bluuebunny/crossref_metadata_2025_split huggingface dataset:
Catholic Charitable Endeavour in London, 1810–1840. Part I
Authors: Carter Brian 
Published: July 2016

The primary focus of this article centres on the two decades that form the prelude to Catholic Emancipation although reference is made to activity outside this time frame and to cities other than London. Charitable endeavour is taken to include all individual voluntary effort to sustain and support Catholic churches, schools and other Catholic organisations in need of assistance. It also relates to assistance given to individuals in need of help. Such ‘endeavour’ also encompasses group and community-based voluntary activity. While it may seem unnecessary to define charitable endeavour, Mary J. Oates in a recent study on the Catholic philanthropic tradition in America heavily circumscribes what she means by the term, and excludes a number of subjects from her examination, thus:Not all contributions to the Church are philanthropic. For example, contributions to support the local pastor, Church, and parish programs which chiefly benefit the congregation itself, do not qualify as charitable giving. Nor do gifts by individual Catholics to extra-ecclesial philanthropic causes.
Anti-Catholic Polemical Writing on the ‘Rising in the North’ (1569) and the Catholic Reaction
Authors: Busse Daniela 
Published: July 2016

This article seeks to investigate the public images of the 1569 Rising in the North, as conceived by government policy, propaganda and loyalist writers on the one hand and by Catholic theologians and sympathisers on the other. It focuses especially on texts such as proclamations, homilies, street and folk ballads, pamphlets and tracts. To date there is only one study which deals extensively with the polemical literature on the Rising. This is that by J. K. Lowers published in 1953. He concentrates on Tudor ideas of civil obedience and its representation in loyalist writing wanting to help literature students to understand contemporary texts. As a literary study his book is valuable and he makes some highly relevant points.To date there is only one study which deals extensively with the polemical literature on the Rising. This is that by J. K. Lowers published in 1953. He concentrates on Tudor ideas of civil obedience and its representation in loyalist writing wanting to help literature students to understand contemporary texts. As a literary study his book is valuable and he makes some highly relevant points.
Classical theism and modal realism are incompatible
Authors: VANCE CHAD 
Published: July 2016

AbstractThe classical conception of God is that of a necessary being. On a possible worlds semantics, this entails that God exists at every possible world. According to the modal realist account of David Lewis, possible worlds are understood to be real, concrete worlds – no different in kind from the actual world. But, modal realism is equipped to accommodate the existence of a necessary being in only one of three ways: (1) By way of counterpart theory, or (2) by way of a special case of trans-world identity for causally inert necessary beings (e.g. pure sets), or else (3) causally potent ones which lack accidental intrinsic properties. I argue that each of these three options entails unacceptable consequences – (1) and (2) are incompatible with theism, and (3) is incompatible with modal realism. I conclude that (at least) one of these views is false.
XIV.—Further Investigations in Factor Estimation
Authors: Lawley D. N. 
Published: July 2016

Summary7. A method of factor estimation is given in which assumptions are made only about the form of the error distributions of the tests administered. This is compared with a method previously suggested in which, on the contrary, the test scores and the individual factor measurements were assumed to be normally distributed over the population of individuals tested. A comparison is also made with other processes at present in use.
XXI.—Sylvester's Unravelment of a Ternary Quartic
Authors: Edge W. L. 
Published: July 2016

SummaryThe paper makes use, for the study of a ternary quartic, of a five-dimensional configuration consisting of a Veronese surface and a quadric outpolar to it, and uses the notation and results of a preceding paper to which reference is made at the outset. In § 1 certain identities are given which are consequences of the form of the matrix of a quadric outpolar to a Veronese surface, and the geometrical theorems equivalent to these identities are stated. In § 2 it is explained how covariants and contravariants of a ternary quartic are represented by curves in the fivedimensional configuration. It is, indeed, not until this technique is used that some of the work of Clebsch, Ciani, Coble, and others is properly appreciated; §§ 3—6 are concerned to emphasise this. But, as is pointed out in § 7–9, it is to Sylvester that these matters must properly be referred; for he has, by his process of unravelment, anticipated practically everything of moment in the ideas of his successors. The word unravelment is used by him on p. 322 of Vol. I of his Mathematical Papers, the process having appeared on p. 294.In opening the second part of the paper with § 10 it is pointed out that the configuration should be used not merely to illuminate the work of previous writers, but also to discover new results. It is not the purpose here to exploit this at length, but it is seen how a covariant conic inevitably appears; its equation is obtained and, in §11, its covariance directly established. Other covariant conies are alluded to in § 12. And it is found, in § 13, that here too reference must be made to Sylvester.
XI—The Identification of Klein's Quartic
Authors: Edge W. L. 
Published: July 2016

SummaryThere is a mode of specialising a quartic polynomial which causes a binary quartic to become equianharmonic and a ternary quartic to become a Klein quartic, admitting a group of 168 linear self-transformations. The six relations which must be satisfied by the coefficients of the ternary quartic were given by Coble forty years ago, but their true significance was never suspected and they have remained until now an isolated curiosity. In § 2 we give, in terms of a quadric and a Veronese surface, the geometrical interpretation of the six relations; we also give, in terms of the adjugate of a certain matrix, their algebraical interpretation. Both these interpretations make it abundantly clear that this set of relations specialising a ternary quartic has analogues for quartic polynomials in any number of variables, and point unmistakably to what these analogues are.That a ternary quartic is, when so specialised, a Klein quartic is proved in §§ 4–6. The proof bifurcates after (5.3); one branch leads instantly to the standard form of the Klein quartic while the other leads to another form which, on applying a known test, is found also to represent a Klein quartic. One or two properties of the curve follow from this new form of its equation. In §§ 8–10 some properties of a Veronese surface are established which are related to known properties of plane quartic curves; and these considerations lead to a discussion, in § 11, of certain hexads of points associated with a Klein curve.
XVIII.—The Riemann Tensor in a Completely Harmonic V4
Authors: Ruse H. S. 
Published: July 2016

If is a fixed point of a Riemannian Vn of fundamental tensor gij, and if s is the geodesic distance between it and a variable point (xi), then the Vn has been called centrally harmonic with respect to the base-point ifis a function of s only, and completely harmonic if this holds for every choice of base-point . A flat Vn (gij=δij) is obviously completely harmonic, since for such a space and
XLVI.—The Mechanics of Continuous Matter in the Relativity Theory
Authors: Clark G. L. 
Published: July 2016

SummaryLittle progress has been made in the development of a relativity theory of elasticity, although it has been realised that no disturbance can be propagated with a velocity greater than that of light. In 1917 Lorentz (1) gave a relativistic formulation of the laws of elasticity in the case of small strain and, applying the theory to the problem of a rotating, incompressible, homogeneous disc, he claimed that the radius as measured by an observer at rest on the disc undergoes a contraction. His result was accepted by Eddington (4) but was attacked by others. A great deal has been written on the subject, but it has never been pointed out that both Lorentz and Eddington were considering material in which the waves of dilatation travel with an infinite velocity. In this paper we define “incompressible” matter as that in which these waves are propagated with the velocity of light and Poisson's ratio tends to the value ½. This gives an upper limit to the modulus of compression k, which in this case is the elastic constant λ, and as a result the expansion determined by the ordinary classical theory has to be taken into account. It is found that the “relativity contraction” is exactly cancelled by the “classical expansion”. Throughout the discussion on the rotating disc the analysis is restricted to the case of small strain.The equations of equilibrium of a continuous static distribution of matter are also investigated in the case of weak fields for which the fourth power of the density may be neglected.
XIV.—Experiments in Diffraction Microscopy
Authors: Rogers G. L. 
Published: July 2016

SynopsisExperiments have been performed, using purely optical methods, to verify and extend the theory of Gabor's diffraction microscope. An elementary theory of the process is first given, from which certain generalizations are provisionally drawn. In particular, a focal length is attributed to any Fresnel diffraction pattern and the hologram derived from it by photography. The variation of this focal length with wavelength and scale factor is postulated by analogy with a zone-plate, and the power-rate for a hologram is denned. These deductions are then verified by experiment, and a summary is given at the end of § 10. Various other confirmatory experiments are then described.Adequate information is given about apparatus and technique to enable new entrants into this field to obtain satisfactory results with the minimum of preliminary trial.
XVII.—The Sargent Diagram for the Electron-capture Process, and the Disintegration Energies of Heavy β-emitters
Authors: Feather N. 
Published: July 2016

SynopsisA Sargent diagram is presented containing 12 plotted points relative to capture-active species in the range of atomic number (Z) from 89 to 98 inclusive. Arguments are adduced to show that the “allowed” line of the diagram is located as theory predicts, and the capture transformations of other heavy capture-active species are discussed with the aid of the diagram. In particular, values are deduced for the energies of capture transformation of 17 species for which 79 ≤ Z ≤ 85, and, taking count of these values, the energies of β-disintegration of 150 species having 76 ≤ Z ≤ 98 are assumed known, and are suitably plotted against neutron number N. Discontinuities are found, for certain values of isotopie number, in the region of N = 126 (and Z = 82). Values of α-disintegration energy are also deduced for certain isotopes of bismuth and lead.
XIX.—A Generalization of the Classical Random-walk problem, and a Simple Model of Brownian Motion Based Thereon
Authors: Klein G. 
Published: July 2016

SynopsisSuggested by the analogy between the classical one-dimensional random-walk and the approximate (diffusion) theory of Brownian motion, a generalization of the random-walk is proposed to serve as a model for the more accurate description of the phenomenon. Using the methods of the calculus of finite differences, some general results are obtained concerning averages based on a time-varying bivariate discrete probability distribution in which the variates stand in the particular relation of “position” and “velocity.” These are applied to the special cases of Brownian motion from initial thermal equilibrium, and from arbitrary initial kinetic energy. In the latter case the model describes accurately quantized Brownian motion of two energy states, one of zero energy.
XX.—On the Estimation of Variance and Covariance
Authors: Lloyd E. H. 
Published: July 2016

SynopsisSuppose we have a number of independent pairs of observations (Xi, Yi) on two correlated variates (X, Y), which have constant variances and covariance, and whose expected values are of known linear form, with unknown coefficients: say respectively. The pij and the qij are known, the aj and the bj are unknown. The paper discusses the estimation of the coefficients, and of the variances and the covariance, and evaluates the sampling variances of the estimates. The argument is entirely free of distributional assumptions.
XXVII.—The Rotational Field behind a Bow Shock Wave in Axially Symmetric Flow using Relaxation Methods
Authors: Mitchell A. R. , McCall Francis 
Published: July 2016

SynopsisThe relaxation technique of R. V. Southwell is developed to evaluate mixed subsonic-supersonic flow regions with axial symmetry, changes of entropy being taken into account. In the problem of a parallel supersonic flow of Mach number I·8 impinging on a blunt-nosed axially symmetric obstacle, the new technique is used to determine the complete field downstream of the bow shock wave formed. Lines of constant vorticity and Mach number are shown in the field, and where possible a comparison is made with the corresponding 2-dimensional problem.
XII.—On the Theory of Unimolecular Gas Reactions: A Quantum Harmonic Oscillator Model
Authors: Slater N. B. 
Published: July 2016

SynopsisThe writer's theory of unimolecular dissociation rates, based on the treatment of the molecule as a harmonically vibrating system, is put in a form which covers quantum as well as classical mechanics. The classical rate formulæ are as before, and are also the high-temperature limits of the new quantum formulæ. The high-pressure first-order rate k∞ is found first from the Gaussian distribution of co-ordinates and momenta of harmonic systems, and is justified for the quantum-mechanical case by Bartlett and Moyal's phase-space distributions. This leads to a re-formulation of k∞ as a molecular dissociation probability averaged over a continuum of states, and to a general rate for any pressure of the gas.The high-pressure rate k∞ is of the form ve-F/kT, where v and F depend, in the quantum case, on the temperature T; but v is always between the highest and lowest fundamental vibration frequencies of the molecule. Concerning the decline of the general rate k with pressure at fixed temperature, k/k∞ is to a certain approximation the same function of as was tabulated earlier for the classical case, apart from a constant factor changing the pressure scale in the quantum case.
XIII.—Layered Systems Subjected to Asymmetric Surface Shears
Authors: Westmann R. A. 
Published: July 2016

SynopsisThis paper formulates a general solution, within the scope of classical elastostatic theory, for the problem of layered systems subjected to asymmetric surface shears. As an illustrative example the solution for the problem of an elastic layer supported on an elastic half-space is presented for the particular loading consisting of a surface shearing force uniformly distributed over a circular area. Numerical results are included indicating some displacement and stress components of interest.
XIV.—Dual Series Relations. I. Dual Relations Involving Fourier-Bessel Series
Authors: Sneddon I. N. , Srivastav R. P. 
Published: July 2016

SynopsisThe solution of the dual series relationswhere {λn) is the sequence of positive zeros of the Bessel function Jν(αλ), arranged in order of increasing magnitude, þ and ν are real numbers (−1 <þ < 1, ν >0), the functions, f1(ρ), f2(ρ) being prescribed, is obtained by giving an integral representation of {αn} in terms of a single function g(t). The problem is reduced to that of solving a Fredholm integral equation of the second kind for the auxiliary function g(t).
XV.—A Matrix Analogue of the Integral
Authors: Jack Henry 
Published: July 2016

SynopsisA multiple integral, whose integrand is an n × n determinant, is evaluated over certain regions of n-dimensional space. Similar integrals are encountered in the theory of Zonal polynomials. In the course of the work a partition problem arises. In the next paper of these Proceedings, Professor Rutherford enumerates these partitions and relates the subject to the theory of the representation of the symmetric group.
XX.—Some New Results in Maximum Likelihood Factor Analysis
Authors: Lawley D. N. 
Published: July 2016

SynopsisUntil now the chief obstacle to the application of the maximum likelihood method of estimation to factor analysis has been the lack of any really good numerical method of solution. In this paper we give a brief review of recent work which remedies this defect. Two factor analysis models are considered. In each case we derive results which are of use in connection with new methods of solution. Formulae are given for the large-sample variances and covariances of the estimates of parameters in the first model.
IX.—The Synthesis of 8-Bromo-3-methoxyfluoranthene.
Authors: Campbell Neil , Hasan Naim M. 
Published: July 2016

SummaryA second method for the synthesis of 8-bromo-3-methoxyfluoranthene from 2-bromo-7-methoxyfluorene is described. The autoxidation of fluorene derivatives including the 9-carboxylic acids and of related compounds, particularly 4-α-cyanobenzyl-7−oxo-7H-benz[de]anthracene, is discussed. Unsuccessful attempts to prepare 3-bromofluorene-9-acetic acid in good yield are reported.
XIV.—On Isotone Homomorphic Boolean Images of Ordered Semigroups
Authors: Blyth T. S. 
Published: July 2016

SynopsisNecessary and sufficient conditions for an ordered semigroup to admit an isotone homomorphic Boolean image are given together with a complete description of how all such images are obtained. Also discussed are the situations arising from a strengthening of the notion of a homomorphism.
VII.—Some Contributions to the Theory of Random Walk and Multiple Scattering of Particles
Authors: Allnutt A. J. , Fürth R. 
Published: July 2016

SynopsisA theory of the random walk with “persistence” of movement of a point in a three-dimensional cubic lattice is presented from which explicit expressions for the moments of the distribution function for the displacements of an ensemble of points after N steps for any arbitrary initial average velocity are derived. The results are applied to the problem of small angle multiple scattering of particles on their passage through a material medium, and formulae for the mean square of the lateral displacements are obtained which, in first approximation, have the form of the expressions, generally used for evaluating the experimental results but, in higher approximation, indicate a deviation from this relationship for greater thickness of matter.Another approach to the same problem of multiple scattering is further presented which is based on Kramer's stochastic differential equation for the distribution function for the position and velocities of an ensemble of particles in phase space. By this method formulae for the mean square of the scatter angles, the lateral displacements and the correlation products between these are derived. The first of these expressions shows again characteristic deviations from the usual ones for greater thickness of matter, the second coincides essentially with the expression obtained from the random walk theory.
XVIII.—Elimination of Toluenesulphinic Acid from 4-Alkylamino-benzhydryl Sulphones: a Route to 4-Aminodiphenylmethanes
Authors: Stevens T. S. 
Published: July 2016

SynopsisOn treatment with t-amyl-alcoholic sodium t-amyloxide, sulphones of the type TsCHAr.C6H4.NPhCH2R lose the elements of toluenesulphinic acid giving the Schiff base ArCH2.C6H4.N = CHR, which can be hydrolysed to ArCH2.C6H4.NH2.
XXII.—A Priori Estimates and Nonlinear Parabolic Equations of Arbitrary Order
Authors: Edmunds D. E. , Stuart C. A. 
Published: July 2016

SynopsisIn this paper it is shown that the question of the existence of a classical solution of the first initial-boundary value problem for a non-linear parabolic equation may be reduced to the problem of the derivation of suitable a priori bounds.
15.—On a Source of Polarised Electrons
Authors: Campbell D. M. , Brash H. M. , Farago P. S. 
Published: July 2016

SynopsisA prototype source of polarised electrons is described, in which electrons trapped by a combination of electric and magnetic fields are polarised through spin exchange interaction with a polarised beam of potassium atoms. Under typical operating conditions, a pulsed electron beam was extracted with 104 electrons per pulse and a polarisation of 0·45 at a repetition rate of 50 S−1. The scope for improvement of these figures is briefly discussed.Values for the total spin exchange collision cross-section at electron energies of 1 eV, 2·5 eV and 4 eV were obtained. These are in reasonable agreement with theoretical predictions.
17.—Remarks on the Prehistory of the Discovery of Slow Neutrons
Authors: Goldhaber Maurice 
Published: July 2016

Segrè in his recent book [1] on Fermi gives an interesting account of the discovery of slow neutrons at the Institute of Physics of the University of Rome on October 22, 1934. He quotes (p. 80) a statement Fermi made many years later in a conversation with S. Chandrasekhar on the process of discovery in physics:‘I will tell you how I came to make the discovery which I suppose is the most important one I have made. We were working very hard on the neutron-induced radioactivity and the results we were obtaining made no sense. One day, as I came to the laboratory, it occurred to me that I should examine the effect of placing a piece of lead before the incident neutrons. Instead of my usual custom, I took great pains to have the piece of lead precisely machined.
21.—Riding Motion and Higher Cumulants in Crystallographic Models
Authors: Pawley G. S. 
Published: July 2016

SynopsisThe motion of hydrogen atoms due to the internal vibrational modes of a molecule is large and curvilinear. Because of the curvilinear motion the mean displacements of these atoms cannot be described by ellipsoids alone, but higher order terms or cumulants are necessary. Equations determining these terms from the usual riding motion are presented. By analysing a neutron diffraction study of high accuracy it is shown that the size of these higher cumulants is sufficient for them to be determinable. For deuterated samples however really high accuracy will be necessary in the diffraction experiment.
1.—On the Existence of Solutions of a Nonlinear Differential Diffusion System.
Authors: Lee C. F. 
Published: July 2016

SynopsisThe existence and the properties of the solutions of a nonlinear differential system describing a diffusion system with concentration-dependent diffusion coefficients are investigated. It is shown that there exists at least one solution which is monotonie decreasing and asymptotically tends to the prescribed value.
4.—A Cauchy Problem for an Ordinary Integro-differential Equation
Authors: Catchpole E. A. 
Published: July 2016

SynopsisIn this paper we study an ordinary second-order integro-differential equation (IDE) on a finite closed interval. We demonstrate the equivalence of this equation to a certain integral equation, and deduce that the homogeneous IDE may have either 2 or 3 linearly independent solutions, depending on the value of a parameter λ. We study a Cauchy problem for the IDE, both by this integral equation approach and by an independent approach, based on the perturbation theory for linear operators. We give necessary and sufficient conditions for the Cauchy problem to be solvable for arbitrary right-hand sides—these conditions again depend on λ—and specify the behaviour of the IDE when these conditions are not satisfied. At the end of the paper some examples are given of the type of behaviour described.