at a pressure of less than ·1 mm., the only product of oxidation of phosphorus trioxide was found to be phosphorus tetroxide, P2O4. The latter was identified by microscopic investigation of its crystals as well as by quantitative analysis.
XXIV.—On the Effects of Vasectomy and of Epididymo-deferentectomy in the Mouse
Authors: Tamura Y. , Crew F. A. E.
Published: June 2016

1. Degeneration of the germinal epithelium of the testis invariably follows the operation of vasoligation or of vasectomy in the mouse, but does not become evident until a considerable period of time has elapsed.

2. Similar degeneration follows the operation of epididymo-deferentectomy, but after a much shorter interval of time.

3. This degeneration is caused perhaps by the pressure within the seminiferous tubules exerted by the accumulation of seminal products, or more probably by the action of toxic substances liberated from the disintegrating cell and sperm debris.
XXVII.—Bothrodon pridii, an Extinct Serpent of Gigantic Dimensions
Authors: Kerr J. Graham
Published: June 2016

The object of this note is to place on record the existence of a specimen which demonstrates the one-time existence of poisonous serpents of hitherto quite unheard-of dimensions.

The specimen, shown in the text-figure, is a poison-fang remarkable for (1) its enormous size, and (2) its curvature. As regards size, the fang measures nearly 65 mm. along the outside of the curve, and 46 mm. in a

straight line along the chord of the curve. It measures close to but clear of the swollen base 11·4 mm. in diameter and 35 mm. in circumference.
XXIX.—On the Cardinal Function of Interpolation-Theory
Authors: Ferrar W. L.
Published: June 2016

If we consider a set of values a0, an, a–n and a set of equidistant points x = a, a±nw, there are many interpolation formulæ which give functions assuming the values a0, an, a–n at the points x = a, a + nw, a − nw respectively. The function with which the present note deals is, writing π/w = m,
IV.—The Life-History of Aphidius avenæ (Hal.), a Braconid parasitic on the Nettle Aphis (Macrosiphum urticæ)
Authors: MacGrill Elsie I.
Published: June 2016

Nettles of the two species Urtica dioica and Urtica urens are commonly infested with the aphid Macrosiphum urticæ, and amid the living aphids and a collection of moulted skins dead examples are almost certain to be found. These dead aphids are almost spherical in shape and are of a brown colour, quite different from the colour of a normal aphid. They are attached to the nettle-leaf, often to the upper surface, by their ventral side, the leaf generally being discoloured at the point of attachment. If a number of these dead aphids are collected it will be found that, after a time, hymenopterous parasites, a species of the family Braconidæ, issue from the swollen body of the dead aphids. This parasite has been identified as Aphidius avence (Hal.), and the present paper deals with the life-history and habits of this species.
V.—Experiments with a Model to illustrate the Combination of Two Atoms consisting of Magnetons round a Positive Nucleus
Authors: Laurie A. P.
Published: June 2016

Sir J. J. Thomson has shown that if two atoms combine, consisting of electrons round positive nuclei, the arrangement of the two combining electrons is as shown in the following figures, the two electrons taking up a lateral position and being both attractedby the +ve nuclei, A and B.

If, on the other hand, the electrons are replaced by magnetons, it has apparently been assumed that the two nearest magnetons on the approaching atom will mutually attract each other, and rotate to face each other, taking up a position as shown in the following diagram.
VII.—The Relation of Size to the Elaboration of Form and Structure of the Vascular Tracts in Primitive Plants
Authors: Bower F. O.
Published: June 2016

In my Presidential Address of October 1920 I cited the stems of certain Zygopterideæ in illustration of size as a factor in Stelar Morphology. But only a few salient facts were adduced from the protosteles of their stems. The relation of increasing size to the elaboration of the vascular tracts of primitive plants deserves further examination: and the results would appear the more cogent if the evidence were collected not only from series of plants which are related to one another, or even from different parts of the same plant, but also from series not so nearly related. A re-examination of the published figures of axial steles and petiolar traces in the fossil Cœnopterideæ has provided interesting results.
XII.—The Interior and Exterior Space-Time Forms of the Poincaré Electron in Weyl's Geometry
Authors: Marshall John
Published: June 2016

It is proposed in this paper to examine the forms obtainable for ds2 in Weyl's generalisation of Einstein's Theory of Relativity, when an isolated electron, considered as a spherical entity carrying a uniform surface distribution of electricity, is present. The problem of the electron on Einstein's theory has been discussed by Nordström (Verslag. Ak. Amsterdam, January 1918). W. Van Der Berg (Vraagstukken mit Einstein's gravitatic theorie, Harlem, 1920) has given an approximation to the solution which has been obtained exactly by H. Vanderlinden (Bull. Acad. Roy. de Belgique, May 1921).
XIV.—The Slow Oxidation of Phosphorus
Authors: Gilchrist Elizabeth
Published: June 2016

It has long been known that yellow phosphorus is slowly oxidised in air at the ordinary temperature and that the oxidation is accompanied by a glow easily visible in a darkened room. If oxygen at atmospheric pressure is substituted for air no glow is perceived, and the oxidation, if it occurs at all, is incomparably slower than in air. If the pressure of oxygen is reduced either directly or by admixture with an indifferent gas the glow may be made to reappear. The seeming contradiction of the law of mass action involved in these phenomena has been the subject of many experiments, and the main object of the present investigation is to attempt to throw some light on this anomaly.
XVI.—The Sizes of Particles in certain Pelagic Deposits
Authors: Douglas A. Vibert
Published: June 2016

The monumental work of the late Sir John Murray and Dr Renard on the examination and classification of deep-sea deposits has left little to be desired either as regards methods or results. There was, however, one respect in which they were handicapped—no satisfactory method was known of ascertaining the distribution of sizes of the particles of which a sample was composed.

In 1915 Dr Sven Odén of Upsala made known a method of soil analysis whereby he obtained by a sedimentation process data from which he could construct the distribution curve representing the relative proportions of particles of various sizes. He later obtained from the Challenger Office several samples of different types of deep-sea deposit which he subjected to the same form of analysis.
I.—On the Pregnancy Rate in the Lactating Mouse and the Effect of Suckling on the Duration of Pregnancy
Authors: Mirskaia L. , Crew F. A. E.
Published: June 2016

1. The pregnancy rate of primiparæ, suckling their young, was, in this experiment, 24·1 per cent.; that of multiparæ suckling their young, 50 per cent. It is shown that this difference is not due to differences in the incidence of ovulation associated with postpartum œstrus. The suggested explanation of this difference between puberal and adult groups is that a certain level of somatic maturity is a prerequisite for full reproductive activity.

2. In all cases the duration of pregnancy was prolonged. The degree of prolongation was variable and could not be related to the number of young in the uterus or suckling. The results provide no support for the suggestion that this prolongation, due to delayed implantation of the fertilised ova, is to be referred to an inhibitory action on the part of the mammary gland. The suggestion is made that the delayed implantation and prolonged pregnancy are due to inability on the part of the corpus luteum to cater adequately for implantation and lactation synchronously.
IV.—A Note on the Secular Changes of Rock Temperature on the Calton Hill
Authors: Whipple F. J. W.
Published: June 2016

1. The observations of rock temperature on the Calton Hill have recently been analysed by Mr R. W. Wrigley, with a view to the discovery of changes going on gradually and independent of weather conditions. Mr Wrigley took groups of years, such that the mean air temperature was the same for each group, and found the mean rock temperature for like periods. He trusted that in this way he would be able “to get rid of the surface temperature variations.” The result of the calculations was that for different periods in which the mean air temperature was the same the temperature of the rock might vary by half a degree Fahrenheit. The rock temperature had a maximum about 1856, fell until 1892, and rose after that date.
XI.—Electromagnetic Phenomena in a Uniform Gravitational Field
Authors: Meksyn D.
Published: June 2016

In two recent papers Professor E. T. Whittaker has solved the electromagnetic equations for the case of a uniform gravitational field. The fundamental tensor associated with such a field makes the Riemannian tensor vanish, since such a field can be transformed away by a suitable choice of coordinates. This property enables us to find the electromagnetic field in a uniform gravitational field without solving Maxwell's equations, but by a mere transformation of co-ordinates.
XIII.—On the Operational Solution of the Homogeneous Linear Equation of Finite Differences by Generalised Continued Fractions
Authors: Milne-Thomson L. M.
Published: June 2016

The homogeneous linear equation of the second order may be solved by means of a, continued fraction whose elements are coefficients in the equation. The two dimensional continued fraction is generalised to m dimensions and yields the solution of the equation of the mth order.
XVI.—Fourier Integrals
Authors: MacRobert T. M.
Published: June 2016

1. Fourier's Integral Theorem.—In a former paper it was shown that certain formulæ, usually obtained by means of Fourier's Integral Theorem, could also be proved by contour integration: and, indeed, Fourier's Integral Theorem can be established by this method. The functions involved must be holomorphic, so that the proof does not justify the application of the theorem to such wide classes of functions as the usual proof by means of Dirichlet Integrals. In what follows it will be assumed that all the integrals are convergent, and the changes of order of integration justified. Fourier's Integral Theorem will be proved in the following form.
XX.—Note on Cayley's Elimination-problem involving Superfluous Data
Authors: Muir Thomas
Published: June 2016

1. The given set of equations in question is

and the problem was solved by Cayley in the Quarterly Journal of Mathematics, viii, pp. 183–185. The method was peculiar and is still interesting. He introduced three additional unknowns, deduced a fresh set of five equations, from which he then proceeded to eliminate four unknowns, namely, the new three and x/y.
IV.—Experiments and Observations on Crustacea: Part I. Immersion Experiments on Ligia
Authors: Tait John
Published: June 2016

Descended from marine ancestors, Ligia oceanica, like other members of the sub-order (Oniscoidea or “slaters”) to which it belongs, has adopted a terrestrial mode of life. The other Oniscoidea have spread inland, invading regions far from the sea. Ligia, known as the sea-slater, is confined to the coastal fringe, and may possibly form a link between marine isopods and the more truly terrestrial forms.
VI.—Experiments and Observations on Crustacea: Part III. Limb-Flexures and Limb-Taxis in the Peracarida
Authors: Tait John
Published: June 2016

1. Each walking leg of Ligia shows three prominent flexures arranged alternately in one plane. Generally speaking, the planes of flexure of the whole series of seven limbs are transverse to the body, the basipodites flexing medially; this arrangement, here called isopodan limb-taxis, is associated with clinging power.

2. In Amphipoda and in Tanaidacea there are likewise three chief flexures in the limb, which are also arranged tri-alternately and in one plane. In the Tanaidacea the basipodites project laterally not medially. In the Amphipoda the basipodites flex antero-posteriorly. Tanaidacean limb-taxis seems to be the primitive form.

3. The tri-alternate flexion-complex in each limb of these Peracarida, as well as in certain limbs of Cumacea, is a reptant feature; so is the separation of the seven limbs into two opposing groups: an analogy with the limbs of reptant vertebrates is here traced. By simple inspection it is usually possible to say if a crustacean limb used for swimming has been secondarily modified from a reptant limb.

4. The flexion-complex in the limbs of reptant Eucarida is neither tri-alternate nor uniplanar as in the limbs of reptant Peracarida. This distinction is of more importance than that suggested by Boas, which relies upon the amount of flexion possible at the mero-carpal and at the carpo-propodal articulation respectively.

5. The Peracarida, like the Decapoda, may be divided into natant and reptant forms, with intermediate links. Of the reptant forms only those with isopodan or amphipodan limb-taxis have shown themselves capable of adopting a land life.

6. It is suggested that Phreatoicus may in progression employ its posterior peraeopods or its pleon in the same way as a Gammarus. Should it be found that the animal does so, one could formulate additional correlations between structure and function; these would involve vertical pleural plates, uropods, and the number of free segments in the pleon.

7. Considerations relating to limb flexures and limb-taxis have been tentatively applied to the classification of the Isopoda.

8. The different forms of limb-taxis in the Peracarida and certain features involving the flexion-complex, present problems analogous to the rotation and torsion that occur in the fore-limb of a developing mammal.

9. In a discussion on homology and analogy it is pointed out that homology in the sense of homoplasy (Lankester) cannot be effectively distinguished from analogy. The systematic study of analogies would appear to be more worthy of consideration than is generally acknowledged.
VIII.—The Family Budgets and Dietaries of Forty Labouring Class Families in Glasgow in War Time.
Authors: Ferguson Margaret
Published: June 2016

The following study of the diet of labouring class families in Glasgow was made as part of an investigation upon the etiology of rickets at present being carried out in the Physiological Department of the University of Glasgow. But the information gathered by Miss Lindsay in her study of the diet of the same class in 1911–1912 makes possible a very interesting comparison between the conditions of living then and under the present war conditions, and the fact that these studies extended over three periods—(1) Summer of 1915, (2) Winter of 1915, (3) Spring of 1916 —enables some idea of the progressive effects of war conditions to be obtained. Forty families have been studied.
X.—Darwinism and Human Civilisation, with special reference to the Origin of German Military “Kultur.”
Authors: Munro Robert
Published: June 2016

In 1859 the scientific world was startled by the publication of Charles Darwin's book on the Origin of Species, a work in which he advocated the doctrine that the various species of animals and plants, now inhabiting the globe, have been evolved by means of secondary causes from pre-existing and less differentiated forms of life—a process which he designated by the name of “Natural Selection.” This theory is founded mainly on the struggle for existence which all living organisms have to undergo, not only against their natural enemies, but the overcrowding of their own species. The intensity of this contest becomes apparent to any careful observer who takes the trouble to look beneath the surface of his environment at the marvellous activity of the agencies at work in producing the countless living organisms which now tenant the earth. The most striking feature of these genetic operations, besides the astonishing number of seeds, fruits, eggs, young animals, etc., which come so profusely into existence, but of which so few come to maturity, is that those who survive have apparently no higher purpose in life than the propagation of their own species. Notwithstanding the activity of the never-ending agencies by which life is thus kept up as a going concern, the stock of wild animals, i.e. animals not in a state of domestication, seldom vary from year to year. The consequence of so profusely overcrowding the environment with the offspring of plants and animals is the premature death of the vast majority.
XIII.—The Arithmetical Mean and the “Middle” Value of Certain Meteorological Observations
Authors: Becker L.
Published: June 2016

The arithmetical mean of similar meteorological observations is usually regarded as their representative value. The object of this paper is to show that in a certain case this assumption is not borne out by observations.
XVIII.—Vanishing Aggregates
Authors: Metzler William H.
Published: June 2016

In 1888 Dr Thomas Muir gave the following theorem:—

Theorem A.—If any two determinants A and B of the nth order be taken, and from these two sets of determinants be formed, namely, first, a set of nCr determinants, each of which is in r rows identical with A and in the remaining rows with B; and, secondly, a set of the same number of determinants each of which is in r columns identical with A and in the remaining columns with B, then the sum of the first set of determinants is equal to the sum of the second set.
XXI.—Contributions to the Knowledge of the Family Chermesidæ. No. I.: The Biology of the Chermes of Spruce and Larch and their Relation to Forestry
Authors: Steven H. M. , MacDougall R. Stewart
Published: June 2016

Extensive and intensive research on the Chermes group has been carried out on the Continent during the last ten years, but there has been no close study of this group in Britain. This paper is a record of introductory research in this country on this complex but interesting and important group.
V.—On the Connexion between Linear Differential Systems and Integral Equations
Authors: Ince E. L.
Published: June 2016

This paper summarises the results of an attempt to extend the theory upon which the relationship between linear differential equations and integral equations is based. The case in which the nucleus K(x, s) of the integral equation arises as a Green's function is well known; the nucleus is there characterised by its having discontinuous derivates when x = s. The method here dealt with is virtually an extension of Laplace's and analogous methods for solving linear differential equations by definite integrals, and leads to nuclei which are continuous and have continuous derivates for x = s.
VI.—Myriapods collected in Mesopotamia and N.W. Persia
Authors: Evans W. Edgar , Brolemann Henry W.
Published: June 2016

The Myriapods recorded in this paper were collected in Mesopotamia—mostly at and around Amara on the Tigris—and in the neighbouring uplands of N.W. Persia, by W. K. Evans, B.Sc., Edinburgh, late Captain R.A.M.C.

They are referable to seventeen forms: of these eight are new and three could not be identified owing to want of appropriate material. Amongst the novelties two specimens deserve special mention as belonging to an lulid group, the known representatives of which are very few. The new genus Calyptophyllum has been erected for these.
XIII.—The Magnetic Character of the Quantum
Authors: Allen H. Stanley
Published: June 2016

Calamoids—the four-dimensional tubes of electromagnetic force introduced by Professor Whittaker in a communication in November 1921—are not referred to in his work “On the Quantum Mechanism in the Atom” (see pp. 129–142), in which he is content to deal with three dimensions; but there is at least one point of contact between the two papers. The four-dimensional tubes include as particular cases both kinds of Faraday tubes (electric and magnetic), and magnetic forces are treated as on an equality with electric forces. In seeking for a mechanism to elucidate the quantum, a magnetic model is employed; and although Professor Whittaker is careful not to insist on the magnetic structure suggested, careful examination of his paper shows that some form of magnetic element is required both for the absorption of energy by the atom from the electron and for the transformation of the absorbed energy into the radiant form.
XV.—The Importance of Professor Whittaker's Atomic Model and of other Atomic Models
Authors: Peddie W.
Published: June 2016

The atom, even in its simplest form, must possess a most complicated structure. The aim of physical science is to find a hypothetical structure, and mode of its functioning, which will give a good account of atomic phenomena. When the phenomena are complicated, and only very partially known, hypothetical investigations are most uncertain and provisional, and make little attempt to work otherwise than by analogy or illustration. In such cases help is often obtained through the discovery of a general law which unifies a wide range of phenomena, and which may be followed by many diverse structures in their activities. Well-known examples are found in the law of conservation of energy, the law of least action, and, recently, the law of quantum action.
XVII.—The Quantum Theory of the Secondary Spectrum of Hydrogen
Authors: Marshall John
Published: June 2016

It is proposed in this paper to consider the spectral lines which would arise in the case of an electron describing an orbit about two centres of attracting force. The assumptions of the Quantum Theory as generalised by Wilson and Sommerfeld are made. The centres of attracting force are assumed, as in the simpler applications of the Quantum Theory, to be at rest. Such a spectrum would arise in the case of a hydrogen molecule which had lost one electron and in which the remaining electron described an orbit about the positive nuclei. Novikoff has shown that this configuration would be stable (vide Whittaker's Analytical Dynamics, 2nd ed., p. 407, ex. 1). It follows that, if at any stage an electron were withdrawn from a molecule, the remaining electron would describe a stable orbit. Much experimental work has been done on the secondary spectrum of hydrogen, but I am not aware that any theoretical explanation has been given of the immense number of lines found by experiment. Dufour in Ann. de Chimie et de Physique, 1906, gives a very complete account of the work done on this spectrum and the various controversies which it has evoked. Dufour's conclusion is that the spectrum of the atom is the primary spectrum, and that the secondary spectrum is due to the molecule. H. E. Watson in Proc. Roy. Soc., vol. lxxxii, 1909, states the main points at issue, and gives the most modern measurements of the lines and compares his results with wavelengths found by Hasselberg (Mém. Acad. Imp. St Petersburg, vol. xxxi, 1883), Ames (Phil. Mag., vol. xxx, 1890), and Frost (Astrophysical Journal, vol. xvi, 1902).
XVIII.—On the Application of the Gyroscope to the Solution of the “Vertical” Problem on Aircraft. Part I
Authors: Gray James Gordon , Gray J.
Published: June 2016

Before the advent of the aeroplane and airship the gyroscope derived its practical importance from its applications to the torpedo and the gyroscopic compass, and neither of these applications originated in this country. With the introduction of aircraft the applications of the gyroscope become very numerous and of great importance. Navigation of such craft must be made precise by the provision of gyroscopic sextants; photography from aeroplanes, to be accurate, must be carried out by means of special cameras stabilised so that the photographs are true vertical productions; war aeroplanes must be steered and controlled in accordance with accurate dynamical principles, and in this respect the claims of the gyroscope cannot be ignored; bombing from aeroplanes must be rendered accurate by designing the bombsight as part of an accurate stabiliser; battleships must be provided with anti-aircraft devices controlled by stabilisers, and the guns on such ships must be controlled both with respect to the vertical and the horizontal, and in azimuth, by means of instruments of the greatest precision.
XX.—On Self Light, Fatigue, Inhibition, and Recurrent Visual Images
Authors: Peddie W.
Published: June 2016

In an earlier note communicated last session the action of self light and fatigue was partially considered. The question of the origin of these effects is one which can only be settled by observation or experiment. The question of the mathematical form of the laws regulating the effects also requires an observational or experimental basis. In the absence of self light, Fechner's well-known law that the change in sensation is proportional to the fractional change in the stimulus forms a close approximation to results of experience throughout a wide range of intensity. Fechner's modification of this law, by the addition of a constant term to the denominator of the fraction, was shown by Helmholtz to account broadly for the action of self light; and he showed also that the introduction of three such constants into three such independent fractions enabled a good description to be given of various phenomena of colour vision in light of different intensities. But, from the phenomena of vision, it is certain that the numerical values of the parameters are influenced by antecedent as well as present illumination. Thus the parameters are really functions which are variable in more than one way, and the form of these functions can only be found by observation. This is the subject of the note referred to above.
XXIII.—Notes on a Correspondence between the French Academy of Sciences and the Royal Society of Edinburgh regarding the Invention of the Pilot Cable (Câble Guide)
Authors:   The General Secretary
Published: June 2016

During 1921 the Academy of Sciences of France awarded a medal and prize to M. W. A. Loth for various important devices having special application to navigation. Among these was mentioned the system of the Câble Guide, which is essentially the system of Pilot Cable invented by Mr C. A. Stevenson, C.E., and described by him in 1893 in the Proceedings of the Royal Society of Edinburgh. In a communication to the Académie des Sciences the Council of the Royal Society of Edinburgh called attention to this fact and to the further fact that apparently no recognition had been given of the pioneer work of Mr Stevenson.
Some Further Results obtained with the Spectroheliometer
Authors: Halm J.
Published: June 2016

In a paper published in vol. xli., part i., of the Transactions of this Society, entitled “Spectroscopic Observations of the Rotation of the Sun,” I communicated the first results obtained with a spectroscope specially designed for the purpose of measuring the displacements of the solar lines on opposite limbs of the sun occasioned by the motions of the absorbing gases to or from the observer in consequence of the sun's axial rotation. The investigation was originally undertaken with the view of ascertaining whether the peculiar law of surface rotation of the sun, first discovered by Carrington from the motions of solar spots, and afterwards confirmed by Dunér from spectroscopic observations similar to my own, was, or was not, subject to alterations depending on the general state of solar activity.
Preliminary Note regarding an Experimental Investigation into the Effects of Varying Diets upon Growth and Nutrition
Authors: Watson Chalmers , Schäfer E. A.
Published: June 2016

I. The use of an excessive meat diet in rats induces a deterioration in the health of the animals. This deterioration is shown in (a) an imperfect physical development, (b) a loss of reproductive power, (c) defective lactation, and (d) a high mortality in early life in the second generation of meat-fed subjects.

II. The recuperative powers of these deteriorated animals, on a normal diet, is very striking.

III. In animals deprived of their ovaries, the minimum amount of proteid required is less than in normal females.
On the Formation of certain Lakes in the Highlands
Authors: Collet Léon W. , Murray John , Johnston T. N.
Published: June 2016

Loch Muick (see fig. 1) lies at the head of Glen Muick, at a height of 1310 feet, on the property of His Majesty the King. On both sides of the loch the mountain slopes rise precipitously from the water's edge, and reach a height of 2400 feet on the south-east and from 2326 to 3352 feet on the north-west. The rocks surrounding the lake are granite.

The loch trends in a N.E. and S.W. direction, and is miles in length, the maximum breadth being ½ mile at the north-eastern end. The maximum depth recorded is 256 feet, and the mean depth calculated from the volume of water is 111·69 feet, approaching the half of the extreme depth. The ratio of maximum depth to the length is 46.
On the Distribution of the Proper Fractions
Authors: Sommerville Duncan M. Y.
Published: June 2016

In statistical work which deals with integral variates, the data frequently appear in the form of ratios, or unreduced proper fractions, e.g. sex- and fecundity-ratios; and to facilitate comparison these are arranged in classes, all the ratios falling within the same class being considered as equivalent. These classes must, as far as possible, contain an equal number of the ratios. Further, in certain fields the different kinds of ratios do not all occur with the same frequency, that is, one denominator will occur more frequently than another, without any reference to the number of fractions having this denominator.
Recherches sur la Glauconie
Authors: Collet Léon W. , Lee Gabriel W. , Murray John , Murray John
Published: June 2016

Depuis Murray et Eenard deux travaux importants sont venus enrichir la bibliographie de la Glauconie: le mémoire de MM. Calderon et Cliaves, “Contribuciones al estudio de la Glauconita,” et l'œuvre magistrale de M. L. Cayeux,Etude micrographique des terrains sédimentaires.

Murray et Eenard avaient étudié spécialement la Glauconie actuelle; MM. Calderon et Cliaves baserent leur synthese de la Glauconie actuelle sur une analyse de Glauconie des roches sédimentaires; M. L. Cayeux limita strictement ses belles recherches à la Glauconie des roches sédimentaires et n'attaquapas le problème de sa genèse.
The Theory of Circulants in the Historical Order of Development up to 1860
Authors: Muir Thomas
Published: June 2016

So far as mathematical writers have as yet noted, a set of equations of the type

had not made its appearance in mathematical work prior to the year 1846: and it is almost absolutely certain that before that year the determinant of such a set had never been considered. It is not at all unlikely, however, that the expression

which is the case of the determinant for n equal to 3 had more than once turned up in other connections, and that its divisibility by a + b + c had been noted: but of this, too, there is no record.
The Hessians of Certain Invariants of Binary Quantics
Authors: Muir Thomas
Published: June 2016

(1) The cubinvariant J of a binary quartic being

its Hessian, H(J), is

Performing on this the operations

and on the result the operations

we obtain

The three-line determinant here is seen to contain c as a factor, because it manifestly vanishes when c is put equal to 0.
The Sum of the r-line Minors of the Square of a Determinant
Authors: Muir Thomas
Published: June 2016

(1) If we temporarily denote the product of the rth and sth rows of a determinant Δ by rs, we shall have conveniently
I.—Lord Kelvin: A Centenary Tribute
Authors: Ewing J. Alfred
Published: June 2016

In this the centenary year of Lord Kelvin's birth it is fitting that the Society should call to remembrance one who was for long its most distinguished Fellow, who first became its President at the age of thirty-nine, and was repeatedly re-elected to the office, which he held for twenty-one years in all, and who used the Society as a medium for the publication of many of his most brilliant discoveries. In the long list of his published papers there are at least one hundred and twenty items communicated to the Royal Society of Edinburgh. No other contributor has done so much to give to our Proceedings and Transactions a world-wide and lasting fame. It was to this Society that he brought, in 1849, his account of Carnot's Theory, which marks the beginning of his study of Thermodynamics, and it was in our Transactions that he published his epochmaking series of papers on the “Dynamical Theory of Heat” from 1851 to 1854. It was here in 1852 that he propounded the doctrine of the Dissipation of Energy. It was here that his investigations of underground temperature and the secular cooling of the Earth appeared in 1860 and 1862. It was here in 1865 that he “briefly refuted” the doctrine of Uniformity in Geology. Here, too, were published his long series of papers on Vortex Motion and Vortex Atoms, from 1867 to 1881, and much of his work on the molecular constitution of matter. Here he first showed, in germ, his mariner's compass, in 1874.
III.—A Series Formula for the Roots of Algebraic and Transcendental Equations
Authors: Aitken A. C.
Published: June 2016

The object of this paper is to communicate a general formula for elementary symmetric functions of any assigned degree of a given number of the roots, in ascending order of magnitude, of an algebraic or transcendental equation with complex coefficients. In virtue of the simple relations that exist between these symmetric functions, the formula gives a literal expression in terms of infinite series for all the roots of an equation. In practice it is generally desirable to transform the equation first into one with roots widely separated in value (e.g. by the root-squaring process) in order to make the convergence of the series sufficiently rapid for satisfactory numerical computation.
XI.—The Modes of Vibration of a Stretched Membrane with a Particular Law of Density
Authors: Ince E. L.
Published: June 2016

In this paper it is proposed to study the problem of the vibrations of a uniformly-stretched membrane whose superficial density σ depends upon the distance r from a fixed point in the membrane in accordance with the law

in which C and a are constants. The constant a will be known as the critical radius and the circle r = a as the critical circle.
I.—Craniological Observations on the Lengths, Breadths, and Heights of a Hundred Australian Aboriginal Crania
Authors: Robertson A. W. D.
Published: June 2016

The present work forms the first portion of an investigation into the craniological characters of the Australian aboriginal crania at present being conducted by the author, and is part of a general scheme for the osteological investigation of the Australian aboriginal initiated by the Professor of Anatomy in the University of Melbourne.

There are, as is well known, two methods of treating craniometric statistics, and which, for convenience, may be designated (1) The Empirical Method; (2) The Rational Method.

The object aimed at in both is to find numbers that shall be characteristic of the race of any country.

“The Empirical method places very little value on the length and breadth of a skull except as a means of arriving at their ratio—the cephalic index—‘the subdivisions of which,’ says Gray (15), ‘are all arbitrary.’ Some, e.g. Retzius, made use of centres; others, e.g. Welcker, made use of limits, and there appears to be no special reason for fixing the limits of the groups at one index more than another. The analysis of craniometrical statistics by this method becomes comparatively simple: calculate the cephalic index and other indices for each individual, and find the average or mean index for the whole group of people measured. The highest and lowest index is usually stated as indicating the range of variation on each side of the mean. As the range of variation of the cephalic index is usually quite as great as the range of variation of the absolute dimensions, it is difficult to understand the belief in the value of indices of the Empirical school.”
II.—A Biometrical Study of the Relative Degree of Purity of Race of the Tasmanian, Australian, and Papuan
Authors: Berry Richard J. A. , Robertson A. W. D. , Cross K. Stuart
Published: June 2016

If the marked divergence of ethnological opinion concerning the degree of racial purity or admixture of theAustralian aboriginalaffords evidence of anything at all, it can only be of the fact that the problems of his origin, as of his degree of racial purity, are not yet solved. Not only are there the most conflicting opinions on these points, but the cognate subjects of the origin, and degree of purity of the Tasmanian, and of his relationship, if any, to the Australian, are equally undetermined, whilst there is lastly the debatable point of the relation of both those primitive peoples to the Papuan.
VI.—Abnormal Bone Growth in the absence of Functioning Testicles
Authors: Geddes A. C.
Published: June 2016

At the instigation of the late Professor D. J. Cunningham, and at first working upon his material, the present writer has reinvestigated the problems of giantism and acromegaly.

In the course of the work a group of facts persistently presented themselves which appeared to indicate the existence of a definite antagonism between growth and sexual activity. Side by side with these, and in apparent contradiction of them, was the undoubted fact that the state of pregnancy does not in the young female impede growth, but, on the contrary, favours it. These are not new discoveries. The fact that sexual activity is inimical to growth has not infrequently been demonstrated, more especially by Pirsche (1), Launois and Roy (2) Poncet (3), and Lortet (4). Indeed Pirsche, in the Thèse de Lyon, “De l'lnfluence de la Castration sur le DéVeloppement du Squelette,” 1902, might almost be said to have established beyond reach of question the fact that castration in youth is followed by abnormal growth of the long bones.
VII.—The Development of the Germ Cells in the Mammalian Ovary, with special reference to the Early Phases of Maturation
Authors: Louise McIlroy A.
Published: June 2016

Although much literature has been published on the minute anatomy of the ovary, there are many controversial points remaining, and therefore the publication of the results of the examination of various mammalian types adds additional proof to the facts already staged by embryologists. Three years ago this work was taken up by me as a preliminary to an investigation into the distribution of the chromatic substance in cells which show malignant degenerative changes. The work has occupied so much time that the publication of the results has been necessarily delayed. In a paper on “Primary Cancer of the Ovary,” published in 1906, I stated, as the result of a somewhat limited observation on the later stages of the development of the human ovary, that the cells of the stratum granulosum were mesoblastic in origin. This view I have modified by the more thorough and extensive investigation of the present paper.
IX.—A Quantitative Study of the Constitution of Calomel Vapour
Authors: Smith Alexander , Menzies Alan W. C.
Published: June 2016

The vapour density of calomel vapour corresponds to the formula HgCl or Hg + HgCl2. Odling showed, by amalgamation of gold-leaf, the presence of free mercury. Harris and V. Meyer separated mercury from the vapour by diffusion, and also showed that solid potassium hydroxide turned yellow (HgO) when plunged into the vapour. Diffusion might naturally increase the dissociation, and even a pure mercurous salt would certainly give mercuric oxide at 240–260°, since at that temperature mercurous oxide is unstable. The quantitative conclusion of these observers, namely, that the vapour is completely dissociated, therefore, was not in any way justified by their qualitative experiments, although it has been accepted by many chemists.
XII.—The Temperature Seiche. Part I. Temperature Observations in the Madüsee, Pomerania. Part II. Hydrodynamical Theory of Temperature Oscillations in Lakes. Part III. Calculation of the Period of the Temperature Seiche in the Madüsee. Part IV. Experimental Verification of the Hydrodynamical Theory of Temperature Oscillations
Authors: Wedderburn E. M. , Williams A. M.
Published: June 2016

This paper is published at length in the Transactions of the Society, vol. xlvii., part iv., p. 619, and describes observations in the Madiisee, Pomerania, made by Professor Halbfass and Mr Wedderburn, with the view of testing the latter's theory of temperature seiches in lakes, arrived at from a consideration of the observations of the Scottish Lake Survey.
XIV.—The Mathematical Theory of Random Migration and Epidemic Distribution
Authors: Brownlee John
Published: June 2016

The general theory of epidemic disease I have already considered in a communication to this Society. In that communication I showed that the course of epidemics of all forms of infectious disease obeyed certain very definite laws. In the same paper it was also shown that the distribution of epidemic disease in a uniformly populated area obeyed a law essentially similar. Certain reasons were given why the normal curve of error might be expected to give an approximate solution in both the cases considered, but why the distribution actually found (type iv.) should be the common form was not at all clear. I think, however, I have now arrived at the solution.
XVII.—The Theory of Recurrent Determinants in the Historical Order of Development up to 1860
Authors: Muir Thomas
Published: June 2016

Like Wronskians, and for the same reason, recurrents were at first dealt with among “Miscellaneous Special Forms”: their previous history is thus to be found under Wronski 1812, Scherk 1825, and Schweins 1825 in the chapter so entitled. (History, i. pp. 472–474, 478–481.)

The name is quite recent, having been first proposed by E. Pascal in 1907 in a paper published in the Rendiconti …. 1st. Lombardo, (2) xl. pp. 293–305.
XX.—On the Determination of Small Degrees of Enzymatic Peptolysis
Authors: Court Dorothy
Published: June 2016

In studying the conditions under which enzymes are produced in seeds at the beginning of germination, two main difficulties have been encountered. The one has been in devising means of maintaining sterility in the material without at the same time interfering with the formation and action of enzymes. Some experiments have been carried out with the object of determining the relative efficiency of some of the more commonly used antiseptics, but, at present, these are not sufficiently far advanced to admit of any general conclusions being drawn. They have, however, shown that saturation with chloroform ensures sterility under the conditions of the experiments which form the subject of this paper. The other difficulty has been in demonstrating small degrees of enzymatic activity. It is with this latter question I wish to deal here.