bluuebunny/crossref_metadata_2025 huggingface dataset:
XLVI.—The Mechanics of Continuous Matter in the Relativity Theory
Authors: Clark G. L.
Published: July 2016

Little 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

Synopsis

Experiments 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

Synopsis

A 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

Synopsis

Suggested 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

Synopsis

Suppose 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

Synopsis

The 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

Synopsis

The 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

Synopsis

This 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

Synopsis

The solution of the dual series relations

where {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

Synopsis

A 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.
XVIII.—The Solution of Equations in a Lattice.
Authors: Goodstein R. L.
Published: July 2016

Synopsis

Necessary and sufficient conditions are given for the existence of solutions of equations, in any number of variables, on distributive lattices with least and greatest elements, together with an algorithm for determining a solution when these conditions are satisfied.
XX.—Some New Results in Maximum Likelihood Factor Analysis
Authors: Lawley D. N.
Published: July 2016

Synopsis

Until 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

A 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

Synopsis

Necessary 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

Synopsis

A 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.
IX.—The Synthesis of 8-Phenyl-7H-Benz[de]anthracene
Authors: Campbell Neil , Walker Jamieson
Published: July 2016

2-Benzylidene-2,3-dihydrophenalen-i-one with ethyl acetoacetate and sodium ethoxide yields four products depending on the concentration of the alkali. One of these, ethyl 7a,8,9,10-tetrahydro-10-oxo-8- phenyl-7H-benz[de]-anthracene-9-carboxylate has been converted into 8-phenyl-7H-benz[de]anthracene and its reduction with sodium borohydride or hydrogen in the presence of platinum oxide or Raney nickel presents points of interest.
XVIII.—Elimination of Toluenesulphinic Acid from 4-Alkylamino-benzhydryl Sulphones: a Route to 4-Aminodiphenylmethanes
Authors: Stevens T. S.
Published: July 2016

Synopsis

On 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

Synopsis

In 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

Synopsis

A 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

Synopsis

The 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

Synopsis

The 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.
7.—The Authorship and Integrity of the Athenaion Politeia
Authors: Morton A. Q. , Michaelson S.
Published: July 2016

The existence of a work by Aristotle on the constitution of Athens is attested by the historians Philochorus, writing before 306 B.C., and Timaeus, writing about 300 B.C. No trace of such a work was known until 1891, when the almost complete text of one was recovered from the sands of Egypt by F. G. Kenyon of the British Museum. It was then recognised that two small and much damaged sheets found ten years before also contained parts of this work.
4.—A Cauchy Problem for an Ordinary Integro-differential Equation
Authors: Catchpole E. A.
Published: July 2016

Synopsis

In 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.
9.—A Note on the Hypergraph of a Mapping between Uniform Spaces
Authors: Hitchcock A. G.
Published: July 2016

The usual ‘closed-graph theorems’ are concerned with the question of which topological structures on sets X, Y will ensure equivalence of continuity and closed-graph conditions for certain mappings t: X → Y. In this paper some stronger closed-graph like conditions are introduced on a mapping between uniform spaces, by considering the ‘hypergraph’, or graph of the induced mapping between hyperspaces. The central result, included in Theorem 1, states that for arbitrary uniform spaces X, Y, t is continuous if its hypergraph is closed. Thus for topological vector spaces (and some others) the closed-hypergraph condition is equivalent to continuity. In section 2 some situations are found in which continuity is implied by certain intermediate conditions to closed-graph and closed-hypergraph conditions. In particular, a closed-hypergraph theorem is shown to hold for locally convex spaces, provided only that X is barrelled. Finally, in section 3, the hypergraph of a relation is studied, and the separatedness of the quotient space of an equivalence relation is shown to replace continuity with regard to closed-graph and closed-hypergraph conditions.
19.—Concavity and the Evolutionary Properties of a Class of General Materials
Authors: Hills R. N. , Knops R. J.
Published: July 2016

Concavity arguments have been used by Knops, Levine and Payne [1] to discuss evolutionary properties of weak solutions to an abstract non-linear differential equation in a Hilbert space. These authors demonstrate that provided the non-linearity is suitably restricted and for specified initial data, the norm of the solution becomes unbounded in a finite time. In other words, the solution possesses a finite escape time.
25.—Spectrum of a Third-order Differential Operator with Large Coefficients
Authors: Unsworth K.
Published: July 2016

Synopsis

This paper sets out to study the spectrum of self-adjoint extensions of the minimal operator associated with the third-order formally symmetric differential expression. The technique employed is the method of singular sequences. Sufficient conditions are established on the coefficients of the differential expression in order that the spectrum should cover the entire real axis. Particular cases in which the coefficients behave roughly as powers of x as the magnitude of x becomes large are then considered, and certain conclusions are drawn regarding the spectra under different restrictions on these powers of x.
31.—Spectral Manifolds for Constant Coefficient Elliptic Operators in Lp(Rn)
Authors: Thompson M.
Published: July 2016

Synopsis

The principal results of this paper concern the spectral properties of the maximal realisation Pp in Lp(Rn) of a formally self adjoint constant coefficient strongly elliptic partial differential operator P(D), assumed to be homogeneous of order 2m, for 1 ≦ p ≦ ∞ and n ≧ 2. If we assume that , for 2n/n + l ≦ p ≦ 2n/n−1, together with certain assumptions on the associated real zero surfaces P(ξ) = λ, λ > 0, then σ(Pp) = σc(Pp) = [0, ∞). We obtain an estimate on the norm of the resolvent of Pp for points near the real axis, which allows us to establish the existence of a generalised resolution of the identity in the sense of Kocan.
19.—Calculations relative to the Experimental Observation of the Products of Disintegration of 5He liberated as a Light Particle in Ternary Fission
Authors: Feather N. , Vass D. G.
Published: July 2016

Synopsis

There is now strong evidence, from observations of directional correlation between the α-particles and neutrons of fission, for the release of 5He as a neutron-unstable light particle with a frequency of a few per 104 low-energy fission events (Cheifetz et al. 1972).

Because the energy spectrum of the neutrons liberated in the disintegration of 5He particles travelling with a fixed kinetic energy is a rectangular spectrum (assuming isotropy of disintegration directions in the centre-of-mass space), it is in principle possible to deduce the kinetic energy spectrum characterising the 5He particles of ternary fission at the moment of disintegration from the energy spectrum of the liberated neutrons.

Detailed calculations have been made in relation to the limitations of actual experimental arrangements with regard to this possibility. These limitations are shown to be severe—not least in respect of statistical accuracy. Indeed, it is shown that considerable difficulty attaches to the ‘simple’ evaluation of the 5He/4He ratio (which Cheifetz et al. estimate as 1 :(8 ± 2) for 252Cf, for α-particles of energy greater than 9 MeV).

An instrumental cause is suggested for the maximum reported by Cheifetz et al. in the energy spectrum ascribed to the 5He disintegration neutrons.
22.—Attempted Synthesis of Dibenzo[a,g]biphenylene.
Authors: Campbell Neil , Macpherson R. S. , Morris R. A. N.
Published: July 2016

α-Truxillic acid (1, R = CO2H) (Criegee and Höver 1960) underwent the Arndt-Eistert reaction to yield l,3-diphenylcyclobutane-2,4-diacetic acid (1, R = CH2·CO2H), cyclisation of which with hydrogen fluoride gave cis-trans-cis-5,6,6a,6b, 11,12,12a, 12b-octahydro-5,11-dioxodibenzo[a,g]biphenylene (11). Attempts to aromatise the compound by bromination with N-bromosuccinimide followed by treatment with pyridine or potassium acetate were unsuccessful. The ketone was therefore reduced with potassium borohydride to the corresponding diol (11, CO replaced by CHOH) in the hope that dehydration of the product followed by mild dehydrogenation would yield dibenzo[a,g]biphenylene, but the only product isolated was naphthalene.
27.—The Quantum Theory of the Klystron and the Modulation of Electron Beams at Optical Frequencies
Authors: Farago P. S. , Sillitto R. M.
Published: July 2016

Synopsis

The relationship between the modulation of electron beams at optical frequencies (the Schwarz-Hora effect) and at microwave frequencies is discussed. At optical frequencies the interaction between the modulating field and the electron beam must be described quantum mechanically, although the field itself may be described classically; in the microwave case the process may be described entirely classically. The interaction modifies the state functions of the individual electrons, but the observable modulation of the total electron beam results from the coherence of the modulating field. The main features of the Schwarz-Hora effect result from ‘single photon’ processes, but the beam modulation in the klystron is a ‘multi-photon’ process.

The exponential decay of the depth of modulation with distance from the interaction region, observable in the optical frequency case but not in the klystron, is not an inherently quantal effect. The periodic variation of the depth of modulation with distance along the beam, observed in the optical frequency case, is an essentially quantum mechanical effect, and is different, in its origins and in its dependence on the modulation frequency, from the space-charge waves which are observed on a klystron beam.
5.—Semi-bounded Dirichlet Integrals and the Invariance of the Essential Spectra of Self-adjoint Operators
Authors: Evans W. D.
Published: July 2016

Synopsis

In the first part of the paper a criterion is given for two self-adjoint operators T, S in a Hilbert space to have the same essential spectrum, S being given in terms of T and a perturbation P. If P is a symmetric operator and the operator sum T+P is self-adjoint, then S = T+P. Otherwise, T is assumed to be semi-bounded and S is taken to be the form extension of T+P defined in terms of semi-bounded sesquilinear forms. In the case when S = T+P, the result obtained generalises the results of Schechter, and Gustafson and Weidmann for Tm- compact (m> 1) perturbations of T. In the second part of the paper a detailed study is made of the Dirichlet integral

associated with the general second-order (degenerate) elliptic differential expression in a domain Conditions under which t is closed and bounded below are established, the most significant feature of the results being that the restriction of q to suitable subsets of Ω can have large negative singularities on the boundary of Ω and at infinity. Lastly some examples are given to illustrate the abstract theory.
XIV.—On Analysing the Physical Evolution of Galaxies
Authors: Reddish V. C.
Published: July 2016

SYNOPSIS

Investigations based on gas masses, bright star counts, and luminosity-mass ratios of galaxies lead to one of two conclusions. If the galaxies are all of the same age, the faint ends of the initial luminosity functions of stars at formation differ greatly from one galaxy to another. On the other hand consistent results in the analysis are obtained with luminosity functions that are more nearly constant and ages which range from one to thirty thousand-million years. The various possibilities can be tested by observations on the Magellanic Clouds.

Equations are set up which describe, as functions of time, the integrated properties of a galaxy as a system of stars and gas.
Praedatrix Praeda Fit Ipsa Suae: Mary Magdalen, Federico Borromeo And Henry Constable's Spirituall Sonnettes
Authors: Salmon Frank
Published: July 2016

THERE EXISTS, in Harleian MS. 7553 of the British Library, a set of seventeenSpiritual1 Sonnettes to the honour of God and hys Sayntes by H. C..In his 1812 edition of the manuscript, Thomas Park attributed these poems to the Elizabethan courtier-poet and later recusant Henry Constable on the grounds of the ‘regular Italian structure, and the sainted names of those addressed’.’ Three years later, in hisHeliconia,Park substantiated his attribution by reference to Constable's known Roman Catholicism and to a recantation found at the end of his secular sonnet cycleDianain Dyce MS. 44: ‘When I had ended this last sonet and found that such vayne poems as I had by idle houres writ did amounte iust to the climatericall number 63, me thought it was high tyme for my follie to die and to employe the remnant of my wit to other calmer thoughts lesse sweet and lesse bitter’. The Dyce manuscript-like the Harleian-is not in Constable's own hand, and one scholar has recently thrown doubt on the authenticity of the recantation. Nevertheless, theSpirituall Sonnetteshave without question continued to be considered as Constable's following Park's broad biographical and stylistic outline. The Harleian manuscript appears to date from the early years of the seventeenth century, and this has been assumed to be the likely date of composition for the sonnets as well.
The Role of the Catholic Laity in Yorkshire, 1850–1900
Authors: Supple Jennifer F.
Published: July 2016

THE ROLE of the laity in the Church is a topic of great interest today. Since the second Vatican Council the part which the people could, and should, play in the Church has been discussed at length, and the shortage of priests has led to demands for the laity to become more actively involved in spiritual affairs. Some, however, still maintain that spiritual tasks must be left to the ordained, but would like to see the laity take a much more active role, as Catholics, in the secular sphere, representing and defending Catholic values in public life. In the light of the current debate, it is interesting to look at the role of the laity in the Catholic Church in Yorkshire during the last century. At that time, too, there was a shortage of priests, while the role of Catholics in public life did not always fulfil the desires of Church leaders.
Richard Smith's Gallican Backers and Jesuit Opponents
Authors: Allison A. F.
Published: July 2016

In May 1629, the President of the English College at Douai, Matthew Kellison, published a book entitled: A treatiseofthe hierarchie and diuers orders of the church against theanarchie of Caluin. In spite of the title, the main purpose of the book was not to defend Catholic teaching on the hierarchy against Calvin. Kellison wrote it is in response to an urgent appeal by Richard Smith, Bishop of Chalcedon, at a crucial moment in Smith's episcopate. During the four years in which he had been in England as bishop, Smith had met with mounting opposition from the regulars and from the Catholic nobility and gentry. Opposition from the laity was greatly strengthened by the publication in 1628 of a work by the President General of the English Benedictine Congregation, Rudesind Barlow, maintaining that the papal brief appointing Smith in 1625, properly interpreted, did not grant him the extensive powers he claimed. What Smith was asking of Kellison in 1629 was not a work in support of his claims in detail—he intended to write that himself—but a general treatise addressed to the lay Catholics explaining the theological basis on which those claims rested. Kellison, as President of the English College and a theologian of international repute, was the ideal man for the task. ‘In these circumstances,’ Kellison a letter two years later, describing how his book came to be written, ‘the Bishop and leading members of the clergy wrote to me urging me to produce a book on the dignity and authority of bishops. Because of my respect for them, and also because of my love for my country, I consented …’
A Note on Bury's Hall in Norfolk
Authors: Holt, S.J. T. G.
Published: July 2016

TWENTY YEARS AGO an article entitled ‘The Eyres of Hassop and some of their connections from the Test Act to Emancipation’ was published in two parts in Recusant History. A section was devoted to the Eyres of Norfolk. Their house in that county—Bury's or Bures or Berries Hall near Swaffham—was acquired by Thomas Eyre at some date shortly before 1688 and passed to three of his six sons, Henry, John and James, in succession, being sold after the death of the last in 1749. In recent years it has ceased to be a private house and is now a country hotel. There remain in the neighbourhood to remind the visitor of the family the monumental inscriptions in the nearby Holme Hale church to Mary, the wife of Thomas Eyre—‘She was very exemplary and eminent for her piety, charity and other virtues, and exchanged this life for a better the 28th of September 1710, Aet. 67’—and to two of her sons.
The differential-difference equation w'(s) = g(s)[w(s-l)-w(s)]
Authors: Slater Gillian L.
Published: July 2016

This paper is concerned with the asymptotic behaviour of solutions of the differential-difference equationw'(s) = g(s)[w(s— 1)—w(s)], whereg(s)is a continuous real-valued function.g(s)is assumed to have one of the following asymptotic behaviours: algebraic, exponential algebraic, periodic or zero.
A generalisation of Niessen's limit-circle criterion
Authors: Bennewitz Christer
Published: July 2016

Synopsis

Let S and T be formally symmetric ordinary differential operators defined on a real interval I. It is assumed that the order of S is constant and everywhere strictly higher than the possibly varying order of T. The main result of this paper (Theorem 2.3) gives necessary and sufficient conditions for maximality of the deficiency indices of the differential relation Su = Tv considered in a Hilbert space with a scalar product which is a Dirichlet integral (see section 2) belonging to S. The conditions generalise those given in [5] for less general choices of operators S and T. For certain choices of Dirichlet integral they are explicit integrability conditions on the coefficients of the Dirichlet integral and the operator T.
Multiplication dans les espaces de Besov
Authors: Zolesio J. L.
Published: July 2016

Synopsis

Let f, g be two functions of two Besov spaces (or Sobolev spaces), we look for the Besov spaces to which the product f × g belongs so that the multiplication is a continuous mapping.
22.—The Linear Transport Equation. The Degenerate Case c = 1. I. Full-range Theory
Authors: Lekkerkerker C. G.
Published: July 2016

Synopsis

The aim of this paper is to give a functional analytic treatment of the homogeneous and inhomogeneous linear transport equation in the case that the parameter c occurring in that equation equals 1. The larger part of the paper is devoted to the study of a certain operator T−1 A in the space L2(– 1, 1). A peculiarity not arising in the case c < 1 (treated amongst others by Hangelbroek) is that, for c = 1, the operator T−1A has a double eigenvalue 0 and that it is no longer hermitian. The Spectral Theorem is used to diagonalise the operator as far as possible, and full-range and half-range formulae are derived. The results are applied inter alia to give a new treatment of the Milne problem concerning the propagation of light in a stellar atmosphere.
Iterative bounds for the stable solutions of convex non-linear boundary value problems
Authors: Mooney J. W. , Roach G. F.
Published: July 2016

Synopsis

We consider a class of convex non-linear boundary value problems of the form

where L is a linear, uniformly elliptic, self-adjoint differential expression, f is a given non-linear function, B is a boundary differential expression of either Dirichlet or Neumann type and D is a bounded open domain with boundary ∂D. Particular problems of this class arise in the process of thermal combustion [8].

In this paper we show that stable solutions of this class can be bounded from below (above) by a monotonically increasing (decreasing) sequence of Newton (Picard) iterates. The possibility of using these schemes to construct unstable solutions is also considered.
13.—The Instability of Two Vortex Sheets enclosing a Subsonic Jet due to an Acoustic Point Source
Authors: Hardisty N.
Published: July 2016

Synopsis

The propagation of sound from a point source placed in a subsonic jet separated by two plane vortex sheets from two semi-infinite still media is considered and it is found that instability waves arise at particular points on the vortex sheets and that their effect is confined to certain regions.
16.—Square Integrable Solutions of Perturbed Linear Differential Equations
Authors: Wong James S. W.
Published: July 2016

Synopsis

This paper is concerned with solutions of the ordinary differential equation

where ℒ is a real formally self-adjoint, linear differential expression of order 2n, and the perturbed term f satisfies

for some σ∈[0, 1]. Here λ(·) is locally integrable on [0,∞).

In particular it is shown, under circumstances detailed in the text, that (*) possesses solutions in the Hilbert function space L2(0,∞).
22.—Analytic, Generalized, Hyperanalytic Function Theory and an Application to Elasticity
Authors: Gilbert Robert P. , Wendland Wolfgang L.
Published: July 2016

Synopsis

Though it is still an open problem for which class of first-order elliptic systems Carleman's theorem holds, this is proven here for a certain class of systems (with analytic coefficients) for which Douglis introduced the hypercomplex algebra and hyperanalytic functions. The proof is based on a representation formula generalising Vekua's approach with Volterra integral equations in C2 to more than two unknowns. The representation formula is of its own interest because it provides the generation of complete families of solutions. The equations of plane inhomogeneous elasticity problems lead to a system of the desired class.
20.—Inequalities for the Capacity of an Electrified Conducting Annular Disc
Authors: Love E. R. , Collins W. D.
Published: July 2016

Synopsis

The simultaneous integral equations of Noble and Cooke, for inter alia the Dirichlet problem for an annular disc, are transformed into equations closely analogous to those recently given by Clements and Love for the corresponding Neumann problem. The transformed equations are relatively simple, and do not involve any artificial preliminary dissection of the known functions. They are also uncoupled, and admit iterative solution for virtually all radius ratios.

In the case of the conducting annular disc, iteration of these equations isused to obtain two series for the capacity, an interim one with all terms positive, and a final one with all terms after the first negative. The final series is more rapidly convergent as well as neater. It is used to provide a family of inequalities which enclose the capacity and determine it to high accuracy with very few terms, failing only when the radius ratio is close to 1.
21.—On Expansive Free Interactions in Boundary Layers
Authors: Brown S. N. , Stewartson K. , Williams P. G. , Collins W. D.
Published: July 2016

Synopsis

When a Mach number dependent parameter σ ≠ 0 is accounted forin an expansive free interaction analogous to that of Stewartson [7], the solution terminates in a singularity with a finite pressure, but with a pressure gradient varying as the inverse three-fifths power of the distance from the singularity, apart from a subtle logarithmic modification.
23.—Oscillation Phenomena in the Hodgkin-Huxley Equations
Authors: Troy William C. , McLeod J. B.
Published: July 2016

Synopsis

A widely accepted model of nerve conduction in the squid axon is the systemof four non-linear partial differential equations developed by Hodgkin and Huxley. Under space clamp and current clamp conditions these equations are reduced to a system of ordinary differential equations.

We find that under appropriate assumptions on the functions and parameters in the resulting fourth order Hodgkin-Huxley equations there occurs a bifurcation of periodic solutions from the steady state. This bifurcation takes place as the current parameter, I, passes through a critical value.
Embeddings of Sobolev spaces of fractional order
Authors: Martins J. S.
Published: July 2016

Synopsis

If Ω is a bounded domain in Rn satisfying certain conditions, Ωk denotes its intersection with a k-dimensional hyperplane, 1 ≦ k ≦ n, it is shown that the embedding of the Sobolev space Ws,p(Ω), s>0, into Lq(Ωk) is of type lm if for q<p<∞. The same result is obtained for the space of Bessel potentials Ls,p(Ω). Piecewise polynomial and Fourier approximations of functions and interpolation theorems areused.
Transformations between second order linear differential equations and a reinterpretation of recurrence relations between Bessel functions with algebraic coefficients
Authors: Heading John
Published: July 2016

Synopsis

A scheme devised by Chandrasekhar for investigating the transformations between various differential equations of the second order governing perturbations of the Schwarzschild black hole demands further investigation. The transformation between two differential equations in normal form is considered, and a wide survey of the properties of the transformation is given. It is shown how Chandrasekhar's equations fit into the scheme, after which some examples with particular properties are considered. A detailed investigation of Bessel's equation is undertaken using various devices, in particular by employing asymptotic methods for products of Bessel functions, and employing matrix methods for dealing with large numbers of matrix equations which necessitates an interesting method of solution, the results being reinterpretations of the standard recurrence relations for Bessel functions.
Operator Siegel Domains
Authors: Harris Lawrence A.
Published: July 2016

Synopsis

A unified description and treatment is given for a large and important class of homogeneous Siegel domains in finite and infinite dimensions. These domains are shown to be linearly equivalent to generalized upper half-planes in spaces of operators having a kind of triple product structure.
Higher monotonicity properties of certain Sturm-Liouville functions. V
Authors: Muldoon M. E.
Published: July 2016

Synopsis

The principal concern here is with conditions onfor on special solutions of the equation

which ensure that the higher differences of the zeros and related quantities of solutions of (1) are regular in sign. In particular, by choosingf(x)= 2v−2x1/v−2, it is shown that if ⅓ ≦|v|<½, then

wherecvkdenotes thekth positive zero of a Bessel function of ordervand Δµk= Δk+1− µk. Lorch and Szego [15] conjectured that (2) should hold for the larger range |v| < ½ but the methods used here do not apply to the range |v<| ⅓.
Development of a laminar boundary layer under conditions of continuous incipient separation
Authors: Curle N.
Published: July 2016

Synopsis

This paper, extending the work of Stratford [6] considers a boundary layer with uniform pressure when x < x0, and with the pressure in x > x0 so chosen that the layer is just on the point of separation for all x >x0. The required pressure distribution is shown to be

The displacement and momentum thicknesses are also derived as series in powers of ξ (and log ξ), and the shape parameter H then obtained as a similar series. The continuous change in H from the Blasius value (when ξ = 0) towards the Falkner-Skan [3] separation value is convincingly demonstrated, with the aid of the leading terms of an asymptomatic expansion for large ξ.
Existence of solutions of non-linear Schrödinger equations
Authors: Schmitt Klaus , Tsai Long-yi
Published: July 2016

Synopsis

The existence of periodic solutions of non-linear Schrödinger equations with periodic potential is investigated. The main result obtained is an intermediate value type theorem for such non-linear differential operators.
The question of uniqueness for dual integral equations of Titchmarsh type
Authors: Walton J. R.
Published: July 2016

Synopsis

The theory of generalised functions is used to develop a uniqueness theory for dual integral equations of Titchmarsh type.
Dual extremum principles for the heat equation
Authors: Collins W. D.
Published: July 2016

Synopsis

Dual extremum principles characterising the solution of initial value problems for the heat equation are obtained by imbedding the problem in a two-point boundary-value problem for a system in which the original equation is coupled with its adjoint. Bounds on quantities of interest in the original initial value problem are obtained. Such principles are examples of ones which can be obtained for a general class of linear operators on a Hilbert space.
The First J. C. Richardson Lecture: “That ‘I Am’ ”
Authors: Williams Denis
Published: July 2016

The first J. C. Richardson lecture was given by Dr. Denis Williams, Editor of “Brain,” and The Senior Physician, The National Hospital, Queen Square, London W.C.I. It was presented in the Medical Sciences Building, University of Toronto on January 28th, 1974 and is printed here in its entirety.
Sex-Linked Hereditary Ataxic Diplegia, the Borderland Between Cerebral Palsy and Pelizaeus-Merzbacher Disease
Authors: Dunn H.G. , Thompson Margaret W. , Bandler Elizabeth , Andrews L.G.
Published: July 2016

After a review of the literature concerning hereditary cases of cerebral palsy, a family is reported in which ataxic diplegia appears to be inherited as a sex-linked and probably recessive condition occurring in 3 males in successive generations. This ataxic diplegia, occurring after an unremarkable perinatal course, is associated with mild to moderate mental retardation, congenital nystagmus and significantly small stature and prevents the acquisition of free walking. Associated extrapyramidal features may gradually become more marked, while the nystagmus may subside. The condition is similar to that described in three previous reports in the literature. No evidence of linkage with other sex-linked disorders has been found, Xga typing showed that recombination between the Xg locus and the locus for hereditary ataxic diplegia has occurred once out of three possible opportunities. In the absence of neuropathological findings or specific biochemical tests, the differential diagnosis from Pelizaeus-Merzbacher disease cannot be made with certainty. The differentiation from other progressive sex-linked neurological disorders is discussed.
Spinal Myoclonus in Association with Herpes Zoster Infection: Two Case Reports
Authors: Dhaliwal G.S. , McGreal D.A.
Published: July 2016

Two cases of segmental spinal myoclonus, attributed to herpes zoster infection, are presented. The findings support the suggestion made by Campbell and Garland (1956) that “subacute myoclonic spinal neuronitis” is of viral origin. Both patients were receiving immuno-suppressive treatment when the myoclonus developed. The value of carbamazepine in therapy is mentioned.
Metastatic Medulloblastoma
Authors: Parkinson Dwight , Ross R.T. , Shields Christopher B.
Published: July 2016

The incidence of metastatic medulloblastoma is probably greater than the thirteen documented patients. Case reports of metastatic medulloblastoma must be carefully analysed. We have added two cases which conform to Weiss’ criteria for metastatic disease. The direction and factors influencing spread have been discussed.
3H Leucine Incorporation Into Myofibrils of Normal and Dystrophic Mouse Skeletal Muscle
Authors: Monckton G. , Marusyk H.
Published: July 2016

The study of 3H leucine incorporation into skeletal muscle of mouse muscular dystrophy (129 ReJ/dy Bar Harbour strain) shows the uptake of isotope into myofibrils. The techniques employed were light and EM autoradiography before and after glycerination (Szent-Gyorgyi 1947). The results indicate a marked drop in uptake of the 3H-Leucine into myofibrils in the dystrophic animals, supporting the contention of Nihei et al (1971) that reduced myosin synthesis occurs in mouse muscular dystrophy.
Semiology Of Tremors
Authors: Molina-Negro P. , Hardy J.
Published: July 2016

Since the description by Galen in the 2nd Century, A.D., clinical neurology has acknowledged the existence of two types of tremor: that which occurs at rest and that occuring during the execution of movement. With the help of refined methods of analysis, E.M.G. and cinephotography, the authors have carried out a detailed clinical assessment in more than 400 patients.

The basic criterion used to define a tremor was the classical definition of Dejerine: “An involuntary, rhythmical and symmetrical movement about an axis of equilibrium.”

As a result of this study, the conclusion has been reached that there are two types of tremor: postural tremor and tremor of attitude. Both are present while the limb remains immobile, whether by wilful design or when at rest in a position of posture and subject only to the action of gravity.

During voluntary movement, tremor is not present. Irregular, asymmetrical and non-rhythmic oscillations may appear however — as in so-called intention tremor, of cerebellar origin — but this abnormal movement can hardly be called a real tremor. It is merely a manifestation of ataxia.

As a consequence of this study, it is suggested that further understanding of the basic mechanism of tremor can be reached by the investigation of the central neural structures which are involved in the physiology of posture and attitude.