bluuebunny/crossref_metadata_2025 huggingface dataset:
XIII.—Ions and Isotopes
Authors: Kendall James
Published: June 2016

The fact that the atomic weight of an element is not invariable, but that the same element may exist in two or more forms which are chemically identical even though their atomic weights differ, was first noted by Soddy (1910, p. 285) in connection with radioactive elements. A little later Thomson (1913) showed, by the method of positive ray analysis, that neon, with an average atomic weight of 20·2, was a mixture of two kinds of atoms with masses 20 and 22 respectively. The brilliant extension of this method of attack by Aston has established that the majority of the common elements are similarly inhomogeneous. Chlorine (35·457) is a mixture of Cl35 and Cl37; lead (207·22) exists in as many as eight forms, with atomic masses ranging from 203 to 210. These chemically-identical species of the same element with diverse masses are known as isotopes.
XXII.—Some Distributions associated with a Randomly Arranged Set of Numbers
Authors: Kermack W. O. , McKendrick A. G.
Published: June 2016

In the course of a search for criteria which would assist in deciding whether a particular series of numbers was randomly arranged, it was found necessary to investigate some of the more obvious characters of a random series of numbers. If the series is an infinite one and all the numbers are unequal (the series of decimals between o and 1 selected in some random fashion may be considered) certain of the numbers will be maximal, that is greater than their immediate neighbours, whilst others will be minimal, that is less than their immediate neighbours. Every maximal number is succeeded by a run down, that is by a series of descending numbers ending in the succeeding minimal number. The length of a run down is the number of numbers it contains, including the maximal number which begins it and the minimal number which ends it. The length of a run up is similarly defined. Clearly the minimum length of a run is 2.
XXIII.—On Rotating Mirrors at High Speed
Authors: Boys Charles V.
Published: June 2016

I have read the observations of Dr R. A. Houstoun at the top of p. 164 of the current volume of these Proceedings, and I gather the impression that he has been dissuaded by general beliefs of what cannot be done from using the simplest of all possible methods. Forty-five years ago when I required a very high speed of rotation I completely ignored or defied these general beliefs with the greatest success, and it seems to me to be possible that a few words on my practice might be useful. If this is the case I should feel that as a newly appointed Hon. Fellow of the Royal Society of Edinburgh I had at least done what I could in recognition of that honour.
II.—Dating of Late-Glacial Clay Varves in Scotland
Authors: De Geer Gerard
Published: June 2016

During a visit to Scotland this autumn I had the opportunity of meeting Dr John B. Simpson and of discussing with him the desirability of definitively dating, by varve-measuring, the interesting ice-oscillation which he had described from the southern slope of the Scottish Highlands (1933).
V.—The Mathematical Representation of the Energy Levels of the Secondary Spectrum of Hydrogen.—II.
Authors: Sandeman Ian
Published: June 2016

In a recent paper (Sandeman, 1933) the question of the mathematical representation of the energy levels of the hydrogen molecule by methods based on the old mechanics has been considered. In view of the fact that the wave mechanics has supplanted the older theory, the further application of newer methods to this spectrum is desirable. Richardson and Davidson (1929 b, p. 45) worked out the potential energy function U(ξ) (ξ is denned on p. 51) for the state IsσЗpπ3Π on the old quantum mechanics and on the wave mechanics with the following results: U(ξ) = 5·50ξ2(1 – 1·556ξ + 1·58ξ2 – 1·56ξ3) volts on the old quantum mechanics and U(ξ) = 5·71ξ2(1 – 1·55ξ + 1·58ξ2 – 1·59ξ3) volts on the wave mechanics. They also (loc. cit., pp. 30 and 31) gave the U(ξ)'s for the states Isσ2pσ1∑, Isσ2sσ3∑, and IsσЗdπ1Πb, and on p. 45 they gave the formulæ, based on Fues's (1926) results, for transcribing the old quantum mechanics into the wave mechanics series. Richardson and Das (1929, pt. ii) gave similar data for the state IsσЗpσ3∑.
VI.—On Singular Pencils of Zehfuss, Compound, and Schläflian Matrices
Authors: Ledermann W.
Published: June 2016

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

When all pencils concerned are non-singular (i.e. when their determinants do not vanish identically), the problem is equivalent to finding the elementary divisors of the pencil. This has been solved by Aitken (1935), Littlewood (1935), and Roth (1934). In the singular case, however, the so-called minimal indices or Kronecker Invariants have to be determined in addition to the elementary divisors (Turnbull and Aitken, 1932, chap. ix). The solution of this problem is the subject of the following investigation.
X.—Note on Fracture
Authors: Jeffreys Harold
Published: June 2016

Dr Anderson's paper (Proc. Roy. Soc. Edin., vol. Ivi, 1936, pp. 128–157) is of considerable interest as a contribution both to geology and to the theory of elasticity. One of his assumptions about fracture, however, has little support, and I am inclined to think that some difficulties that he mentions towards the end would be lessened if it were removed. This assumption is that the complete form of a fracture surface can be inferred directly from the distribution of stress before fracture, intersecting the surfaces of principal stress at some constant angle. It is often to be found in both geological and mechanical literature; but it rests on no theoretical grounds and is, I think, untrue.
III.—Supernumerary Pectoral Fins in Raia circularis Loudon
Authors: Harper W. F.
Published: June 2016

A Male Sandy Ray (Raia circularis Loudon) caught in the North Sea, off Aberdeen, measured 47·5 cm. broad by 43 cm. long (excluding the tail) and exhibited an abnormality which is of very rare occurrence. This consisted of two well-developed fins situated ventrally and associated with the pectoral girdle and the last two branchial arches. The measurements of the fins in the formalin-hardened specimen were as follows: length, 8 cm.; breadth at base, 1·3 cm.; breadth at free end, 2 cm. (left), 3·2 cm. (right); thickness at base, 0·7 cm. The integument covering the lateral and medial borders of the proximal portion of each fin was continuous with that over the fourth and fifth gill clefts respectively. In addition, a strong fold of integument bound the proximal fourth of each fin to the ventral aspect of the body of the fish (fig. 1). A brownishred pigment was present on the ventral aspect of the terminal third of each, and a less marked pigmentation of the same colour on the dorsal aspect of the middle third. Small denticles, similar to those found elsewhere on the fins, were numerous on the distal third, but were more abundant on the dorsal aspect.
IX.—The Intellectual Resemblance of Twins
Authors: Herrman Louis , Hogben Lancelot
Published: June 2016

The characteristics of social behaviour in man are conditioned by previous experience. What is observed is the product on the one hand of a certain genetic constitution and on the other of an intricate, prolonged, and at present largely obscure, process of training and physical environment, including both the environment of the fœtus and family influences, social and physical. The experimental methods for detecting differences due to single gene substitutions cannot be applied directly. Indeed, we can see no immediate prospect of applying to social behaviour methods of genetic analysis such as have led to the mapping of the chromosomes in animals and in plants. With methods available at present, genetic inquiry can undertake to detect whether any gene differences are associated with observed differences, and whether such gene differences are recognisable throughout a comparatively wide or narrow range of social and physical environment.
XVII.—The Effect of Consanguineous Parentage upon Metrical Characters of the Offspring
Authors: Hogben Lancelot
Published: June 2016

The theoretical treatment of consanguineous unions in human populations has been the subject of several publications, notably by Dahlberg (1927), by Haldane and Moshinsky (1933), and by the present writer (1933). In these attention has been directed to the concentration of discrete characters among the offspring of related parents in a community mating at random. This communication is a contribution to the more general problem of variability which can be expressed in metrical terms. Its theoretical interest resides in the fact that deductions from the genetical theory of inbreeding are open to little, if any, ambiguity, when used as an instrument for detecting gene differences whose manifestation is considerably modified by differences of environment prevailing in human societies. Two criteria will be examined. The first is the effect of consanguineous parentage upon the correlation of their offspring both when autosomal and sex-linked transmission occur. The second is the comparison of the variance of a group of individuals with consanguineous parents with that-of a group of individuals with unrelated parents taken from the same social environment. Since first cousin marriages constitute the type of relatively close inbreeding most commonly encountered in practice, the inquiry which follows is confined to the treatment of unions between first cousins.
XX.—On the Theory of Statistical Regression
Authors: Bartlett M. S.
Published: June 2016

1. The product moment distribution in the general case of p normal variates, obtained in 1928 (1), and again in 1933 (2), has been awaiting further analysis. Some indication has already been given (Wishart, 1928) that new results might be expected from it; in the particular case of two variates obtained previously by Fisher (3), it has been used to deduce the distributions of the correlation coefficient (3), co-variance (4), and regression coefficient (5). In the general case, it has been used by Wilks (6) to furnish a proof of Fisher's distribution of the multiple correlation coefficient (7), and also in connection with his idea of a generalized variance (8). Further analysis appears to be most fruitful in studying statistical regression in general. It is shown in Part I of this paper that the product moment distribution can be split up into a chain of independent factors. Most of the known distributions related to regression or partial correlation are simply obtained, in a manner which clearly indicates the relations they bear to one another; the distribution of a partial regression coefficient of any order is also readily derived.
Remarks on the Rainfall Records in the Talla Drainage Area during the years 1896 to 1902
Authors: Donald P. D.
Published: June 2016

A striking feature of the results obtained at the seven gauges in the drainage area is the divergence from the commonly accepted relation between rainfall and height above sea-level. The following table shows the “theoretical” amounts of rainfall, averaging 62·51 inches, that might have been expected at the several gauges, on the assumption that there was a uniform increase of 3 per cent. for every 100 feet of rise ; and in comparison with these, the amounts actually recorded, also averaging 62·51 inches.
Some further Results in the Mathematical Theory of Seiches
Authors: Chrystal
Published: June 2016

§ 1. In the practical calculation of the periods and nodes of the lakes we have hitherto examined it has been found that the use of the Seiche Functions gives the best results. Indeed, as will appear from details presently to be submitted to the Society by Mr E. M. Wedderburn and myself, the agreement between theory and observation, so far as we have gone, is beyond what might reasonably have been expected. Also the phenomena of concave lakes, i.e. such as have no shallows or points of minimum depth, are easily deducible from the formulæ given in an abstract (Proc. R.S.E., vol. xxv. p. 328, 6th Oct. 1904) which I communicated to the Society on 18th July 1904. On the other hand, the theory of convex lakes is less easy of manipulation, chiefly owing to the difficulty in calculating the roots of the equations
Variant Forms of Vanishing Aggregates of Minors of Axisymmetric Determinants
Authors: Metzler W. H.
Published: June 2016

1. Vanishing aggregates of determinant minors have of late received considerable attention and are now becoming well known. From aggregates for axisymmetric determinants of the form given by Kronecker,* Muir,† or the present writer‡ we may get other forms, and it is the object of this paper to consider some of these new forms, and in particular to show that the general theorem given by Professor Nanson § is readily obtained from the vanishing aggregates of the type given by the present writer.
The Constitution of Complex Salts.—I. Derivatives of the Sesquioxides
Authors: Cameron Alexander T.
Published: June 2016

In a recent communication I described how I had obtained crystals of potassium hydrogen succinate showing only curved faces, from an attempt, up to the present unsuccessful, to prepare complex derivatives of succinic acid corresponding to the chromoxalates. In searching the voluminous literature of the subject for particulars of such complex salts I especially noticed two things,—first, the frequent but hitherto scarcely noted parallelism exhibited by these compounds; and second, the noticeable lack of uniformity in the formulæ attributed to them.
A Form of Bolometer adapted for Physiological Investigation
Authors: Colquhoun Walter
Published: June 2016

After a lecture on animal heat towards the end of last session, in which I described Langley's original form of bolometer, with its two iron gratings, and mentioned that Dr Stewart, of Philadelphia, had referred to the use of tinfoil and leadfoil gratings for physiological purposes in his text-book, I started to make a bolometer for our department. I should mention that some time ago Professor M'Kendrick, impressed by the probability of the bolometer being of use to physiologists, had communicated with Professor Langley, who kindly sent him, from Baltimore, literature dealing with the subject, and stated that the instrument was not made by an instrument-maker.
Complete Heart-block, with Dissociation of the Action of the Auricles and Ventricles
Authors: Ritchie W. T.
Published: June 2016

The ventricular rhythm differs from the auricular, firstly, on the occurrence of a ventricular extra-systole, and, secondly, in cases where there is allorhythmia due to depression of conductivity of the heart muscle. When conductivity is depressed, the contraction stimulus at regular or irregular intervals may be blocked at the auriculo-ventricular muscle bridge; so that whereas some stimuli induce both auricular and ventricular systole, others induce auricular systole alone, the ventricular systole being missed. That condition, incomplete heart-block, is of not infrequent occurrence in the human heart, and has been graphically recorded by Mackenzie (1), Finkelnburg (2), and other writers.
A Preliminary Communication on the Electrical Resistance of Various Urines
Authors: Turner Dawson
Published: June 2016

The object of this enquiry was to ascertain and compare the electrical resistances of various kinds of urine, both in states of health and of disease.

The measurements were made by means of a Wheatstone's bridge, with alternating currents, and a telephone according to Kohlrausch's method.

The fluids were held in a U-shaped electrolysis tube (a drawing of which accompanies this paper), of an internal diameter of about 1·55 centimetres, and containing a delicate thermometer. Two disc shaped platinum electrodes, each with a diameter of 1·4 c'm., were arranged so as just to rest upon the surfaces of the urine, with a very thin film of the fluid upon their upper surfaces.
The Tactics adopted by certain Birds when Flying in the Wind
Authors: Western R. W.
Published: June 2016

All who watch the flight of hawks or kites are struck by the extraordinary power they have of sustaining themselves for a long time, sailing about in the air without flapping their wings or making any conspicuous effort whatever.

Most birds of prey, as distinguished from game, are able to do this, and thus hold commanding heights from which, to descry food. The expression “wind-sucker,” as used by Ben Jonson, refers to the kestrel, a kind of hawk unsuited for falconry ; the astonishing way in which it keeps itself poised in the air, facing the wind with beak outstretched, led to the name, which implies the only explanation of the phenomenon that the science of those days could furnish. Sea-birds are also very proficient.
Ptomaïnes extracted from Urine in certain Infectious Diseases
Authors: Griffiths A. B.
Published: June 2016

The author has extracted ptomaïnes from the urine of patients suffering from certain infectious diseases by the following method :— (a) A considerable quantity of urine was made alkaline by the addition of a solution of sodium carbonate, and then agitated with half its volume of ether, (b) The ethereal solution (after standing) was filtered, and agitated with a solution of tartaric acid. The tartaric acid combines with any ptomaïnes present, forming soluble tartrates ; and the solution of tartrates forms the lower layer of the liquid mass, (c) The tartaric acid solution (after being separated from the ether) was also made alkaline by the addition of sodium carbonate, and was once more agitated with half its volume of ether. (d) The ethereal solution (after standing) was separated, and the ether allowed to evaporate spontaneously, (e) The residue (after drying over sulphuric acid) was treated with water, an excess of pure calcium hydroxide added, and the mixture evaporated on a water-bath. The residue so obtained was treated with chloroform and filtered. The filtrate (after evaporation) yielded the ptomaïne in an isolated and a crystalline condition.
Notes on the Wanyoro Tribe of Central Africa
Authors: Felkin Robert W.
Published: June 2016

The paper which I have the honour of presenting to you to-night is similar in construction to those I have previously brought under your notice on the For, Madi, and Waganda tribes.

As in former papers, I have written from notes of my own observations made when in the country and from information supplied me by people of the tribe. This time, however, in order to complete the description of the people, I have had recourse to the works published by Sir Samuel Baker, Dr Emin Pasha, Capt. Casati, and the late Dr W. Junker, and I have to acknowledge my indebtedness to these authors for information gleaned from their pages.
On the Renal Organs of the Asteridea
Authors: Griffiths A. B.
Published: June 2016

I have already shown that the secretion of the five large cardiac sacs of the stomach of Uraster rubens contains uric acid; and consequently these sacs are considered to be the necessary apparatus for eliminating the nitrogenous products of the waste of the tissues, “it is possible that the uric acid arrived into the starfish's stomach in the interior of small mussels, &c., whose excretory organs contain that body, and of which as food the starfish appears to be very fond: anyhow, such a source of the uric acid must be eliminated before Griffiths’ conclusion can be accepted; for obviously, if the presence of urates were demonstrated in the gastric contents of an individual who had recently supped off oysters, it would by no means follow that the stomach was the organ whereby the individual excreted his urates.” Certainly not; but Mr Durham has overlooked the fact that if the uric acid had been introduced along with the food, I should also have found urea in the contents of the starfish's stomach; but I conclusively proved that urea was absent.
XI.—The Minors of a Product-Determinant
Authors: Muir Thomas
Published: June 2016

1. If for aα+bβ+cγ+…we put

the the product of |a1b2c3| and |f1g2h3| may be written
XIV.—The Relation between Normal Take-up or Contraction and Degree of Twist in Twisted Threads when the Singles are of Unequal Sizes
Authors: Oliver Thomas
Published: June 2016

In a former paper (vol. xxvi., pt. iii., p. 186) the author proved that the contraction due to forming a single thread,

and the contraction due to the two-ply twisting,

where D = diameter of circle in which the axes of singles revolve.

d = diameter of single.

l = length of untwisted single.

L = length of twisted single.

n = turns of twist in single.

x = turns of twist in 2-ply.
XVI.—The Theory of Axisymmetric Determinants in the Historical Order of its Development up to 1860
Authors: Muir Thomas
Published: June 2016

A general account has already been given of this interesting paper—interesting as regards the subject, and interesting as being the author's first prentice effort. All that remains to be noticed here is what may be called Cayley's series of vanishing axisymmetric determinants.
XVII.—The Composition of the Red Clay
Authors: Clarke F.W.
Published: June 2016

In the volume upon Deep-Sea Deposits, issued as one of the reports of the Challenger Expedition, there are published twenty-five analyses of the “red clay.” This sediment is now recognised as the most extensive and important of all the oceanic deposits, for it covers 51,500,000 square miles of the sea-floor, and is characteristic of the greatest depths. It is therefore obviously desirable to know its average composition as exactly as possible, and for that reason the following investigation was undertaken.
XIX.—On Vibrating Systems which are not subject to the Boltzmann-Maxwell Law. (Second Paper.)
Authors: Peddie W.
Published: June 2016

1. In the first part of this paper (Proc. Roy. Soc. Edin., vol. xxvi., 1905.-6, p. 130), a method was suggested by means of which it might be found possible to discriminate amongst certain oscillatory dynamical systems according as they did, or did not, follow the law of equipartition of energy in their respective vibratory freedoms.
XXII.—Note on a New Species of Lepidodendron from Pettycur (Lepidodendron Pettycurense)
Authors: Kidston R.
Published: June 2016

Among the undescribed species of plants occurring in the well-known material of Calciferous sandstone age found near Pettycur, Fife, is an interesting specimen belonging to the older type of Lepidodendroid structure which has a solid primary xylem.
XXIII.—On the Application of a Differential Densimeter to the Study of some Mediterranean Waters
Authors: Manley John J.
Published: June 2016

From time to time various methods have been employed for the examination of samples of sea-water. Of these, the four which have been received most favourably by oceanographers are:—

(1) Estimation of the total combined chlorine per unit volume of water.

(2) Determination of the relative density.

(3) Measurement of the refractive index.

(4) Determination of the specific electric conductivity.
XXIV.—The Electric Conductivity and Refracting Power of ninety samples of Sea-Water, and a comparison of these with the Salinity and Density
Authors: Hill E.G.
Published: June 2016

There has been considerable discussion as to whether any physical constant of sea-water can be used to give an accurate measure of its total salinity, and from theoretical reasoning it would appear obvious that, in so complex a mixture, no physical constant can give an accurate measure of either the total amount of dissolved salts or of the chlorine present. In a paper communicated to this Society, Mr J. J. Manley showed that the optical method for distinguishing between various samples was as delicate as the relative density method, but the refractometer used was expensive and not fitted for use on board ship.
III.—The Optical Rotation and Cryoscopic Behaviour of Sugars dissolved in (a) Pormamide, (b) Water
Authors: Mackenzie John Edwin , Ghosh Sudhamoy
Published: June 2016

The optical rotation of a solution of sucrose in water was first measured by Biot (Mém., 1819, ii, 41) in 1819. He introduced the term “optical saccharimetry” for the method of estimation of sugar by measurement of its optical rotation.

In 1846, Dubrunfaut (Ann. Chim. Phys., 1846, xviii, 99) observed that the specific rotation of a freshly prepared aqueous solution of glucose decreased from an initial value of about + 110° to a constant value of +52°. The initial value being approximately double the constant value, he called the phenomenon “bi-rotation.” This term proved unsuitable in the case of other substances where a similar change of rotation took place, the initial and final values being rarely in the proportion of 2: 1; hence the expression “multi-rotation” came into use.
V.—Properties of the Determinant of an Orthogonal Substitution
Authors: Muir Thomas
Published: June 2016

(1) If we seek to extend the definition of an orthogonant by making the square of each row equal to σ instead of 1, this fixed quantity will naturally be found to appear in the statement of almost all the properties of the determinant in question. It is therefore convenient and appropriate to call it the base of the orthogonant, and to speak of an orthogonant to the base σ or an orthogonant of base σ.

It is a simple matter to ascertain what modifications are necessary in the statement of the known properties of the ordinary orthogonant to make them applicable to the extended definition.
VII.—On an Integral-Equation whose Solutions are the Functions of Lamé
Authors: Whittaker E. T.
Published: June 2016

§ 1. Object of Paper.—The chief object of the present paper is to establish the following theorem:

The functions of Lamé [that is to say, the doubly-periodic solutions of the differential equation

are the solutions of the homogeneous integral-equation

where η denotes an arbitrary constant.
IX.—On the Resistance experienced by a Body moving in a Fluid
Authors: Levy H.
Published: June 2016

A necessary condition in any hydrodynamical problem is that the pressure exerted by the fluid at any point must always be positive, and be given by

C being a constant determined by the boundary conditions of the problem, ν the velocity, and ρ the density of the fluid, provided there are no external forces involved. Should the velocity at any point, however, be so great that the expression C — ρν2/2 becomes negative, the problem in this respect at least loses its validity as an approximation to actual fact. Now it can easily be shown that, in any form of potential streaming about a body with sharp edges, the velocity at the sharp edges becomes infinite, and the pressure therefore negative. The equations of motion of the fluid having been obtained on the assumption of continuity of motion, this suggests at once that some form of discontinuity of the fluid probably exists near the sharp edges.
X.—Fossil Micro-organisms from the Jurassic and Cretaceous Rocks of Great Britain
Authors: Ellis David
Published: June 2016

The work embraces the results of the systematic examination, for fossil micro-organisms, of slides prepared from ironstones and ferruginous limestones from various districts of Great Britain.

Abundant traces were found in the Frodingham Ironstone of a fossil fungus allied to the modern Phycomycetes. This is named Phycomycites Frodinghamii. The traces include hyphæ, sporangia, and spores. These are described, measured, and photographed, and details of the life-history, so far as ascertainable, are given.
XIII.—The Reflective Power of Pigments in the Ultraviolet
Authors: Cochrane Charles
Published: June 2016

The eye is sensitive only to light of wave-length 7600 to 4000 A.U. With the ordinary dry photographic plate and glass lenses we can get an effect down to wave-length 3300 A.U.; with the same plate and quartz lenses we can get an effect from a wave-length as short as 2000 A.U. The gelatine of the plate absorbs the wave-lengths immediately above this limit, and their effect is very faint. A camera fitted with a quartz lens can take a picture in which all the wave-lengths down to 2000 A.U. produce their share, and hence can extend the range of the eye another octave, but the disadvantage of this picture is that it integrates all the different colours. We cannot, for example, tell whether a mark is due to light of wave-length 3500 A.U. or 2500 A.U. Such a picture makes the ultraviolet appear the same as the visible would appear to a man with monochromatic vision. All the detail due to variety and wealth of colour is lost. Now if we could photograph the same objects in succession with monochromatic light of wave-length say 3500 A.U., 3000 A.U., 2500 A.U., and 2000 A.U., it is possible that a great amount of new detail might be obtained of the utmost value to science. It was with the purpose of obtaining monochromatic photographs in the ultraviolet that the present research was undertaken.
XVII.—Quaternion Investigation of the Commutative Law for Homogeneous Strains
Authors: Hitchcock Frank L.
Published: June 2016

1. If a plastic body be subjected to a uniform change of shape, any two equal, similarly placed cubes become equal, similarly placed parallelepipeds. It is well known that the character of the deformation may be determined by a set of nine constants; but the physicist naturally prefers to regard the strain as an operator, and to represent it by a single symbol. The resulting operational algebra may even react favourably on the mathematical aspect of the question, and give us new methods of attack for old problems.
XXIV.—Chalk Boulders from Aberdeen and Fragments of Chalk from the Sea Floor off the Scottish Coast
Authors: Hill William
Published: June 2016

In December 1908 I received from Mr A. Earland a fragment of a rock, believed to be chalk, which had been dredged from the bottom of the North Sea. Mr Earland also informed me that he believed boulders of a similar rock occurred in some profusion near what is known as the Kinnaird Deep, off the northern coast of Aberdeenshire. As a result of our correspondence a little later, Professor D'Arcy Thompson asked me to investigate such boulders as might presumably be chalk, dredged from the northern parts of the North Sea during the operations of the s.s. Goldseeker, a vessel employed by the North Sea Fisheries Commission, and he has kindly permitted me to include a description of the boulders found by the Goldseeker in the details of this paper.
X.—On a Possible Explanation of the Satellites of Spectral Lines
Authors: Houstoun R. A.
Published: June 2016

It is well known that, when examined with a modern high-power spectroscope, the bright lines in the spectra of the different elements exhibit an individual character. Some are diffuse, some are sharp, some are diffuse on the one side and sharp on the other, and some are accompanied by fainter lines in their neighbourhood. To the latter the name of satellites has been given. The most celebrated satellites are those of the green line of mercury, which have been investigated very often owing to the ease with which the mercury spectrum can be produced. They are much fainter than the main line, and at least six can be seen. But there are cases occurring in which a satellite is so strong that it is hardly possible to say which is the main line. Thus the red line of hydrogen is a close doublet with a separation of ·14 A.U., the two components of the doublet being of approximately equal brightness.
XI.–The Optical Rotation and Cryoscopic Behaviour of Sugars dissolved in (a) Formamide, (b) Water. Part II
Authors: Mackenzie John Edwin , Ghosh Sudhamoy
Published: June 2016

In a recent communication (Proc. Roy. Soc. Edin., 1914–15, vol. xxxv, p. 22) measurements of the optical rotation and cryoscopic behaviour of the following sugars, viz. β-l-arabinose, l-xylose, α-d-glucose, α-d-galactose, d-mannose, d-fructose, α- and β-lactose, dissolved in (α) formamide, (b) water, were described. The investigation has been carried a step further by the addition of β-d-ghicose, β-d-galactose and maltose to the above list. Thus the change in rotation or mutarotation in formamide solution has now been measured, starting from both the α and β-form of d-glucose, d-galactose and lactose. As in the case of the water solutions of these sugars, the constant rotation shown when there is equilibrium between the two modifications is found to be the same whether the startine-point be the α- or the β-modification.
VIII.—On the Life-History and Bionomics of Myzus ribis, Linn. (Red-Currant Aphis)
Authors: Haviland Maud D.
Published: June 2016

M. ribis, Linn, (red-currant aphis), on Ribes rubrum is dimorphic in respect of certain features of the antenna and of abdominal and wing dimensions.

The nature of the food, whether healthy or blistered by the attack of the fundatrix, seems to be the determining factor of this dimorphism.

The form from healthy leaves is probably identical with M. whitei, Theobald, and M. dispar, Patch.

M. ribis is migratory, and in summer colonises certain Labiatæ and other weeds; but this migration is not obligatory, and the entire life-cycle may be passed on currant.

On its summer host plant this species has been previously described as Phorodon galeopsidis, Kaltenbach.

There is a decline in fertility in the later part of the summer among the forms remaining on currant.

This is caused by a lower birth-rate, and not by the shortening of the life of the parent.

This decline, together with the attacks of predaceous and parasitic enemies, accounts for the frequent disappearance of the species from currant in August and September.

Both sexual forms may be produced, and eggs may be laid, on either host plant. Males transferred from Labiatæ to Ribes can fertilise the females on the latter plant.
X.—The Cooling of the Soil at Night, with Special Reference to late Spring Frosts
Authors: Franklin T. Bedford
Published: June 2016

In this paper I am mainly concerned with the surface soil temperature, but as we are accustomed by long usage to think of the grass minimum temperature as determining the occurrence or non-occurrence of frost, a few words of explanation on this point is perhaps necessary at the outset.

The grass minimum on nights of rapid radiation certainly does fall considerably below the surface soil minimum, but this is due to the very fact that it is the grass minimum, i.e. the air temperature just on the grass.
XIV.—The Minimum System of Two Quadratic Forms in n Variables
Authors: Turnbull H. W. , Williamson J.
Published: June 2016

The following pages deal with the simultaneous system of two general quadratic forms in n homogeneous variables. It is a special case of Gordan's Theorem which proves such systems to be finite, for the general projective group of linear transformations. While several works have dealt with the cases when n = 2, 3, or 4, nothing seems to have been written on the general case except a memoir in the year 1908. We continue, and simplify, the results there obtained, and now establish that

(1) All rational integral concomitants of two quadratic forms in n variables and any number of sets of linear variables may be expressed as rational integral functions of (3n + 1) concomitants, and forms derivable by polarisation.

(2) These (3n + 1) forms, called the H system, constitute a strictly irreducible system.

This system is exhibited in §7 as

together with polars.

The work is divided into three chapters: I §§ 1–4 is introductory notation, II §§ 5–17 provides a proof of these theorems, while III §§18–21 gives the non-symbolic and canonical forms of the results.
XV.—The Law of Blackening of the Photographic Plate at Low Densities
Authors: Baker E. A.
Published: June 2016

The following paper is ancillary to certain investigations in stellar photometry which are in progress at the Royal Observatory, Edinburgh, and require the establishment of data relating to the blackening of the plates employed. It describes the laboratory work carried out for this purpose, generally over the very restricted range of exposure times and densities used in the stellar work, but occasionally extended to cover a wider field. The conditions are chosen in order to give the maximum accuracy and range to the stellar work and not with a view to highly accurate laboratory work; on the other hand, the periodical change of emulsion which must occur in any lengthy investigation introduces an element which, though of considerable interest, is lacking in most of the published work on the subject.
XXV.—Some Points in the Anatomy of Dicksonia
Authors: Williams Samuel
Published: June 2016

Our knowledge of the anatomy of Dicksonia is mainly based on the description of D. Barometz given by Gwynne-Vaughan. The stem of this species possesses a radial dictyostele, which, on account of the shortness of the leaf gaps, is not far removed from the solenostelic condition. The leaf trace arises as a broad ribbon of tissue with inwardly folding margins, which soon, however, breaks up to form a horse-shoe of isolated strands.
II.—The Employment of Intracardiac Injection of Adrenaline in Asphyxia
Authors: Sharpey-Schafer E. , Bain William A.
Published: June 2016

The efficacy of intracardiac injection of adrenaline to assist recovery from asphyxia having been recently disputed, we have instituted a number of experiments with the object of determining what effect, if any, is produced by such injection in asphyxiated animals in which the respirations and/or the heart had entirely stopped, and the blood-pressure had become reduced almost or quite to zero.
III.—The Absorption Spectra of Cyanogen and the Cyanogen Halides
Authors: Mooney R. B. , Reid H. G.
Published: June 2016

The ultra-violet absorption spectra of C2N2, CNCl, CNBr and CNI have been photographed.

Measurements are given of band edges of the C2N2 absorption spectrum in the region 2380 A–1850 A. The influence of temperature on the relative intensities of the bands has been studied.

The long wave-length limits of the regions of continuous absorption due to the cyanogen halides are: CNCl, 2240 A; CNBr, 2540 A; CNI, 3100 A and 2150 A.

We desire to thank Dr Baker, of the Royal Observatory, Edinburgh, for making photometer records of several spectra, Dr Ludlam for his helpful interest in our work, and Imperial Chemical Industries, Ltd., for a grant towards the cost of quartz apparatus.
IV.—The Effect of Malnutrition on Root Structure
Authors: Bond George
Published: June 2016

1. Reference is made to experiments conducted by Flaskämper as a result of which he stated that the removal of the cotyledons at an early stage from seedlings of Phaseolus sp. and of Vicia Faba resulted in an elimination of the pith from the subsequently formed part of the root in both species, and further induced a reduction in the number of poles in the root of the second species.

2. The significance of such observations in a consideration of the theory of the Size Factor is pointed out.

3. The experiments have been repeated. The malnutrition resulting from the decotylation affected the varieties employed in the present work more adversely than with Flaskämper, and usually caused the death of the seedling after a shorter or longer period.

4. Sufficient evidence has been obtained, however, to throw very serious doubt on Flaskämper's conclusions. The two reduction phenomena he described are now shown to occur in the normal development of the roots of these species, and there is no indication that their occurrence is affected by decotylation.

5. A teleological explanation, based on the theory of the Size Factor recently advanced by Bower, is made of this reduction in the number of protoxylem poles which occurs in the normal development of the roots of these plants.

6. The significance of the appearance of a pith in the basal parts only of these roots is discussed.

In conclusion, I desire to express my indebtedness to Professor F. O. Bower, F.R.S., for his constant interest in this work, and to thank Dr S. Williams and other members of the Botany Department for much valuable help. Also my best thanks are due to the Executive Committee of the Carnegie Trust for a grant towards the expense of the illustrations both of the present work and those of a recent paper on “The Stem-Endodermis in the Genus Piper,” published in the Transactions of the Royal Society of Edinburgh.
VI.—On the Definition of Spatial Distance in General Relativity
Authors: Ruse H. S.
Published: June 2016

In a recent paper, Professor E. T. Whittaker discussed the problem of defining, in a general riemannian space-time, the concept of spatial distance between material particles. It is the object of this paper to give an alternative definition, and to compare the new formula with that of Whittaker.
VIII.—On the Structure of Vertebraria
Authors: Walton John , Wilson Jessie A. R.
Published: June 2016

Vertebraria is one of the commonest and most characteristic fossils in those Upper Carboniferous and Permian strata in which Glossopteris is the dominant fossil plant. It has been found in the form of coaly incrustations, impressions, and casts, and accounts of these various forms have been given by Arber and Seward. In view of our very inadequate knowledge of Vertebraria and Glossopteris any information about them is of importance. The genus Vertebraria Royle was founded on impressions of plant axes, some of which, from the evidence of the attachment of roots, must be judged to be roots or rhizomes. Vertebraria axes are usually found lying in the plane of the bedding of the matrix (Pl. I, fig. 2) and less frequently at right angles to the plane of bedding (PL I, fig. 3).
XXII.—Tables of the Elliptic-cylinder Functions
Authors: Ince E. L.
Published: June 2016

Although the physical problem which originally led to the Mathieu equation

is now well over sixty years old, and although other problems studied in more recent years, such as the scattering of electric waves by an elliptic cylinder, depend essentially on the same equation, no thorough investigation of detail has hitherto been possible owing to the lack of tables of the functions defined by the equation. In fact, until 1924 all attempts to reduce the functions to a form suitable for calculation had failed. In that year a successful method of attack was discovered by the present writer, who then undertook the computation of the tables which are here published.
VI.—The Estimation of Factor Loadings by the Method of Maximum Likelihood
Authors: Lawley D. N.
Published: June 2016

1. When a battery of intelligence tests is administered to a set of persons it is a common practice among psychologists to “explain” the scores obtained in terms of a number of “factors.” Thus if we suppose that there are altogether t tests and that xi, denotes the score of any one person in the ith test, then it is assumed that

where f, g, …, h represent the person's measures in one or more general or group factors, and Si, is the person's specific ability in the ith test. It is further assumed that for a given and supposed infinite population of persons all the factors, specific and otherwise, are distributed normally and independently and that they are standardised, i.e. that their standard deviations are unity.
XII.—Reciprocity. Part IV: Spinor Wave Functions
Authors: Fuchs Klaus
Published: June 2016

This paper is the continuation of the papers by Born (1939, Part I) and by Born and myself (1940, Parts II and III). Here the theory is extended to the case of spinor wave functions satisfying the Dirac equation.
XIV.—The Genetical and Mechanical Properties of the Sex Chromosome. VI. Hexacentrus mundus
Authors: Koller P. C.
Published: June 2016

Cytological studies carried out by McClung (1905, 1914) on various species of Orthoptera have shown that the male is the heterogametic sex. The male has only one X-chromosome, whereas the female has two. During spermatogenesis two kinds of gametes are produced, one with the X-chromosome and the other without it. It was also found that the segregation of the single sex chromosome takes place at first meiotic anaphase. The present paper describes the sex chromosome of the male Hexacentrus mundus Walker, from India. During the meiotic division this chromosome exhibits peculiarities which it is believed have not hitherto been seen in any species of the Orthopteræ.
XVI.—The Loss of Heat by Conduction from the Earth's Crust in Britain
Authors: Anderson E. M.
Published: June 2016

The object of this paper is to record certain temperatures which were measured in the deep Boreland Bore, near Dysart, in Fife, and to discuss the bearing of these and some other observations on the amount of heat which escapes from the crust, by conduction, in Britain.
XVII.—The Energy Levels of a Rotating Vibrator
Authors: Sandeman Ian
Published: June 2016

The energy levels of a rotating vibrator have been calculated by the late J. L. Dunham (1932). The theory of the rotating vibrator is important, because it provides a method for direct quantitative study of molecular structure from the band spectra of diatomic molecules. The purpose of this paper is to extend Dunham's results and to express them in a form more convenient for numerical calculation.
XVIII.—On the Histogenesis of some Teleost Pituitaries
Authors: Kerr T.
Published: June 2016

The importance of the pituitary in relation to many body processes has long been recognised, and may be due either to its direct influence on the body or to its control over other endocrine organs, in particular the thyroids and gonads. It is evident that various hormones are elaborated in the gland, and it appears likely that they originate in particular regions or even in particular cell types. It is of interest therefore to ascertain at what period in the development of the animal these hormones first appear. This problem can be approached from two directions, experimental and histological.
XIX.—The Effect of the Inhibition of Respiration and Assimilation on the DiatomDitylum Brightwelli(West)
Authors: Bhatia D.
Published: June 2016

Ditylum Brightwelli, a marine plankton diatom, shows very peculiar osmotic relations which have recently been investigated by Gross (1939). The cells (fig. 1) consist of a central mass of protoplasm containing the nucleus and connected by a few protoplasmic strands with the peripheral plasma membrane in which are embedded numerous chromatophores. The remainder of the space inside the cell is filled with cell sap. As in other diatoms, the protoplast is enclosed by a siliceous cell wall. Gross found thatDitylumplasmolyses rapidly in isotonic and hypotonic NaCl and sugar solutions, being reduced in a few seconds to a small spherical body about one-third to one-twentieth of its original volume, similar in all respects to a resting spore. In a solution of NaCl + CaCl2, and in unbuffered artificial sea-water, plasmolysis occurs in all cells, but the process is considerably delayed and completed only after several hours. In artificial sea-water, the pH of which is adjusted to about 8, the cells remain unchanged.
XXIII.—An Analysis of the Influence of Weather upon a Migratory Movement of Birds
Authors: Ritchie James
Published: June 2016

The fundamental impulse determining the migration of birds is connected with the reproductive cycle; but when that has been recognised it must also be admitted that there are secondary conditions of environment which regulate the actual movements of which a migration is compounded. Of these weather has long been looked upon as one of the most important. There is still, however, much divergence of opinion as to the extent and nature of the influence of weather, and indeed in recent years statistical analysis has led workers, such as Bretscher (1915), to doubt whether any satisfactory connection between meteorological conditions and migration can be demonstrated, and Lincoln to announce boldly that “the state of the weather at any point has little if anything to do with the time of arrival of migratory birds” (1935, p. 59).
XXVI.—Some Confluent Hypergeometric Functions of Two Variables
Authors: Erdélyi A.
Published: June 2016

1. This paper is the continuation of a former one (Erdélyi, 1939), and deals with the integration of the system of two partial linear differential equations of the second order

The former paper will be referred to as I; all the notations of I will be retained without further explanation.