bluuebunny/crossref_metadata_2025 huggingface dataset:
On Two Liquid States of Sulphur Sλ and Sμ and their Transition Point
Authors: Smith Alexander
Published: June 2016

It is well known that melted sulphur when heated becomes suddenly dark brown and viscous in the neighbourhood of 160- 170°. These and other facts rendered it probable that there was a transition point in liquid sulphur, and that two liquid states could be proved to exist, one of them being stable below the transition point, and the other above it. According to the phase rule, a single substance can exist in three phases (two liquid and one vapour phase) only as a non-variant system at a single temperature and pressure. Thus, if the two liquid forms were not completely miscible, the lower one might form the greater part of the material until, as the temperature rose, it became saturated with the upper one and a new phase separated out. This phenomenon would mark the transition point, and the smallest further rise in temperature would cause the complete disappearance of the first phase. The substance would then contain a small proportion of the lower form in solution in the upper, and this proportion would diminish with rising temperature. No case of an exactly parallel nature is known; but the transition from “liquid crystals” to an isotropic liquid in the case of certain organic compounds is to a certain extent analogous.
II.—The Effect of Load and Vibrations upon Magnetism in Nickel
Authors: Russell James
Published: June 2016

The initial irreversible effects of applying or of removing stress resemble those produced by vibrations, although these processes “may be conducted in such a way that no actual vibration takes place.” Ewing has investigated the initial effects of tension in iron, Cree the initial effects of pressure in cobalt. In iron and cobalt, tension and pressure respectively increase the induction before the Villari reversal in both metals is reached. Vibrations also in non-cyclic fields increase induction. Consequently in low fields the initial irreversible and final reversible effects of tension and pressure in iron and cobalt respectively augment each other. In nickel, on the other hand, the irreversible and reversible effects of tension must oppose each other; the latter effect lowering the induction at all stages of field increasing from zero. In Ewing and Cowan's paper, however, no mention is made of any initial effects tending towards induction increase.
VI.—On the Reducing Action of Electrolytic Hydrogen on Arsenious and Arsenic Acids when liberated from the Surface of Different Elements
Authors: Thomson William
Published: June 2016

This research was commenced with a view to find the velocity at which arsenic was liberated as arseniuretted hydrogen from cathodes of different elements:

(a) From arsenic in the form of arsenious acid.

(b) „ „ „ „ arsenic acid.
X.—Laboratory Note on a Study of Polarisation by means of the Dolezalek Electrometer
Authors: Ewan A. F.
Published: June 2016

The following experiments originated in a series of laboratory exercises which I performed on the use of the Dolezalek electrometer. The instrument which I used was made by Bartels, and had its needle suspended by a phosphor-bronze strip. This needle was raised to a potential of about 160 volts by being connected to one terminal of a battery of eighty small secondary cells, the other terminal of which was connected to earth. When at this potential the instrument gave, for a potential difference of 1 volt between its two pairs of quadrants, a deflection of 200 divisions on a scale 200 centimetres distant from it. The maximum deflection in the experiments described was 166 divisions, i.e. 33·2 cms., giving tan−1 ·166 as maximum angle of deflection; and therefore, by taking the deflection as proportional to the potential difference, a maximum error of 0·7 per cent, is introduced.
XI.—A Special Form of Photographic Camera for Recording the Readings of the Scales of Scientific Instruments
Authors: Milne James Robert
Published: June 2016

Some years ago, when employed in work that involved the use of a polarimeter. there was brought forcibly to my notice the great loss of time which the frequent reading of the Nicol dial necessitates. To avoid this, I had a special form of camera made for the purpose of recording the readings automatically. This method proved successful from the first, but it is only lately that the mechanism of the camera attained its final form; for it has required several years of experiment and alteration to evolve a form of camera which should be wholly automatic and yet reasonably simple. It will be readily understood that the function of the camera is to make a series of photographs of the scale-and-vernier of the polarimeter or other instrument, which, on subsequent examination, will show the relative position of the scale-and-vernier at the time of each exposure.
XVI.—On the Discharge of Water from Circular Weirs and Orifices
Authors: Gulliver G. H.
Published: June 2016

The discharge of water through a vertical circular orifice is represented by an expression which does not admit of a direct mathematical solution, but from which results have been obtained by graphical means. The shape of the curve of actual discharge is similar to that found for the theoretical discharge; both curves are sensibly straight lines for positions of the water surface between the centre and the top of the orifice. The value of the coefficient of discharge probably lies between 0·625 and 0·630 for low heads.
XXV.—Strophanthus sarmentosus: its Pharmacological Action and its Use as an Arrow Poison
Authors: Fraser Thomas R. , Mackenzie Alister T.
Published: June 2016

An extract of the seeds of Strophanthus sarmentosus appears to be an important ingredient of the arrow-poison of Nigeria and other parts of West Africa. While some of the other ingredients of this arrow-poison may possess toxic power, others of them have little or no toxicity and are introduced into the arrow-poison with the object, apparently, of rendering it more viscous and adhesive or with a superstitious intention.
XXVIII.—On the Friction at the Extremities of a Short Bar subjected to a Crushing Load, and its Influence upon the Apparent Compressive Strength of the Material
Authors: Gulliver G. H.
Published: June 2016

The effect of the friction of the crushing plates upon the yield point of short compression specimens has been investigated.

With plates harder than the material under test, the end friction causes an increase in the apparent yield point. This increase is calculated as 18 per cent. for wrought iron and mild steel, 20 per cent. for cast iron, and 50 to 200 per cent. for stones, bricks, and concrete. These figures, except the first, may apply almost equally well to the crushing strength, but they require experimental support. The corresponding inclinations of the surfaces of shearing are 37° for wrought iron and steel, 36° for cast iron, and 27° to 15° for stones, etc. The first value is seldom obtained, but the others agree fairly well with average experimental results.

When the crushing plates are of material softer than that under test, the lateral flow of the former diminishes the apparent strength of the specimen. With stones crushed between lead plates the strength is calculated as 0·35 to 0·15 of that obtained when iron or steel plates are employed. Experiments give 0·65 to 0·43 as the value of this ratio, but the specimens do not rupture by shearing in the manner contemplated.

The total crushing load of a short specimen of cast iron is increased by diminishing the length of the piece, but the crushing stress per unit of area is simultaneously decreased.
XXIX.—On Group-Velocity and on the Propagation of Waves in a Dispersive Medium
Authors: Green George
Published: June 2016

§ 1. The theory of group-velocity has been developed by Stokes, Osborne Reynolds, Lord Rayleigh, and later by Professor Lamb. The application of the theory to light-waves was made by Gouy and Lord Rayleigh, and its importance in this connection was emphasised by Professor Schuster in his paper “On Interference Phenomena,” Phil. Mag., vol. xxxvii., 1894.
III.—Note on the Determinant whose Matrix is the Sum of Two Circulant Matrices
Authors: Muir Thomas
Published: June 2016

Perhaps the most interesting theorem as yet known in regard to circulants concerns the determinant whose matrix is the sum of two circulant matrices, one of the latter being taken symmetric with respect to the primary diagonal and the other with respect to the secondary diagonal: for example, the determinant

whose matrix is the sum of the matrices

that is to say, the matrices of
VI.—Note on the Scattering of X-Rays
Authors: Houstoun R. A.
Published: June 2016

§ 1. The scattering of X-rays is one of the most promising methods of approaching the constitution of the atom. Sir J. J. Thomson's theory undoubtedly gives the main features of the phenomenon. But there are certain facts, namely:

(i) the increase of scattering with heavy elements for soft rays,

(ii) the extra-radiation, and

(iii) the low value of the scattering coefficient for γ-rays,

for which it affords no explanation. It seems worth while trying to extend the theory so as to cover these facts also.
VII.—An Unnoticed Point in the Theory of Newton's Rings
Authors: Marshall J.
Published: June 2016

The consideration of the passage of light waves through three media elucidates an interesting point in the Theory of Newton's Rings.

Let the three media be denoted by the numerals 1, 2, 3, and let z = 0 be the plane of separation between media 1 and 2 and z = −a the plane of separation between media 2 and 3. Also let the axis of x in the plane z = 0 be parallel to the wave front of the incident plane waves.
XI.—The Daily Temperature Curve
Authors: Becker L.
Published: June 2016

(1) Outline of Investigation.—During the last half-century the temperature of the air has been recorded by thermographs at a number of places, and the registered graphs have been measured and mean daily temperature curves have been calculated from them for each month of the year. The amount of labour entailed in these operations is enormous, and it may well be asked whether the figures cannot be put to some further use. It appears to me that a comparison of the daily curves obtained at various places would furnish important information in regard to climate. To effect this the curves may be represented by Fourier's Series, and the values of the constants at the various places may be compared. Another method of comparison, however, seems to me more promising.
XIII.—On a Class of Graduation Formulæ
Authors: Sherriff Catherine W. M.
Published: June 2016

The problem of Graduation or Adjustment, with which the present paper is concerned, may be defined as follows. Let a number u be a function of a number x: and suppose that, corresponding to the values … −3, − 2, −1, 0, 1, 2, 3 … of x, we have obtained, as a result of observation, values … u−3, u−2, u−1, u0, u1, u2, u3 … for u. Owing to errors of observation, these observed values when plotted against the corresponding values of x do not lie on a smooth curve, although for theoretical reasons we believe that they would do so if freed from errors. The problem is to determine the most probable set of “graduated” or “adjusted” values

which differ only slightly from the above observed values, and which lie on a smooth curve.
V.—Observations on the Interruption of the Endodermis in a Secondarily Thickened Root of Dracæna fruticosa, Koch
Authors: Mann Annette G.
Published: June 2016

It is generally accepted that the position and development of any one tissue in a plant is to be studied from the point of view of function: nevertheless the physiological need for it may alter as the plant develops. The endodermis is an illustration of this. Its primary function (1) is to restrict the passage of water and soluble substances to certain definite channels: it follows that its best development is in those parts nearest to the source of supply, e.g. in roots and young stems. The cell-walls are at first relatively thin, with the characteristic suberised strip on the radial and transverse walls. Its cells are in uninterrupted contact one with another, there being no intercellular spaces. This leads incidentally to its being also a barrier to gaseous interchange. The ventilating system of the cortex is limited by it internally, and cut off from such intercellular spaces as may lie within.
XIII.—The Adsorption of Gas under Pressure
Authors: Briggs Henry , Cooper William
Published: June 2016

1. Experiments made at 15° C. with various adsorbents and gases (chiefly nitrogen and hydrogen) show that a cylinder filled with adsorbent granules has a capacity for dry gas under a given pressure which is generally greater than its capacity when containing no adsorbent. For example, a cylinder charged with nitrogen at 35 atmospheres has its capacity increased by 66 per cent. by filling it with cocoanut charcoal.

2. Sudden outbursts of firedamp in coal-mines are the result of releasing immense quantities of gas adsorbed under pressure in coal.

3. The logarithmic relation derived by Williams is shown to apply to the adsorption isotherms of gases above their critical temperature up to pressures of 100 atmospheres, providing a correction be applied for the gas in the capillaries which is not adsorbed, but which exists under simple compression.
XVII.—The Annual Incidence of Intelligence, and its Measurement by the American Army Tests
Authors: Fairgrieve M. McCallum
Published: June 2016

The following investigation was undertaken to verify by the American Army Tests a result previously obtained by the use of Mr Cyril Burt's tests of intelligence (Journal of Experimental Pedagogy, vol. vi, No. 1), i.e. that there appears to be some likelihood that boys born in the spring months are slightly less intelligent on the average than those born in other months. Of these American tests (see Mental Tests in the American Army, C. S. Yoakum and R. M. Yerkes, pp. 220–230) the groups of tests marked “form 6” were used; but “test 8” was modified to suit British conditions by using test 8 of group 9 (p. 274, loc. cit.) as a basis, and replacing tests 1, 3, 7, 8, 9, 11, 13, 19, 35, 36, 38 by 8,1; 6, 3; 7, 39; 8, 39; 6, 35; 7, 36; 7, 38; 6, 39, and by three others of local interest.
On the Thermo-electric Properties of Solid and Liquid Mercury
Authors: Peddie W. , Shand A. B.
Published: June 2016

By means of a large quantity of solid carbonic acid, obtained from the University Chemical Laboratory, it was found possible to solidify, and maintain in the solid form for a considerable time, a large mass of mercury. Preliminary experiments made about a year ago, in the usual manner, by means of a triple circuit (iron, german silver, mercury), did not give results of a satisfactory kind. This was apparently due to the difficulty of maintaining steady, or steadily varying, temperatures.
Further Investigations on the Life-History of the Salmon in Fresh Water
Authors: Paton D. Noël , Newbigin M. I.
Published: June 2016

In the “Report on Investigations into the Life-History of the Salmon in Fresh Water,” published in 1898, the changes which the fish undergoes between the months of May and November were dealt with, but there was no material available to enable the observations to be extended throughout the remaining five months of the year, from December to April.
The Presence of Enzymes in Normal and Pathological Tissues
Authors: McKendrick John Souttar
Published: June 2016

The unorganised ferments or enzymes which are present in the digestive juices have for many years occupied the attention of physiologists. Although their chemical nature is still doubtful, yet most of their physical and chemical characters are known, and there are methods by which they may be extracted from the tissues and digestive juices. They are generally believed to play the most important part in the digestive process, and within recent years physiologists and pathologists have speculated as to the existence of similar substances in other tissues, and so have endeavoured in many instances to offer a hypothetical explanation of some of the changes that occur in tissue cells themselves. During the last eighteen months I have endeavoured to ascertain the presence or absence of these enzymes in normal and pathological tissues generally. Before describing the method adopted in carrying out this research, with the enumeration of the tissues examined and the results obtained, I shall briefly refer to our present knowledge of the existence of these enzymes in tissues other than those of the digestive tract, as well as to their presence in plants.
Observations on some Nemerteans from Singapore
Authors: Punnett R. C.
Published: June 2016

The Nemerteans which form the subject of this communication were collected by Messrs F. P. Bedford and W. F. Lauchester during a year's stay in and near Singapore. The number of species procured is ten, nine of which have not hitherto been described. These are Eupolia pholidota, Cerebratulus natans, C. brunneus, C. robustus, C. insignis, C. erythrus, C. sordidus, C. ulatiformius and C. bedfordii. The species previously known is Eupolia quinquelineata (Bürger), but for reasons given it has been considered desirable to change the name to E. melanogramma.
The Theory of Alternants in the Historical Order of its Development up to 1841
Authors: Muir Thomas
Published: June 2016

The first traces of the special functions now known as alternating functions are said by Cauchy to be discernible in certain work of Vandermonde's; and if we view the functions as originating in the study of the number of values which a function can assume through permutation of its variables, such an early date may in a certain sense be justifiable. To all intents and purposes, however, the theory is a creation of Cauchy's, and it is almost absolutely certain that its connection with determinants was never thought of until his time.
The Action of Silver Salts on Solution of Ammonium Persulphate
Authors: Marshall Hugh
Published: June 2016

Although the action of potassium persulphate on silver nitrate solution was one of the first persulphate reactions observed (vol. xviii. p. 64), I had not until lately paid any special attention to the behaviour of the ammonium salt in this respect. It appears, however, that in the latter case there are additional actions of great interest, not possible with the potassium salt. A general description of these will be given now, but there are still some points deserving of further investigation.
Hyperbolic Quaternions
Authors: Macfarlane Alexander
Published: June 2016

It is well known that quaternions are intimately connected with spherical trigonometry, and in fact they reduce that subject to a branch of algebra. The question is suggested whether there is not a system of quaternions complementary to that of Hamilton, which is capable of expressing trigonometry on the surface of the equilateral hyperboloids. The rules of vector-analysts are approximately complementary to those of quaternions. In this paper I propose to show how they can be made completely complementary, and that, when so rectified, they yield the hyperbolic counterpart of the spherical quaternions.
Note on Dr Muir's Paper on a Peculiar Set of Linear Equations
Authors: Tweedie Charles
Published: June 2016

In Dr Muir's Paper on a Peculiar Set of Linear Equations (communicated December 3, 1900) there occur two Determinants of the nth order, the expansions of which are given by Dr Muir, As the paper in question has so much to do with Symmetric Functions, the following simple method of obtaining their expansions may not prove uninteresting, based, as it is, upon the elementary theory of Symmetric Functions and the so-called Principle of Indeterminate Coefficients.
The Biology of the Genus Pissodes. (George Heriot Research Fellowship Thesis.)
Authors: Stewart MacDougall R.
Published: June 2016

In the case of any harmful insect of economic importance, in order to war against it, or apply remedial measures at all intelligently, a knowledge of the life-history of the pest is necessary. This proposition will, I think, meet with such ready acceptance as to render proof unnecessary, but I might in illustration mention two cases which came under my own observation, where in the one case a knowledge of the round of life of the attacking insect saved a whole forest, and in the other proved of great importance.
On the Thermo-electric Properties of Solid Mercury
Authors: Peddie W. , Shand Alex. B.
Published: June 2016

This paper contained an account of a redetermination of the thermo-electric position of solid mercury, by a method described in a note read last session. The only difference was that, by the use of three galvanometers, simultaneous readings of the deflection due to the Hg-Fe circuit, and of the deflections due to thermoelectric circuits giving the temperatures of the two Hg-Fe junctions, were taken.
I.—Recent Developments of the Committee of the Privy Council for Scientific and Industrial Research
Authors: Horne John
Published: June 2016

At the opening of another session the attention of the Fellows ought to be directed to certain points concerning the administration of the affairs of this Society. One gratifying feature is the completion of the card catalogue of the volumes in the Society's library. After the removal to our present quarters in 1909 it became apparent that the old catalogue in three large volumes was unsatisfactory. The original entries were not up to modern requirements, and, in view of a new catalogue being prepared, the new marks caused by the altered arrangement of rooms and shelves had been imperfectly registered. The library staff realised that nothing short of a card catalogue prepared from the volumes as they stand on the shelves would meet existing requirements. This was an arduous undertaking, involving considerable outlay. Dr Knott has estimated that the library at present contains forty-six thousand volumes, the greater part of which consists of scientific serials. To accomplish the task of cataloguing this large collection it was necessary to obtain outside expert assistance.
VIII.—A Determinantal Equation whose Roots are the Products of the Roots of Given Equations
Authors: Metzler William H.
Published: June 2016

Given two sets of linear homogeneous equations in n1 and n2 variables respectively

Let us form another set by multiplying every equation of (1) by every equation of (2). Thus

or

where

This set (A) of n=n1·n2 equations is linear and homogeneous in the n=n1·n2 variables w.
XVI.—Mirage on the Queensferry Road
Authors: Ramage Alexander G.
Published: June 2016

Most of us who have thought at all of mirage have thought of it as a phenomenon belonging essentially to distant parts of the world, such as the great Sahara Desert. Few of us would not be surprised to find it almost a daily spectacle on a familiar road so near our city.

You may imagine my surprise when, in the early days of April of this year, while walking westward along the Queensferry Road, and when opposite the quarry at the north end of Corstorphine Hill near the point at which the Corstorphine Hill road joins the Queensferry Road, I saw on the surface of the road, at a distance of about one and a half the spacing of the telegraph poles (they are about 50 paces apart), what appeared to be pools of clear water reflecting the green grass and foliage very clearly, and further down the road other pools. As I watched, a white horse with a rider went along, and as it passed beyond the “pools” of the mirage water (the road being perfectly dry) it was reflected, with the effect that the horse appeared to be about twice its height, as if on stilts.
III.—Quantitative Evolution. V. The Free and Apparent Dp‐ages of Compositæ
Authors: Small J.
Published: June 2016

The average ages in doubling periods (Dp‐ages) of the tribes and subtribes of Compositæ have been collated with geological time (Small, 1937, Q.E. II), but the Dp‐ages of individual tribes and sub‐tribes show considerable variation within each of the geological periods. When plotted as Dp‐ages against a time‐scale the tribes and the sub‐tribes show rather scattered positions, and the sub‐tribes within each tribe follow rather zigzag lines instead of being points on a straight line for each tribe.
XI.—Studies in Practical Mathematics. III. The Application of Quadratic Extrapolation to the Evaluation of Derivatives, and to Inverse Interpolation
Authors: Aitken A. C.
Published: June 2016

In an earlier paper (Aitken, 1932) the author put forward a method of polynomial interpolation which was designed to make full use of the speed and power of modern calculating machines in forming and summing products of two factors. The present paper is devoted to two further applications of the method. It is necessary to give a brief review and explanation of the process used, in order that these applications may be properly understood.
XVI.—Two Cases of Malformation of the Gill‐covers in Salmon
Authors: Tchernavin V.
Published: June 2016

Only a small number of salmon smolts (Salmo salar) that leave the river for the sea return for spawning (Calderwood, 1930, p. 180; 1931, pp. 36, 56; Menzies, 1931, p. 60; and others). The large loss of adolescent fish seriously affects the stock of salmon in the rivers, so that the question of possible causes of the death of salmon in the sea is one of some practical interest.
II.—Notes on some Oligochæts found on the Scottish Loch Survey.
Authors: Martin C. H.
Published: June 2016

These notes deal mainly—

(1) With the structure of the genital organs of Stylodrilus Gabreteœ (Vejd.), and with its possible identity with Bathynomus Lemani (Grube).

(2) A new species of oligochæt (Stylaria Lomondi).

I owe my opportunity of working on these forms to Sir John Murray, whom I must again thank for his great kindness.
VIII.—A Note on the Roman Numerals.
Authors: Barrett James A. S.
Published: June 2016

Mathematics accepts the Roman numerals as symbols for definite numerical values, without regard to the question of their origin and early history; but this paper is concerned primarily with the form and origin of these symbols, and only incidentally with their numerical values. Yet, though our subject is only indirectly related to mathematics, a survey of some of the hypotheses that have been put forward to account for the forms of these symbols cannot but prove interesting to mathematicians, as the symbols were in general use until the sixteenth century and are still current everywhere, on the dials of clocks, the title-pages of books, and in printed references to authorities.
X.—The Theory of Compound Determinants in the Historical Order of its Development up to 1860.
Authors: Muir Thomas
Published: June 2016

Determinants whose elements are themselves determinants made their appearance at a very early stage in the history of the subject, the first foreshadowing of them being contained in Lagrange's “équation identique et très remarquable” of 1773, namely,

where

This, viewed as a result in determinants, is a case of Cauchy's theorem of 1812 regardingthe adjugate, and the adjugate of course is an instance of the special form to which we have now come. Jacobi's theorem regarding any minor of the adjugate has a like history and may be similarly classified. Passing from the case of the adjugate, where each element is a primary minor of the original determinant, Cauchy also considered the determinants of other “systèmes dérivés,” that is to say, the determinants whose elements are the secondary, ternary, … minors of the original, and gave the theorem that the product of the determinants of two “complementary derived systems” is a power of the original determinant, the index of the power being where n is the order of the original determinant and p the order of each element of one of the “derived systems.”
XVI.—The Problem of a Spherical Gaseous Nebula.
Authors: Kelvin Lord
Published: June 2016

THIS paper was begun about the close of 1906, in order to fulfil a promise given at the end of the paper “On the convective equilibrium of a gas under its own gravitation only,” published in the Philosophical Magazine, 1887; and part of it was communicated by Lord Kelvin to the Royal Society of Edinburgh at its meeting on 21st January 1907. Since then, however, important additions have been made to it, and the subject has been dealt with more fully than was originally intended. Unfortunately the manuscript was left incomplete at Lord Kelvin's death. It ended with § 35.
XVII.—The Theory of Skew Determinants in the Historical Order of Development up to 1865.
Authors: Muir Thomas
Published: June 2016

MY last communication in reference to the history of skew determinants dealt with the period 1827–1857 (Proc. Roy. Soc. Edin., xxiii, pp. 181–217). The present paper continues the history up to the year 1865, but in addition contains an account of two writings belonging to the previous period, namely, by Brioschi (1855) and Bellavitis (1857).
XXIII.—On the Cohesion of Steel, and on the Relation between the Yield Points in Tension and in Compression.
Authors: Gulliver G. H.
Published: June 2016

(a) On the assumptions that resistance to deformation is due to simple friction, and that the coefficient of friction is independent of the load, the ratio of the yield point in tension to the yield point in compression, for what is ordinarily known as mild steel, is calculated as 2·384 to 3·384, or as 0·705 to 1. Experimental results so far obtained do not agree well with these figures, the value for the tensile yield point being relatively high, and that for compression relatively low.

(b) On the further assumption that a cohesive force acting between the metallic particles gives rise to a frictional resistance which may be added (algebraically) to that due to the effect of the external load, the value of this cohesive force is deduced as equal to 3·384 times the stress which corresponds with the tension yield point, or to 2·384 times that corresponding with the compression yield point. Experimental results from a large number of tests agree very fairly with the calculated figures for the case of tension.
XXVII.—Experiments with Heusler's Magnetic Alloy.
Authors: Gray James G.
Published: June 2016

IN 1903 Heusler made the important discovery that alloys of copper, manganese, and aluminium are strongly magnetic. It was shown in the paper published by Heusler that by properly adjusting the amounts of the component metals present an alloy is obtained the permeability of which is comparable with that of cast iron. Heusler also demonstrated the fact that the properties of this alloy are profoundly modified by thermal treatment.
XXIX.—On the Origin of the adaxially-curved Leaf-trace in the Filicales.
Authors: Gwynne-Vaughan D. T. , Kidston R.
Published: June 2016

WHILE studying the fossil Osmundaceœ several interesting points illustrating the origin of the leaf-trace were brought under our notice, which are exhibited with such exceptional clearness in Thamnopteris Schlechtendalii, Eichwald, sp., that they deserve especial recognition. The full discussion of the subject, however, is reserved until the publication of the next part of our memoir on the fossil Osmundaceœ.

The departure of the leaf-trace in Thamnopteris is typically protostelic. That is to say, the xylem of the leaf-trace first of all appears as a protuberance on the surface of the xylem of the stem (fig. 1).
XLII.—An Improved Method of Esterification.
Authors: Gibson G. E.
Published: June 2016

WHEN a mixture of ethyl alcohol, benzene, and water is fractionated, a ternary mixture of all three distils over first at a temperature of 68°C.

Taylor has made use of this fact in the preparation of the ethyl esters of high boiling-point acids.

His method is a great improvement on the old methods, but it is not continuous, and is tedious when large quantities of ester have to be prepared.

To remedy these defects the apparatus described in this paper was devised.
X.—On the Invariance of Quantized Field Equations
Authors: Fuchs K.
Published: June 2016

Heisenberg and Pauli (1929) developed a general scheme for the quantization of a field, if the field equations can be derived from a variation principle,

Here za denotes the field variables, L is the Lagrangian, and

The scheme of Heisenberg and Pauli is known to be Lorentz invariant. It is the purpose of this paper to show that it is also invariant with regard to all co-ordinate transformations allowed by the general theory of relativity. The method adopted to prove this is that used by Infeld (1937) and Pryce (1937) to prove the invariance of the “New Field Equations” against Lorentz transformations.
XVII.—Relations between the Elliptic Cylinder Functions
Authors: Ince E. L.
Published: June 2016

The elliptic cylinder functions, or solutions of the Mathieu equation

that have the period π or 2π, are of four distinct species. These are denoted respectively by ce2n(x, θ), se2n+1 (x, θ), ce2n+1 (x, θ), se2n+2(x, θ), where n indicates the number of zeros in the open interval o < x < ½π. The object of this paper is to show that a function of any type can be expressed in terms of functions of other types, or of their derivatives. This provides the analogies to such trigonometrical relations as

but the single terms on the right-hand side of this and similar relations are replaced, in the results to be proved, by infinite series. These results are quite distinct from Whittaker's recurrence-relations (Journ. London Math. Soc., vol. iv, 1929, pp. 88–96); in particular, they do not involve the non-periodic second solutions.
XXIII.—Genetic Algebras
Authors: Etherington I. M. H.
Published: June 2016

Two classes of linear algebras, generally non-associative, are defined in § 3 (baric algebras) and § 4 (train algebras), and the process of duplication of a linear algebra in § 5. These concepts, which will be discussed more fully elsewhere, arise naturally in the symbolism of genetics, as shown in §§ 6–15. Many of their properties express facts well known in genetics; and the processes of calculation which are fundamental in many problems of population genetics can be expressed as manipulations in the genetic algebras. In cases where inheritance is of a simple type (e.g. §§ 10–13, 15) this constitutes a new point of view, but perhaps amounts to little more than a change of notation as compared with existing methods. §14, however, indicates the possibility of generalisations which would seem to be impossible by ordinary methods.
III.—On the Reduction of Ferric Iron (1) by Sulphurous Acid and (2) by Zinc Dust
Authors: Cumming Alexander Charles , Smith E. W. Hamilton
Published: June 2016

So many papers have appeared on this subject that some apology seems desirable before making an additional contribution. The amount of published work on reduction with sulphurous acid is in itself an indication that many workers have found difficulties. It has been shown that the reduction does not take place in presence of large excess of hydrochloric or sulphuric acid, but the reduction will still occur while the reaction of the solution is strongly acid. On the other hand, Hillebrand (“Analysis of Silicate and Carbonate Rocks,” U.S. Bulletin, 442, p. 113) states if the solution after addition of sulphite is red in colour, it is too alkaline and acid must be added.
VIII.—The Absorption of Light by Inorganic Salts. No. VI.: The Cobalt Chloride Colour Change
Authors: Brown Alex R.
Published: June 2016

In No. II. of this series of papers, measurements were given of the striking change shown by cobalt chloride when an aqueous solution was heated or was altered in concentration, and it was announced that a more accurate investigation was being made in the hope of finally determining its cause. Chemists suppose the cause to be the dehydration of the hexahydrate, but the matter is not beyond doubt.

First of all, aqueous solutions were used. Except in regard to the heating arrangements the methods and apparatus were those used in the previous research. The heater in this case was a rectangular copper casting 8 cm. long, 2·5 cm. broad, 4·5 cm. high, which at one end was attached to a tin in which water was boiled. At a distance 1·2 cm. from the other end a rectangular hole was cut down through the casting, of dimensions such that it was just filled by the cell containing the solution to be heated. At each side of the hole from the base upwards a part of the casting 1·6 cm. high and 1·1 cm. broad was cut away. This permitted the transmission of light horizontally through the lower part of the vertical cell, which was of the ordinary rectangular type, and obviated the use of mirrors. As in the previous research glasses were inserted in the cell to reduce the thickness of the layer of solution examined, and the temperature of the solution was read by a thermometer.
IX.—Observations on the Structure and Affinities of Branchiomaldane vincenti Langerhans
Authors: Ashworth J. H.
Published: June 2016

The genus Branchiomaldane, represented by a single species vincenti, was founded by Langerhans to contain certain small Polychætes, which he discovered living in sand-covered tubes, among algæ, on the northern shore of Teneriffe. Professor Mesnil has since found specimens, inhabiting mucous tubes situated on the lower side of the calcareous alga Lithothamnion, in rock-pools at St Martin, near Cape la Hague, and has given an account of some of the structural features of these worms, which he showed to be adult and hermaphrodite. Professor Fauvel considered B. vincenti to be a dwarf Arenicola, arrested in development; he therefore merged Branchiomaldane with Arenicola, and designated the worm Arenicola vincenti. The writer has investigated the anatomy of several specimens of this worm, kindly sent to him by Professor Mesnil, and has concluded that the genus Branchiomaldane should be retained; the original name of the worm—B. vincenti—is therefore employed in the following account.
X.—A Method of Measuring Mental Processes in Normal and Insane People, with special reference to Maniac Depressive Insanity
Authors: Jeffrey George Rutherford
Published: June 2016

Among the problems which confront the psychiatrist in arriving at a judgment upon a mental case, few are more difficult than the estimation of the patient's mental working capacity. A rough approximation may be attained by careful observation of the patient's daily reaction to his surroundings—by the attitude he adopts to the little problems of his daily life; but such is, at best, only a very vague and unsatisfactory measure. To impose simple tasks for the purpose of obtaining objective criteria upon which to base our judgment is unusually difficult, and patients who were incapable of comprehending the new task would have to be excluded from its action; and to interest the patients in such a task sufficiently to persuade them to do their best is often not possible. The estimation of the working capacity of a large proportion of patients would thus seem at first sight to be beyond our powers to ascertain.
XIII.—“On the Singular Solutions of Partial Differential Equations of the First Order.”
Authors: Levy H.
Published: June 2016

The complete integral of the differential equation

φ(xyzpq) = 0

is a relation among the variables, which includes as many arbitrary constants as there are independent variables. But it is important to distinguish carefully between differential equations which have been formed by the elimination of constants from some complete primitive, and those whose origin is quite unknown, or which may have been constructed by some method totally different from the first.

In the original case, the differential equation can always be integrated in finite terms, while in the latter, only under the conditions laid down in Cauchy's Existence Theorem can an integral be obtained, and even then usually as an infinite series.
XV.—The Fata Morgana
Authors: Forel F. A.
Published: June 2016

Among optical phenomena which originate over the surface of water there is one so ill-defined and ill-observed as to be still mysterious; till now it has received no valid explanation. The Italians call it the Fata Morgana. Under conditions still lacking precise description, there appear on the far side of the Straits of Messina certain fantastic visions, fortresses and castles of unknown cities, which seem to emerge from the sea, soon to vanish again. These are the “palaces” of the “fairy Morgana,” which appear and disappear at the capricious stroke of the magician's wand.
XXII.—Preliminary Note on the Effect of Vibration upon the Structure of Alloys
Authors: Gulliver G. H.
Published: June 2016

Of late years a great deal of experimental work has been carried out with the object of determining the effect upon various metals of a load applied and removed many times in quick succession. The chief object of such researches is to determine the maximum stress which can be applied and removed indefinitely without causing fracture of the piece. Little attention has been given to any change in the structure of the metal, except in cases where there has been well-marked permanent distortion. The writer accordingly undertook some simple preliminary experiments in order to ascertain the effect upon the structure of a few alloys of numerous small blows, each of insufficient force to cause a permanent deformation of the specimens.
XXIII.—On a Continuous-current Motor-Gyrostat with accessories for demonstrating the Properties and Practical Applications of the Gyrostat
Authors: Gray James G. , Burnside George
Published: June 2016

No branch of dynamics or physics provides a more profitable or interesting subject of study to the student of physics or engineering than that which deals with the phenomena presented by spinning-tops. Within the last few years the most interesting form of top, namely the gyrostat, has advanced from being a piece of lecture-room apparatus, or a toy, to a position of great practical importance. In the dirigible torpedo, Brennan's monorail car, the Schlick device for rendering a ship steady at sea, and in the gyrostatic compass, the results are obtained by utilising the properties of the gyrostat. Undoubtedly, too, the gyrostat is destined to play an important part in many inventions still to be brought to light.
XXXI.—On Inheritance of Hair and Eye Colour
Authors: Brownlee John
Published: June 2016

Some time ago, in a paper published by the Royal Anthropological Institute, I applied a Mendelian analysis to that part of the observations made by the late Dr Beddoe (1) which refers to the colour of the hair. In that paper (2) I showed that these observations obeyed in a highly remarkable degree the law referred to, and that this result held from the north of Scotland, through the whole of England, Ireland, France, and Germany, to the south of Italy. At that time I was unable to make any application to the observations on eye colour also published in the same work, but I have now succeeded in completing the analysis.
IV.—Some Factorable Minors of a Compound Determinant
Authors: Metzler W. H.
Published: June 2016

If we start with a determinant A of order n, and, using exclusive umbral
notation, take the minor of the (n — k)th compound of A, Sylvester has shown that
IX.—Principia Atmospherica: a Study of the Circulation of the Atmosphere
Authors: Shaw W.N.
Published: June 2016

Every science has two aspects or two stages in its development. In the first, the inductive stage, observations are made and compiled, and axioms or laws are laid down. In the second or deductive stage the laws are applied by syllogistic reasoning, mathematical or otherwise, to elicit conclusions which either disclose new facts or show the inevitable connection between facts already known, and, in either case, complete the claim of the study to the rank of a science.
X.—Enzymatic Peptolysis in Germinating Seeds
Authors: Court Dorothy
Published: June 2016

In a previous paper (Proc. Roy. Soc. Edin., vol. xxxi. p. 342) a method was described for measuring small degrees of enzymatic peptolysis, and in a subsequent paper (Proc. Roy. Soc. Edin., vol. xxxii. p. 251) the conditions were dealt with under which such experiments could be carried out with the greatest possible guarantee of sterility combined with the least interference with the reaction.

The intention was to employ these methods for the purpose of pursuing the main object of research—the activation of zymogens in germinating seeds—and it was accordingly decided to carry through a series of experiments on germinating barley. This material was selected on account of the readiness with which it may be obtained.
XVI.—Some Factorable Continuants
Authors: Metzler W. H.
Published: June 2016

1. In the Transactions of the South African Philosophical Society for January 1905, Dr Thomas Muir gives the most general continuant resolvable into factors by means of a given set of line-multipliers. He starts with the multipliers and determines the continuant resolvable by them. At the end of his paper he gives another continuant and its factors, but not the line-multipliers, which he says “is equally interesting in itself and equally full of promise as a base for investigation.” Throughout his paper Muir is dealing with one of the two determinant factors of order n into which every centro-symmetric continuant of order 2n can be broken up. Starting with the larger continuant of which Muir's is a factor, one of the objects of this paper is to determine a set of row and column multipliers that will cause the continuant to break up into quadratic factors and thence into linear factors. Other and more general types of continuants are given which these same multipliers reduce to quadratic factors. Another and more convenient way to determine the factors of these determinants is obtained in the form of reduction formulas It is also shown how, for the two parts of order n into which the larger continuant of order 2n breaks up, the linear factors come out by reduction.
II.—Some Formulæ for the Associated Legendre Functions of the Second Kind; with corresponding Formulæ for the Bessel Functions
Authors: MacRobert T. M.
Published: June 2016

In two former papers (Proc. Roy. Soc. Edin., vol. liv, 1934, pp. 135–144; vol. lv, 1935, pp. 85–90) a number of integrals and series, involving Associated Legendre Functions of the First Kind regarded as functions of their degrees, were evaluated. In this paper similar integrals and series for the Associated Legendre Functions of the Second Kind, and also for Bessel Functions, are discussed. The latter are deduced from Bessel's Integral in its generalised form and from the corresponding integral for the Modified Bessel Function of the First Kind; the former from an analogous formula for the Associated Legendre Functions of the Second Kind.
XI.—The Time Lag of the Vacuum Photo-cell
Authors: Houstoun R. A.
Published: June 2016

(1) It is generally assumed that the vacuum photo-cell has no appreciable time lag. The electrons start out from the surface as soon as the light falls on it. The most important investigation on the subject is that of Marx and Lichtenecker (1913). By means of a mirror rotated 170 times per second an image of a narrow slit was swept over the cathode of a photo-cell at a distance of 8·3 metres from the mirror; the cathode was a potassium one sensitised with hydrogen. The electrometer reading was noted, and then the mirror was rotated at a much slower speed and the electrometer read again. No appreciable difference was recorded. In the words of the authors an alteration of the time of illumination from 4·38 × 10-3 to 1·46 × 10-7 sec., the intensity of radiation being 0·56 erg/sec. cm.2, had no effect on the result to an accuracy of one or two per cent. Theoretical deductions have been drawn from this statement which have been much quoted. It seemed to me that the statement itself was worth verifying, and this paper is the record of an attempt to verify it and push the limit of accuracy further.