bluuebunny/crossref_metadata_2025_split huggingface dataset:
Some Results in the Mathematical Theory of Seiches
Authors: Chrystal  
Published: June 2016

AbstractI propose in this preliminary communication to lay before the Society some results of investigations in the theory of Seiches in a lake whose line of maximum depth is approximately straight, and whose depth, cross section, and surface breadth do not vary rapidly from point to point.As the seiche disturbance is small compared with the length of the lake, I shall make the assumptions usual in the theory of long waves:—viz., that the squares of the displacements and of their derivatives are negligible.
On Two Liquid States of Sulphur Sλ and Sμ and their Transition Point
Authors: Smith Alexander 
Published: June 2016

AbstractIt 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.
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.
XVI.—On the Discharge of Water from Circular Weirs and Orifices
Authors: Gulliver G. H. 
Published: June 2016

SummaryThe 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

AbstractAn 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

SummaryThe 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.
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 determinantwhose matrix is the sum of the matricesthat 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.
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” valueswhich differ only slightly from the above observed values, and which lie on a smooth curve.
XIII.—The Adsorption of Gas under Pressure
Authors: Briggs Henry , Cooper William 
Published: June 2016

Summary1. 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.
On the Thermo-electric Properties of Solid and Liquid Mercury
Authors: Peddie W. , Shand A. B. 
Published: June 2016

AbstractBy 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.
On the Thermo-electric Properties of Solid Mercury
Authors: Peddie W. , Shand Alex. B. 
Published: June 2016

AbstractThis 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.
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 respectivelyLet us form another set by multiplying every equation of (1) by every equation of (2). ThusorwhereThis 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.
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.
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,whereThis, 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.”
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

SUMMARY(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.
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, andThe 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 equationthat 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 asbut 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.
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.
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 equationφ(xyzpq) = 0is 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.
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.
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.
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.
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.
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.