bluuebunny/crossref_metadata_2025_split huggingface dataset:
XVIII.–The Musical Scale
Authors: Goold Joseph 
Published: June 2016

I. The Tonal Order of the Chromatic Scale.The exact ratios of the chromatic scale were first made known by Claudius Ptolemy of Alexandria about A.D. 150. We give them here as he found them, unaltered and unalterable.It is a most remarkable fact that while the ratios of the chromatic scale have thus been known for nearly two thousand years, its mathematical symmetry and origin have remained unrecognised down to the present day.For the concrete musical faculty is compounded of two distinct elements, physical and mathematical.In its physical aspect (with which we are familiar), the scale is a series of notes arranged in order of pitch upwards from the tonic (or keynote).In its mathematical aspect, the scale is a system of intervals measured symmetrically upwards and downwards from tonic and dominant as central interval (or tonal centre).The physical order of the scale is that which we most easily appreciate, but the mathematical order is that in which it originates. The chromatic scale therefore is, primarily, not a series of notes, but a system of intervals (or tonal system).Diagram I shows the scale in its familiar order of pitch, and it is remarkable how effectually this physical order conceals the mathematical from view.
II.—On the Equations of Motion of a Single Particle
Authors: Wedderburn J. H. M. 
Published: June 2016

§ 1. When solved for the second derivatives, the Lagrangian equations of motion for a system in which there are no extraneous forces have the formor, disregarding the parameter t, being the second Christoffel symbol † of the matrix associated with the kinetic energy. If there are extraneous forces Fk and, denoting t by xn+1, we add to the set of equations, the equations of motion are
The Torsional Constants of Iron and Steel
Authors: Peddie W. 
Published: June 2016

AbstractThis paper gave details of a series of experiments made on the same iron wire as was used in experiments described in previous papers. This series was made on the wire after it had been heated to redness and allowed to cool. A linear relation was again found to hold between log. b and n, where b and n are the quantities (constant in any one experiment) symbolised in. the equation yn(x + a) = b, y being range of oscillation and x being number of oscillations of the wire which have taken place since the commencement of the experiment. It was further found that the line representing that relation passed (as did all other such lines previously obtained with this wire) through the point log. b = 2·3, n = 1. Thus the quantity provisionally called the Oscillation Constant in the preceding paper, and regarded as characteristic of the material of the wire, retains its old value even after the wire has been heated to redness.
The Theory of Skew Determinants and Pfaffians in the Historical Order of its Development up to 1857
Authors: Muir Thomas 
Published: June 2016

Sets of equations of the formwhere the coefficient of xr in the sth equation differs only in sign from the coefficient of xs in the rth equation, had often made their appearance in analytical investigations before the determinant of such a set came to be considered. An instance is to be found in a memoir of Poisson's, read before the Institute in October 1809, and printed in the Journal de l'École Polytechnique, viii., pp. 266 — 344; and similar instances of an earlier date in writings of Lagrange and Laplace therein referred to. The mathematician who first referred definitely to the determinant appears to have been Jacobi.
IX.—A Reduction-formula for the Functions of the Second Kind connected with the Polynomials of Applied Mathematics
Authors: Humbert Pierre 
Published: June 2016

In the course of an investigation regarding rotating fluids, I have had occasion to make considerable use of Legendre's function of the second kind, which, as is well known, may be expressed in the formwhere Pn is Legendre's polynomial, and fn−1 a polynomial of degree n−1. Various expressions of fn−1 have been given, particularly in terms of Legendre's polynomials of lower degrees; but I found that none was satisfactory in regard to the practical computations which I had to perform.
XVIII.—The Quadratic Relations between the Determinants of a 4–by–8 Array
Authors: Muir Thomas 
Published: June 2016

1. The theorem which expresses the product of two determinants as a sum of like products is the main instrument for investigating the relations between the determinants of an oblong array. It is justifiably spoken of as “Sylvester's theorem of 1839 and 1851,” although simple cases of it date back to far earlier times; for example, the casewhich was brought to light by Bezout in 1779.
XXXIII.—On the Rate of Elimination of Chloroform when Administered by Different Channels.
Authors: Lindsay Dorothy E. , Paton D. Noël 
Published: June 2016

One of us (D. N. P.) has shown in the preceding paper that chloroform, when administered to dogs by the respiratory passages, may produce a purely stimulating action upon hepatic metabolism; whereas when it is given by the mouth, and to a less extent when it is given hypodermically, it exercises a distinctly toxic action, decreasing the activity of hepatic metabolism and leading to degenerative changes in the liver cells.In attempting to find an explanation of these phenomena, it was necessary to know whether any difference existed in the distribution of the drug throughout the system after it had been given by these channels.To elucidate this, the following series of observations were undertaken upon rabbits.
XLIII.—Nitric Anhydride as a Nitrating Agent.
Authors: Gibson G. E. 
Published: June 2016

IN the ordinary methods for the preparation of tartaric acid dinitrate, a mixture of fuming nitric acid with concentrated sulphuric acid is used as a nitrating agent.The product is treated with iced water to remove the sulphuric and nitric acids.As the dinitrate is decomposed by water, even at 0° C, it is impossible to avoid some loss in this process.By using nitric anhydride as a nitrating agent this difficulty is avoided. Nitric acid, which is the only other product of the reaction, can be removed by evaporation in vacuo.
XLIV.—Combustion Analysis.
Authors: Walker James , Blackadder Thomas 
Published: June 2016

The process of Dennstedt for the elementary analysis of organic compounds by combustion in oxygen with the help of platinised quartz was tried in this laboratory, and in expert hands was found to be both rapid and accurate. The average student, however, experienced great difficulty in the conduct of the combustion, and it occurred to us that the advantages of the apparatus of Dennstedt, so carefully worked out by him in detail, might be applied to the ordinary method of combustion by means of copper oxide.If one inspects a tube in which a copper oxide combustion is being conducted, it is found that the oxide actually reduced to metallic copper, after the combustion of the volatile matter is completed, rarely extends for more than an inch or two along the tube, unless the process has been accidentally “rushed.”
XXII.—Integration of a Certain System of Linear Partial Differential Equations of Hypergeometric Type
Authors: Erdélyi A. 
Published: June 2016

1. The integration of systems of linear partial differential equations of hypergeometric type has been the subject of a great number of recent investigations (e.g. Appell, 1925; Appell-Kampé de Fériet, 1926). Especially Professor Horn (see references) and his pupils, for instance Borngässer (1933), have done much valuable work in this field.The first method that suggests itself for integrating systems of this type is to try power-series expansions of the solutions in the neighbourhood of the singular points of the system. This method, however, does not yield in general a complete set of solutions. Those singular points of the system in which more than n singular manifolds intersect, n being the number of independent variables, give rise to considerable difficulties.
XI.—An Investigation into the Effects of Seasonal Changes on Body Temperature
Authors: Simpson Sutherland 
Published: June 2016

SummaryMonthly observations, extending over one year, were made on the rectal temperature of 114 domestic fowls (Gallus gallus, ♀) and records from forty-one of these were obtained for two years. Six different breeds were used, each located in a separate pen, all under similar conditions, and the mean temperatures for each group were plotted out to form an annual temperature curve. It was found that—1. The lowest temperatures occur in December, January, and February, and the highest in June, July, and August, corresponding in a general way with the temperature of the external air.2. Barometric pressure does not appear to have any influence on the body temperature of the hen.3. The curve of egg-production does not coincide with the annual temperature curve, the former reaching its highest level in April and May, the latter in June, July, and August.If we compare the mean rectal temperature at two periods of the year when the external or weather conditions are approximately the same (April-May and September-October), but when the vitality of the birds, as indicated by the curve of egg-production, moulting, etc., is at a maximum and minimum respectively, we find that the figures are practically identical. This would seem to show that cyclical bodily changes have little effect on body temperature as compared with outside influences.
XII.—The Theory of Circulants from 1861 to 1880
Authors: Muir Thomas 
Published: June 2016

Robert's theorem concerns the circulant C whose elements are the terms of the expansion of and is to the effect (1) that there are no odd powers of t in the development of the circulant, and (2) that if in the said development ξ be put for t2, the equation in ξ
XX.—Changes of Electrical Resistance accompanying Longitudinal and Transverse Magnetizations in Iron and Steel
Authors: Knott C. G. 
Published: June 2016

In January 1913 I communicated a paper on the changes of resistance of nickel when subjected to a combination of longitudinal and transverse magnetic fields (1). The following paper contains an account of exactly similar experiments with iron and steel.Each steel or iron strip formed the core of an anchor-ring coil which was double-wound, with two exactly equal coils of copper wires. When the current was passed through the two contiguous coils in series in the same direction the metal cores were magnetized longitudinally. When the current was passed in opposite directions through the two coils there was no magnetization produced in the cores, but the heating effect was the same as in the first case. At the beginning of each experiment the current was applied in the latter or unmagnetizing arrangement, and was sustained for a sufficient time to permit the temperature to become practically constant. With reversal of the current in the one half of the enveloping coil a longitudinally magnetizing force was established within the region occupied by the iron or steel core. By means of a succession of reversals and rereversals the core could be subjected to a cyclical variation of magnetizing force, while the temperature remained practically constant.
XII.—Matrices and Continued Fractions
Authors: Turnbull H. W. 
Published: June 2016

In a communication to this Society in 1916 Professor E. T. Whittaker gave an illuminating exposition of the use of matrices in dealing with continued fractions. In particular he discussed the problem of differentiating the following function of x:—the value of f′(x) being obtained in the first instance from the leading element in the square of a certain reciprocal matrix {M(x)}−1 (cf. formula (9), § 3, below) by a method which I have recapitulated at the opening of § 4. The expression for f′(x) was then given as the quotient of two determinants obtained in a simple and specific manner from the matrix M(x) itself. It was remarked that this treatment of continued fractions takes its rise in a work by Sylvester, who incidentally showed that the fraction f(x) could be expressed as the quotient of two determinants. It was clear that this quotient expressed the leading element in the reciprocal of the matrix M(x): and the question naturally arose, what were the values of the other elements of this reciprocal?
The Rhizopods and Heliozoa of Loch Ness
Authors: Murray James 
Published: June 2016

Dr Penard has examined and reported upon the Rhizopods and Heliozoa collected in Loch Ness at depths exceeding 250 feet. No littoral samples were sent to him, as his object was to investigate the sarcodine fauna peculiar to deep lakes. The majority of the species found in the deep collections were recognised as belonging to the fauna of the littoral region, or of the adjacent moors, only some half a dozen species or varieties being regarded as peculiar to the abyssal region.In order to complete the list of the Sarcodina of Loch Ness, in so far as this can be done from the observations made by the Lake Survey, I now add the names of several species which were not detected in any of the collections sent to Dr Penard. Nearly all are common bog species.
Note on the Rainfall on the Drainage Area of the Talla Reservoir
Authors: Blyth B. Hall , Tait W. A. 
Published: June 2016

In 1895 the Edinburgh and District Water Trustees obtained an Act of Parliament for the introduction of a new water supply to the city of Edinburgh drawn from the Talla Water, one of the upper tributaries of the river Tweed.The Bill as originally introduced contained provisions for giving off 4,000,000 gallons a day as compensation to the stream, and for appropriating the remainder of the water.The Tweed Salmon Fisheries Commissioners and other proprietors interested were advised that the proposed amount of compensation was too small, and after various negotiations a clause was ultimately adjusted providing that rain gaugings should be taken over the drainage area for a period of seven years from the 1st January 1896 by the authors of this note (Mr Tait having been appointed in lieu of his predecessor), and that thereafter they should fix—taking all the circumstances into consideration—what was the available annual rainfall of the district.
On the Opacity of Aluminium Foil to Ions from a Flame
Authors: Carse George A. 
Published: June 2016

The apparatus used to show that aluminium was opaque to the ions from a flame consisted (see fig. 1) of a tube A, which wasfunnel-shaped at one end, the other end of which led to an enclosure B, one side of which (a b) was made of aluminium foil connected to earth, and on the other side there was an insulated metallic plate (c d), which could either be connected to earth or to a high potential battery. On the other side of the aluminium foil there was an electroscope in a closed case C. The electroscope was of the type used by C. T. R. Wilson in his experiments on the natural ionisation of air in closed vessels.
Note on some generally accepted Views regarding Vision
Authors: Peddie W. 
Published: June 2016

The following beliefs regarding vision meet with very general acceptance:—First. Very intense light of any wave-length produces practically the sensation of whiteness.Second. Very weak light of any wave-length produces practically the sensation of whiteness.Third. A coloured area of normal brightness retains its colour, though with diminished purity, when gazed at steadily for a long time.Fourth. Small, faintly luminous, objects are seen more easily by indirect vision than by direct vision.
Chairman's Opening Address
Authors: Maclagan Douglas 
Published: June 2016

It is in conformity with time honoured custom, and in the performance of duty, that I offer a short address on the occasion of the opening of the Society's 109th Session.I confess that I have little to say which can be expected to attract the notice of the Fellows, or to bear to be recorded in our proceedings; but I am glad to be able to state that alike as regards Fellowships, Finances, and the work of the past Session, the Society is in a prosperous condition.
Note on a Theorem regarding a Series of Convergents to the Roots of a Number
Authors: Muir Thomas 
Published: June 2016

If the positive integral powers of be taken, and the expansion of each be separated into two parts, rational and irrational, thus—then the ratio of the rational portion to the coefficient of in the other portion is approximately equal to , the convergence being perfect when the power of the binomial is infinite. This is the simplest case of a theorem discovered by the late Dr Sang, and enunciated by him as the result of a process of induction in his paper “On the Extension of Brouncker's Method to the Comparison of several Magnitudes” (Proc. Roy. Soc. Edin., vol. xviii. p. 341, 1890–91).
Note on Uniform Convergence
Authors: Cayley  
Published: June 2016

It appears to me that the form in which the definition or condition of uniform convergence is usually stated, is (to say the least) not easily intelligible. I call to mind the general notion : We may have a series, to fix the ideas, say of positive termsthe successive terms whereof are continuous functions of x, for all values of x from some value less than a up to and inclusive of a (or from some value greater than a down to and inclusive of a): and the series may be convergent for all such values of x, the sum of the series øx is thus a determinate function øx of x; but øx is not of necessity a continuous function; if it be so, then the series is said to be uniformly convergent; if not, and there is for the value x = a a breach of continuity in the function øx then there is for this value x = a a breach of uniform convergence in the series.
III.—The Effects of Diet on the Development and Structure of the Uterus
Authors: Campbell Malcolm 
Published: June 2016

The investigation was undertaken to discover what changes, if any, were produced in the development and structure of the uterus by various diets.The animals employed in the research were rats. The uteri of 86 animals were examined, both macroscopically and microscopically. The tissue for microscopic examination was removed in all cases from, as nearly as possible , the same area, viz., the junction of the distal and middle thirds of the uterus.
V.—Note on the Change produced in the Conductivity and Density of Lead Wires by Permanent Stretching
Authors: Donaldson James A. , Wilson Robert 
Published: June 2016

The wires used were of good commercial lead and well drawn.The special difficulty in experimenting with lead is due to its softness, involving initial lack of uniformity in section, which is increased on stretching. That the variability of the section of the wire might be allowed for in the computation of specific resistance, etc., the diameter was measured at the ends, at two points respectively one inch from each end, and at eight other points dividing the rest of the length of the wire into equal parts. The ends of the wire were soldered into copper pieces to prevent serious thinning near the ends when it was stretched.
XII.—On the Electrical Conductivity of Aqueous Hydrochloric Acid, saturated with Sodium Chloride; and on a new form of Conductivity Cell
Authors: Miles F. D. 
Published: June 2016

Summary(1) Determinations have been made, at 18° C, of:—(a) the specific electrical conductivity, (b) the percentage composition by weight, of a series of mixtures made by saturating, with sodium chloride, solutions of hydrochloric acid containing from 16 to 27 per cent, of hydrogen chloride.(2) Within this range of concentration the salt-saturated acid has lower specific conductivity than the aqueous solution of hydrogen chloride alone, from which it may be supposed to be derived. Of the salt-saturated acid mixtures, that one has maximum conductivity which could be prepared by adding salt to hydrochloric acid containing 2·9 per cent, of hydrogen chloride. Of solutions of hydrogen chloride alone, in water, that containing 19·1 per cent, hydrogen chloride has maximum conductivity.(3) The critical concentration of hydrogen chloride at which hydrochloric acid is able to affect the colour of cobalt chloride is changed, in the same sense as the concentration of hydrogen chloride corresponding to maximum conductivity is changed, by saturating the solution with salt.(4) A new form of conductivity cell is described. It is specially suitable for solutions which are saturated with dissolved solid, or contain a volatile solvent.
XV.—An Analysis of an Electron - Transference Hypothesis of Chemical Valency and Combination
Authors: Marshall John 
Published: June 2016

In this paper it is proposed to analyse in a tentative way the Electron-Transference Hypothesis of Chemical Combination which has been put forward by Lord Kelvin in his paper entitled “Aepinus Atomised” (Phil. Mag., 1902), and by Sir J. J. Thomson (Phil. Mag., 1904).This hypothesis postulates that on the combination of two or more atoms to form a chemical compound electrons are transferred from atoms playing an electro-positive part to those playing an electro-negative part in the molecule, the number of electrons thus transferred being taken as a measure of the valencies of the respective atoms in the molecule. Such an hypothesis would not lead to conceptions at variance with the facts of electrolytic dissociation.
XVII.—Discontinuities in the Atmosphere
Authors: Goldie A. H. R. 
Published: June 2016

This paper contains the results of an investigation, on empirical and dynamical lines, into the following matters:—(1) The origin of surfaces of discontinuity in the atmosphere;(2) The precise processes occurring at such surfaces in well-defined cases;(3) The physical processes which lead to the obliteration or movement of the discontinuities;(4) The part played by the discontinuities in the development of the cyclones of temperate latitudes.
XI.—The Zeta Function of Jacobi. A seven-decimal table of Z(u/m) at interval 0·01 for u and for values of m(= k2) from 0·1 to 1·0
Authors: Milne-Thomson L. M. 
Published: June 2016

The elliptic integral of the second kindcan, by substitution, be made to depend uponWriting E(K) = E, Jacobi's Zeta function is defined bywhereZ(u) is an odd function of u with period 2K.
XIII.—The Genetic Basis of Alkaptonuria
Authors: Hogben Lancelot , Worrall R. L. , Zieve I. 
Published: June 2016

Summary1. The overwhelming majority of cases of alkaptonuria are consistent with the hypothesis that this disease is determined by a single autosomal recessive gene substitution.2. The observed proportion of alkaptonurics in recorded fraternities with two normal parents and the incidence of consanguineous parentage conform quantitatively to the requirements of Mendelian hypothesis in a system of random mating.3. There appears to be an alternative form of alkaptonuria which is dominant.Grateful acknowledgment is made to Sir Archibald Garrod for advice regarding the sources consulted.