bluuebunny/crossref_metadata_2025 huggingface dataset:
Anstruther Analysed: The Elizabethan Seminary Priests1
Authors: McGrath Patrick , Rowe Joy
Published: July 2016

THE FIRST VOLUME of Fr. Godfrey Anstruther'sTheSeminary Priests: A Dictionary of the Secular Clergy of England and Wales, 1558-1850appeared in 1968, and in subsequent years it was followed by three other volumes. For various reasons, Fr. Anstruther did not complete the fifth and final volume, although he had collected a great deal of material for it. His achievement was remarkable, all the more so because it was carried out single-handed, not with the assistance of a team of scholars, and he used a great range of source-material in foreign as well as in British archives. This major contribution to the history of post-Reformation Catholicism has not always received the credit it deserves, and it is a sad comment on the historical awareness of the English Catholic community that the volumes did not sell as well as they should have done. Inevitably in a work of such magnitude, there were a number of errors, but those who are ready to point out details which Fr. Anstruther got wrong must never forget how much he got right and how his monumental and much-used dictionary has provided scholars with a solid foundation on which to build.
The Imprisonment of Papists in Private Castles
Authors: Parmiter Geoffrey de C.
Published: July 2016

IT is well known that during the latter part of the reign of Elizabeth I prominent papists were, from time to time, imprisoned in castles or large houses. That was done whenever the privy council felt that there were dangers threatening England which would become more dangerous if influential papists were allowed to remain at liberty. It was a cheap way to restrain the liberty of papists, as the owners of the buildings used as prisons were required to put them into repair and maintain them at their own expense, while the prisoners were required to pay for their board and lodging. Although the practice is a commonplace, its origins and development are less well known.
William Alabaster:Rhetor, Meditator, Devotional Poet—I
Authors: Caro Robert V.
Published: July 2016

IT has been commonplace in the literary criticism of the past thirty years to acknowledge the influence of the Counter-Reformation devotional tradition on English metaphysical poetry of the seventeenth century. The sonnets of William Alabaster, a little known recusant poet writing just before the dawn of the century, provide an early example of this influence. Even when Alabaster does not rise above his craftmanship, his poems offer insights into the cultural equipment and habits of mind of the age in which he lived, revealing how meditation could vivify rhetorical invention, injecting it with feeling and passion and transforming the persona of a lyric poem into a dramatic speaker.
Cloak Without Dagger: Dr Thomas Hussey, 1746–1803
Authors: Murphy Martin
Published: July 2016

CHARLES BUTLER, who knew Thomas Hussey well, wrote of him that he ‘would long live the memory of his friends:—a man of great genius, of enlightened piety; with manners at once imposing and elegant; and enchanting conversation. He did not come into contact with many whom he did not subdue: the highest rank often sunk before him. One notes, straightaway, the language of avoirdupois: the man ‘imposes’, he ‘subdues’, and beneath him others ‘sink’. Thomas Hussey had weight. That is evident in the portrait which hangs today in the building that rests on his foundations, Spanish Place: it conveys the force of character of one who was, in the words of another acquaintance, ‘by talents, nerves, ambition and intrepidity fitted for the boldest enterprise’.
‘The Slightest Suspicion of Avarice’: The Finances of the English Jesuit Mission
Authors: McCoog Thomas M.
Published: July 2016

THE instructions given to Robert Parsons and Edmund Campion upon their embarkation for England in 1580 left no doubt that, no matter what the English government might say, their tasks were the confirmation of the faith of the Catholics there and the recovery of those who, through ignorance, had lapsed. In order to attain these objectives, Father General Everard Mercurian urged the Jesuits to an exemplary life of extraordinary virtue. Amongst the more specific recommendations, the General exhorted the missionaries, in words that echoed the Society's Constitutions, to avoid ‘even the suspicion of avarice and greed.’ They were, therefore, neither to seek nor to accept any alms unless their need became extremely urgent. Even then, they should only ask one or two of their loyal friends for assistance. If the Jesuits could only turn to their friends as a last resort, if they could neither elicit nor accept alms from the people whom they served, one wonders how the General thought the mission's expenses would be met? For a document as reasonable and as thorough as the instructions, it is surprisingly naive about finances, a naiveté that would with experience give place to sophistication.
The Elizabethan Priests: Their Harbourers and Helpers1
Authors: McGrath Patrick , Rowe Joy
Published: July 2016

This paper is concerned primarily with the people who sheltered and helped in various ways the priests without whom Catholicism could not have survived in Elizabethan England. The Marian priests were, of course, the first who needed harbouring, and some of them continued to be protected by the laity to the end of Elizabeth's reign and beyond. From 1574 the seminary priests began to come to this country, and in due course they as well as the Jesuits were singled out for special treatment as far as harbouring was concerned. In the fifteen-eighties and the fifteen-nineties the number of seminary priests at work in England seems to have fluctuated between 120 and 150 in any one year. The Elizabethan Jesuits active in this country were never more than three or four in any one year in the fifteen-eighties, and rarely more than twelve in the fifteen-nineties. Compared with the surviving Marian priests and the seminary priests, the Jesuits were very few, but they have left a great deal on record relating to harbouring, and historians sometimes give the impression that they organised the whole business.
‘Stirring up the Pool’, Bishop Thomas Joseph Brown OSB (1798–1880) and the Dispute between the Hierarchy and the English Benedictines’
Authors: Hood Dom Alban
Published: July 2016

In November, 1850, in his first Pastoral Letter as Bishop of Newport and Menevia, Thomas Joseph Brown OSB described the unfavourable reactions to the recent restoration of the Catholic Hierarchy as ‘… wild passions that are agitating the land,’ but confidently prophesied that ‘a reaction will succeed, favourable to the progress of Catholic truth, as followed the healing of diseases from the stirring up of the pool of Bethsaida’. ‘Stirring up the pool’ was a well chosen image not only for the Restoration of the Hierarchy, but also for the ensuing controversy it unleashed between the new hierarchy and the regular clergy and specifically the English Benedictine Congregation, to which Brown belonged.
Sir Robert Cecil, Edward Squier and the Poisoned Pommel
Authors: Edwards Francis
Published: July 2016

It seems beyond controversy to say that the most controversial subject of study for the Jacobethan period is the series of plots that occurred between 1571 and 1605. The word Jacobethan—not the writer’s—is a useful reminder of the essential continuity in important respects of the historical scene between 1558 and 1612. The continuity during this period was mainly supplied by the domination of the Cecils, father and son, William and Robert. In what would appear to be an unique occurrence of a virtual reign within two reigns in our island history, the Cecils, dominating the two monarchs with subtlety and discretion, pursued with skill, intelligence and determination the policy of turning England into a Protestant country. With their allies and subordinates in government, the aim was to turn the clock not back but into a direction from which it would never turn again.
The Pigott Family: Eighteenth Century Connections with Church, Science and Law
Authors: Brech Alison , McConnell Anita
Published: July 2016

This branch of the Pigotts can be traced back to Adam Pigott (d.?1737), a London merchant, member of the Cutlers’ Company where his mark of a dolphin was registered in 1664, who was residing near Temple Gate in 1676. In 1678 Adam Pigott and James Allen negotiated a lease from the Duke of Bedford for the construction of Covent Garden Market, with the obligation to pave the area and construct houses and shops. Adam’s wife is not mentioned in his will and presumably predeceased him, but there were at least two sons, Nathaniel (1661–1737) who died shortly after his father, but through whom this story continues, and Adam (1673–1751) who entered the Society of Jesus at Watten, near St. Omer, was professed in 1694 and, after serving as chaplain at Calehill, Kent, the home of the Darell family, died at Crondon Park, Essex, the seat of the Petre and Mason families, on 30 April 1751. In common with virtually every priest of the period, Adam Pigott used analiasfor security reasons, thisaliasbeing in many cases the mother’s maiden name. Adam Pigott’saliaswas Griffin, which may therefore have been his mother’s original surname.
Religious Drama in Kendal; The Corpus Christi Play in the Reign of James I.
Authors: Parkinson Anne C.
Published: July 2016

A study of the persistence of Catholic practices and traditions in the old counties of Cumberland and Westmorland highlights the great concern felt by Bishop Robinson of Carlisle (1598–1616) in regard to popish practices in his diocese at the end of Elizabeth’s reign and the beginning of that of James I. The incidence of such persistence in the Carlisle diocese, however, was slight in comparison with that of the Chester diocese in which lay the market town of Kendal in Westmorland. Here the continuance of Catholic practices was typified, not only by the persistent use of sites of old wayside crosses in funeral processions, but echoed in the townspeople’s equal determination to keep the long-established custom of the performance in their town of the Corpus Christi Play.
An Analysis of the Controversy Caused by Mary Ward’s Institute in the 1620s
Authors: Lux-Sterritt Laurence
Published: July 2016

During the reign of Elizabeth I, English Catholicism experienced a degree of persecution that was meant to ensure the extirpation of the old faith. However, Elizabethan anti-Catholic laws had an ambiguous effect upon the recusant population of England. Although the Roman Catholic faith initially suffered greatly, yet by the end of the reign it was rising again with force. The unique vocation of Yorkshirewoman, Mary Ward (1585–1645), can be seen as an eloquent illustration of this new English Catholic spirit and as the embodiment of an English missionary determination to further the Catholic cause.
The Identity of ‘Anthony Rivers’
Authors: Martin Patrick , Finnis John
Published: July 2016

Since Henry Foley in 1877 published extensive extracts from a set of letters purporting to have been written from London to correspondents in Venice, between January 1601 and April 1603, ‘by Anthony Rivers S.J.’, a ‘socius of Fr. Henry Garnet S.J.’, historians have found these letters valuable evidence concerning Queen Elizabeth’s declining days, the government’s secret involvement in the Appellant controversy within the Catholic priesthood (1597–1602), the ‘inch thick’ paint reference in Hamlet, the possible originating circumstances of Twelfth Night, and other matters. But no Jesuit Anthony Rivers has ever been found, and Jesuit historians have speculated about the letter-writer’s identity: Philip Caraman at one time took him to be Fr. Anthony Hoskins S.J., and Francis Edwards recently argued for Fr. Henry Floyd S.J. But Hoskins was not sent to England until 1603, and Floyd was in prison for much of the time when the letters were retailing, in a weekly rhythm, many pages of first-hand observations of events in the Court and Council, sometimes if not always in three near-identical versions dispatched simultaneously to three separate addressees.
British Catholicism and the British Army in the First World War
Authors: Snape Michael
Published: July 2016

The history of British Catholic involvement in the First World War is a curiously neglected subject, particularly in view of the massive and ongoing popular and academic interest in the First World War, an interest which has led to the publication of several studies of the impact of the war on Britain’s Protestant churches and has even seen a recent work on religion in contemporary France appear in an English translation. Moreover, and bearing in mind the partisan nature of much denominational history, the subject has been ignored by Catholic historians despite the fact that the war has often been regarded by non-Catholics as a ‘good’ war for British Catholicism, an outcome reflected in a widening diffusion of Catholic influences on British religious life and also in a significant number of conversions to the Catholic Church. However, if some standard histories of Catholicism in England are to be believed, the popular Catholic experience of these years amount to no more than an irrelevance next to the redrawing of diocesan boundaries and the codification of canon law.
‘A Recurring Grief, The Rankling of a Thorn’: The Unhappy Conversion of Richard Sibthorp
Authors: Trott Michael J.
Published: July 2016

As an undergraduate, Gladstone was enchanted by the preaching of Richard Sibthorp, but was unsure whether he could be trusted as a sound guide. So in December 1829 he wrote to his theological mentor, Edward Craig, an episcopal minister in Edinburgh, seeking an opinion. In reply, Craig described Sibthorp as a ‘very judicious man.’ Few would have dissented.

At a time of major divisions in the Protestant religious world, Sibthorp had established a reputation as a conciliator. In 1827, when the British and Foreign Bible Society was being torn apart by the Apocryphal controversy, he had been trusted by both sides to visit the Continent and report on adherence to the Society's revised rules. In the same year, he became Clerical Secretary of the Religious Tract Society, an office he held until 1836. In an inter-denominational Society, disputes over what should be published were constantly threatening to boil over and Sibthorp played no small part in ensuring that it did not suffer the convulsions that almost wrecked the B.F.B.S.
The Conversion of the Reverend George Dudley Ryder, 1846
Authors: Hunting Penelope
Published: July 2016

The Reverend George Dudley Ryder (1810–80), grandson of the Earl of Harrowby and son of England’s first evangelical bishop, had a promising career ahead of him in the Anglican Church. He was examined for matriculation by Newman at Oriel College, Oxford, in 1828 and soon joined the circle of Newman’s disciples: he was tutored by Newman, Richard Hurrell Froude and Robert Wilberforce, and was known as Froude’s protégé. A somewhat idle student, Ryder obtained a fourth class degree in classics in 1833 and the following January he was ordained by his father, Henry Ryder, Bishop of Lichfield. Many years later J.R. Bloxam, Newman’s curate at Littlemore, revealed that Ryder and some of his contemporaries had been refused testimonials for Holy Orders because they were known to be friends of Newman, while The Christian Observer alluded to Ryder’s advancement as an example of the abuse of Church patronage. Nevertheless Ryder’s ecclesiastical and aristocratic connections worked in his favour and he was installed as vicar of St. Werburgh, Hanbury, in Staffordshire in 1834.
‘A Work to Do’: Edward Caswall and Pastoral Ministry at the Birmingham Oratory During the 1850s and 1860s
Authors: de Flon Nancy M.
Published: July 2016

The middle years of the nineteenth century witnessed the crest of a wave of rapid growth in English towns begun when workers, attracted by the higher wages offered by industry, started to migrate from rural areas to the towns, thereby swelling the populations of the latter at enormous rates.

Birmingham was no exception to this growth spurt. During the last forty years of the eighteenth century Birmingham’s population doubled, a phenomenon that owed not a little to its canal system. ‘By the end of the eighteenth century, the canals [crucial to a region farther away from a coast than any other industrial area in England,] had already transformed the Birmingham neighbourhood, and factories and workshops clustered along their banks.’ Then, between 1831 and 1871 its population increased from 144,000 to 344,000.
The Rising of the Northern Earls
Authors: Parkinson Anne C.
Published: July 2016

In considering the period from 1559–1603, and the attitudes within the recusant community to the acceptance or rejection of the Elizabethan Settlement, the first major event giving extensive evidence of political attitudes in the northern region is the Rising of the Northern Earls, a crisis which, as elsewhere in Elizabethan England marked the watershed for the fortunes of Catholicism during the reign. An analysis, conducted at some length, of its causes, events and consequences is, indeed, indispensable to understanding Catholic survival in Elizabethan northern England.
An Unpublished History of Early Britain from Saint Alban’s College in Valladolid: Philip Perry’s Sketch of the Ancient British History
Authors: Quirós Carlos Herrero ,   Colleagues of the Saint Alban’s Project
Published: July 2016

With a rich history of over four centuries behind it, St. Alban’s English College in Valladolid possesses bibliographical and documentary sources of an exceptional wealth. The present paper reports on the constitution of a team of researchers in the University of Valladolid permanently devoted to the study of such documentary holdings. Extensive reference is made, more particularly, to the preparation of a critical edition of one of the manuscripts kept in the College Archive: ‘A Sketch of the Ancient British History . . . ’, an ecclesiastical history of early Britain written by former College rector Philip Mark Perry (1720–1774).
Some Chaplains at the Stuart Court at Saint-Germain-en-Laye
Authors: Holt Geoffrey
Published: July 2016

It was to be expected that at the court of a Catholic king and queen there would be from the beginning of the exile at Saint-Germain-en-Laye a royal chapel and an establishment of Catholic chaplains and that this would last as long as the court remained there. It continued in fact after the departure of James Edward to Lorraine in 1712 and Avignon in 1716 and for a while after the death of Queen Mary Beatrice in 1718. The priests of the English Jesuit Province—the subjects of this article—remained in office until 1720 or perhaps a year or two later. It may be presumed that they stayed on, after the court had ceased to be, to care for the Jacobite exiles who over the years had gathered round it.
Atoning in purgatory
Authors: THUROW JOSHUA C.
Published: July 2016

This article develops a new argument – The Argument from Atonement – that commonplace Christian assumptions about heaven imply the existence of purgatory. According to this argument, many Christians will die with residual moral guilt due to possessing unfulfilled moral debts towards fellow non-divine humans. Some of these debts cannot be fulfilled immediately after death and are not completely fulfilled or cancelled by Jesus's atoning work. Christians with such debts are fit neither for heaven nor for hell and thus must occupy purgatory until their moral debts are fulfilled.
XII.—Some Remarks occasioned by the Geometry of the Veronese Surface
Authors: Edge W. L.
Published: July 2016

The subject-matter of these pages may be briefly summarised as follows: the geometry of the Veronese surface, with an algebraic representation of it that does justice to its self-dual character; the relations of the secant planes of the surface to quadrics which either contain the surface or are outpolar to it; and the derivation of an invariant and two contravariants of a ternary quartic in the light of the (1, 1) correspondence between the quartic curves in a plane and the quadrics outpolar to a Veronese surface. There is no suggestion of discovering fresh properties of the surface, though possibly the results in § 12 § 13 may be new; but the geometrical considerations lead naturally to some algebraical results which it seems worth while to have on record, such as, for example, the identity 8.2 and the remarks concerning the rank of the determinant which appears there, and the form found in § 13 for the harmonic envelope of a plane quartic curve. These algebraical results lie very close to properties of the surface; so close in fact that one might say that the Veronese surface is the proper mise en scène for them.
XVI.—Simultaneous Linear Partial Differential Equations of the Second Order
Authors: Ince E. L.
Published: July 2016

In the system of two linear partial differential equations of the second order

a,…,f were supposed to be polynomials in x, and a1…, f1 polynomials in y. These polynomial coefficients were subjected to certain restrictions, including conditions for the system having exactly four linearly independent solutions, and conditions for preserving the symmetrical aspect, in x and y, of the system. It has been proved that any compatible system of the contemplated form whose coefficients satisfy the stipulated conditions is equivalent with, i.e. transformable into, a hypergeometric system. More particularly it has been shown that the hypergeometric systems involved are the system of partial differential equations associated with Appell's hypergeometric function in two variables F2 and the confluent systems arising herefrom.
XVII.—Axiomatic Treatment of Kinematical Relativity
Authors: McVittie G. C.
Published: July 2016

The suggestion has recently been put forward that the laws of nature can be established by purely deductive reasoning instead of by induction from observation. We may, with Eddington, start the chain of reasoning from epistemological premises or, with E. A. Milne, from axiomatic statements regarding the nature of the system to be studied. Different opinions may be held regarding the value of a deductive method, but a final judgment can hardly be passed on a deductive theory until the initial premises are clearly revealed. We may, indeed, justly require of the author of such a theory that he fulfil the following conditions. He should, firstly, be himself aware of all the axioms which he employs. If he is not, there is the obvious danger that he may use inductions from observation without being aware of doing so. But he may also arrive at quite erroneous conclusions about the range of validity of his results. For instance, a deductive theory may produce a formula which is interpreted as the inverse square law of gravitation. It is then very necessary to know whether the initial premises are axioms concerning the nature of the universe as a whole or whether they merely define local conditions. In the first case the law of gravitation is deduced from the nature of the universe as a whole, in the second it is shown to be merely a “local” law.
IX.—On the Line-Geometry of the Riemann Tensor
Authors: Ruse H. S.
Published: July 2016

In this paper the curvature tensor Rijkl in a Riemannian Vn is used to define a quadratic complex of lines in an (n – I)-dimensional projective space Sn–1. Work in this direction has been done for a V4 by Struik (1927–28), Lamson (1930), and Churchill (1932). Of these, Struik and Lamson both use 3-dimensional projective geometry, the former for the purpose of defining sets of “principal directions” in V4 by means of the Riemann tensor, and the latter for the purpose of discussing some of the differential and algebraic consequences of the field equations of general relativity. Churchill considers the geometry of the Riemann tensor from the point of view of 4-dimensional Euclidean geometry. In this paper an indication is given of the nature of the general n-dimensional theory, which, by way of elementary illustration, is then applied in moderate detail to a V3. A few general formulae are also obtained for a V4.
XV.—Quantum Mechanics of Fields. III. Electromagnetic Field and Electron Field in Interaction
Authors: Born Max , Peng H. W.
Published: July 2016

Studying the interaction of different pure fields, we have been led to some essential modifications of the ideas on which our quantum mechanics of fields is based. We shall explain these here for the example of the interaction of the Maxwell and the Dirac field.

In Part I we showed that a pure field in a given volume Ω can be described by considering the potentials and field components as matrices, not attached to single points in Ω (as the theory of Heisenberg and Pauli), but to the whole volume. Further, we assumed the total energy and momentum to be the product of Ω and the corresponding densities. In Part † we showed that this conception has to be modified; the eigenvalues of the energy and momentum as defined in Part I represent neither the states of single particles nor of a system of particles, but of something intermediate which corresponds to the simple oscillators of Heisenberg-Pauli and which we have called apeirons. The total energy and momentum of the system is a sum over the contributions of an assembly of apeirons. Mathematically the differences of the quantum mechanics of a field from that of a set of mass points (as treated in ordinary quantum mechanics) is the fact that the matrices representing a field are reducible (while those representing co-ordinates of mass points are irreducible); each irreducible submatrix corresponds to an apeiron.
XIX.—A Theory of Regraduation in General Relativity
Authors: Walker A. G.
Published: July 2016

1. It was remarked by me a few years ago that temporal regraduations, other than trivial changes of zero and unit, had not so far been considered in General Relativity. An interesting paper by Dr G. C. McVittie has now appeared in which regraduations are examined in certain spherically symmetric space-times. Under the assumptions made by McVittie it is shown that regraduations can exist for some but not all space-times, those for which they can exist being of a very special form which excludes many space-times generally regarded as significant or interesting. In the present paper I take the matter further and discuss the problem with more generality. It will be shown that the existence of non-trivial regraduations depends firstly upon which theory is being assumed for the derivation of the conservation equations There are two alternatives, and regraduations are found to be excluded by one, the “geodesic” theory, but not necessarily by the other, the “equivalence” theory.
XX.—Evaluation and Application of Certain Ladder-Type Networks
Authors: Bruges W. E.
Published: July 2016

This paper has for object the calculation of a ladder network, using trigonometrical functions of real multiples of (– I)¼ which, in many cases, simplify practical formulae. The work was prepared particularly for application to transmission lines, conductors in electrical machines, and isolated cylindrical conductors. The effect of the conjunction of two or more dissimilar networks is considered, leading to a method of assessing the impedance of a conductor of any shape embedded in an open slot cut in highly permeable material.
XXVI.—The Universal Integral Invariants of Hamiltonian Systems and Application to the Theory of Canonical Transformations
Authors: Lee Hwa-Chung
Published: July 2016

I. Introduction.—Consider a Hamiltonian system of differential equations

where H is a function of the 2n variables qi and pi involving in general also the time t. For each given Hamiltonian function H the system (1.1) possesses infinitely many absolute and relative integral invariants of every order r = 1,…, 2n, which can all be written out when (1.1) is integrated. Our interest now is not in these integral invariants, which are possessed by one Hamiltonian system, but in those which are possessed by all Hamiltonian systems. Such an integral invariant, which is independent of the Hamiltonian H, is said to be universal.
XXVIII.—The Discriminant of a Certain Ternary Quartic
Authors: Edge W. L.
Published: July 2016

I. By the discriminant D of a homogeneous polynomial ø is, in accordance with the general custom, to be understood that function of its coefficients whose vanishing is the necessary and sufficient condition for the locus ø = o to have a node. It is the resultant, or eliminant, of the set of equations obtained by equating all the first partial derivatives of ø simultaneously to zero. If ø contains n variables and is of order p, the degree of D in the coefficients of ø is n(p–I)n−1.
XXX.—On Hill's Problems with Complex Parameters and a Real Periodic Function
Authors: Strutt M. J. O.
Published: July 2016

Hill's differential equation (1.1) derives its importance from being the prototype of the different equations of Lamé and of the equation of Mathieu, which are connected with wave and potential problems in mathematical physics. Besides this, numerous instances of its occurrence in problems of elasticity and of dynamical or statical stability are known. In the present treatment, conditions are reversed with respect to most of the older publications, since the characteristic multiplier σ of equations (1.2) is not sought as a function of the given parameters λ and γ of equation (1.1), but σ is supposed given and the corresponding values of λ and γ are regarded as unknown. Thus a linear homogeneous boundary value problem of the second order and of non-self-adjoint type ensues, the values of σ and of λ, σ being in general complex. On this latter point the present paper considerably enlarges the scope of some previous papers published by the author during the war along somewhat similar lines but for real characteristic values (Nos. 13–18 of the references at the end).
XLVIII.—On Commuting Matrices and Commutative Algebras
Authors: Rutherford D. E.
Published: July 2016

The structure of commutative associative linear algebras is well known and is usually derived from more general results concerning non-commutative algebras (Cartan, Frobenius). The novelty of the present treatment is that while it avoids the complexities of the non-commutative case, it exhibits the essential relationship between the theory of commuting matrices and that of commutative algebras.

While theorems 1 and 2 of this paper are implicit in the writings of Voss (1889), Taber (1890), and Plemelj (1901), it has been considered worth while to recapitulate these results in the explicit form required for the discussion of commutative algebras. In doing so, some new facts emerge.
XLIX.—Generalizations of a Problem of Pillai
Authors: Mirsky L.
Published: July 2016

I. Throughout this paper k1, …, k3 will denote s ≥ I fixed distinct positive integers. Some years ago Pillai (1936) found an asymptotic formula, with error term O(x/log x), for the number of positive integers n ≤ x such that n + k1, …, n + k3 are all square-free. I recently considered (Mirsky, 1947) the corresponding problem for r-free integers (i.e. integers not divisible by the rth power of any prime), and was able, in particular, to reduce the error term in Pillai's formula.

Our present object is to discuss various generalizations and extensions of Pillai's problem. In all investigations below we shall be concerned with a set A of integers. This is any given, finite or infinite, set of integers greater than 1 and subject to certain additional restrictions which will be stated later. The elements of A will be called a-numbers, and the letter a will be reserved for them. A number which is not divisible by any a-number will be called A-free, and our main concern will be with the study of A-free numbers. Their additive properties have recently been investigated elsewhere (Mirsky, 1948), and some estimates obtained in that investigation will be quoted in the present paper.
XVIII.—The Elementary Proof of the Prime Number Theorem
Authors: Wright E. M.
Published: July 2016

Synopsis

The author presents a modification of the recently discovered “elementary” proof of the Prime Number Theorem. Nothing is assumed from the theory of numbers except the Fundamental Theorem of Arithmetic. In the second part of the proof the elements of the integral calculus are used to make clearer the basic ideas on which this part depends.
XXIV.—The Solution of a Functional Equation
Authors: Read A. H.
Published: July 2016

Synopsis

Analytic solutions of the functional equation f[z, φ{g(z)}] = φ(z), in which f(z, w) and g(z) are given analytic functions and φ(z) is the unknown function, are investigated in the neighbourhood of points ζ such that g(ζ) = ζ. Conditions are established under which each solution φ(z) may be given as the limit of a sequence of functions φn(z), defined by the recurrence relation φn+1(Z) = ƒ[z, φn{g(z)}], the function φn(z) being to a large extent arbitrary.
XXV.—The First Chemical Society, the First Chemical Journal, and the Chemical Revolution
Authors: Kendall James
Published: July 2016

In very olden days chemists did not forgather merely as chemists; they merged themselves in broader organizations such as the Royal Society. The “chemical revolution”, which had its real beginning with the work of Joseph Black and which culminated in the overthrow of the phlogiston theory by Lavoisier, aroused for the first time a popular interest in the special science of Chemistry. Until recently, world priority among the chemical societies that resulted therefrom was by general agreement conceded to the Chemical Society of Philadelphia, founded by James Woodhouse in 1792. The distinguished chemical historian Edgar F. Smith (I), late Provost of the University of Pennsylvania, may be quoted in this connection:
XVII.—Invariant Matrices and the Geometry of Numbers
Authors: Mahler K.
Published: July 2016

Synopsis

With every matrix representation of the (real) full linear group can be associated a multi-linear mapping of one affine space, Rn, into another, RN. This mapping is studied from the viewpoint of the geometry of numbers of convex bodies, and a general arithmetical property of such mappings is proved. The result generalizes my recent work on compound convex bodies.
XIX.—Metrisable Lie Groups and Algebras
Authors: Tsou S.-T. , Walker A. G.
Published: July 2016

A Lie group is said to be metrisable if it admits a Riemannian metric which is invariant under all translations of the group. It is shown that the study of such groups reduces to the study of what are called metrisable Lie algebras, and some necessary conditions for a Lie algebra to be metrisable are given. Various decomposition and existence theorems are also given, and it is shown that every metrisable algebra is the product of an abelian algebra and a number of non-decomposable reduced algebras. The number of independent metrics admitted by a metrisable algebra is examined, and it is shown that the metric is unique when and only when the complex extension of the algebra is simple.
VII.–The Effect of the Transport of Heat on the Rate of Evaporation of Small Droplets I. Evaporation into a Large Excess of a Gas
Authors: Wright P. G.
Published: July 2016

Synopsis

Beginning with fundamental results obtained by Mason for the effect of self-cooling on the evaporation of drops, and by Fuchs for the diffusional retardation of evaporation for small droplets of any radius, explicit expressions for the effect of the transport of heat on the rate of quasi-stationary growth or evaporation, are discussed.

The simplest algebraic formulation of the results lends itself to interpretation as expressing a resistance to evaporation, the total resistance being the sum of four resistances in series. Two of these resistances, one to diffusion and one to the conduction of heat, are offered by the gaseous phase in bulk; and there are two corresponding resistances at the interface. Corrections are formulated for the effect of the heating of the droplet by radiation. These corrections may be expressed as a (finite) resistance in parallel with the other two resistances to the transfer of heat. Simplified equations are obtained for the evaporation of a liquid whose latent heat of vaporization is very large.

Some remarks are made on the formation of a monodisperse aerosol by the growth of smaller droplets. Integrated expressions are obtained for particular cases of the evaporation of a droplet over a finite period of time.
XI.—On the Construction of Metrisable Lie Algebras
Authors: Tsou S-T.
Published: July 2016

The concept of metrisable Lie algebras was introduced in a previous paper, where some fundamental properties of metrisable Lie algebras have been given. It was shown that, associated with an admissible metric tensor of a metrisable Lie algebra, there is a unique antisymmetric tensor of the third order. A complete solution of the converse problem will be given in this paper; it is first reducedto the solution of a system of algebraic equations and then it is proved that, there always exists a unique metrisable Lie algebra corresponding to each symmetricsolution of the system, even when the solution is trivial. The Lie algebra thus obtained is a reduced metrisable Lie algebra.
XI.—Matrix Analysis of Beam-Columns by the Method of Finite Elements
Authors: Smith R. G. , Webster J. A.
Published: July 2016

Synopsis

A matrix analysis is derived, using the concept of finite elements, for beam-columns of continuously varying cross-section and “small” initial curvature subject to tangential and normal forces acting at discrete points along the centroidal axis.

The relationships between loads applied to the ends of the member and their corresponding deformations are established in the form of stiffness matrices, which are the basis of the Equilibrium Method of Analysis of linear or non-linear elastic plane frames composed of such membeis. In addition, the end loads induced by the tangential and normal forces for various types of boundary conditions are obtained.

Finally, it is shown that the buckling load may be calculated by the determination of the lowest eigenvalue of a certain matrix, provided there is no lateial translation of the ends of the member.
XII.—The Lattice of Congruences on a Bisimple ω-Semigroup
Authors: Munn W. D.
Published: July 2016

Synopsis

A necessary and sufficient condition is determined for the modularity of the lattice of congruences on a bisimple inverse semigroup whose semilattice of idempotents is order-anti-isomorphic to the set of natural numbers.
XVI.—On Certain Numerical Coefficients Associated with Partitions
Authors: Rutherford D. E.
Published: July 2016

§ 1. The principal object of this note is to establish formula (16) of the preceding paper by H. Jack (1966). This formula, which was conjectured by Jack, evaluates a certain coefficient which is attached to a symbol {p, q, …, r}. In this symbols, p, q, …, r form a partition of m such that o≤p≤q≤…≤r,p+q+…+r=m. The symbol however vanishes if any two of the integers p, q, … r are equal but non-zero. In the remaining cases we have to show that the coefficient in question has the value
XVII.—Generalized Hypo-Elasticity
Authors: Green A. E. , McInnis B. C.
Published: July 2016

Synopsis

The theory of Hypo-Elasticity is generalized so as to include the theory of (anisotropic) elasticity as a special case, and to include thermal effects. Explicit restrictions on the constitutive equations, arising from thermodynamics, are obtained.
XIX.—On the Determination of the General Term in Green-type Expansions
Authors: Jorna S.
Published: July 2016

Synopsis

A formal method is developed for deriving a series expansion of the general term in Green-type expansions. The technique is exemplified by detailed calculations for modified Bessel functions of large order.
XXV.—On the Groups of Units of Ternary Quadratic Forms with Rational Coefficients
Authors: Mennicke J.
Published: July 2016

Synopsis

Fuchsian groups that are unit groups of ternary quadratic forms with rational integer coefficients are studied. By means of the well-known Nielsen classification of finitely generated Fuchsian groups, a complete survey of the unit groups is given. For this, we have to use the arithmetical methods of B. W. Jones. In the second part, the relations between Fuchsian groups arising from different quadratic forms are studied. It turns out that, with a finite number of exceptions, all these Fuchsian groups are subgroups of a particular one.
II.—The Attempted Synthesis of Benzo[a]biphenylene
Authors: Campbell Neil , Morris Robert A. N.
Published: July 2016

Unsuccessful efforts to synthesize benzo[a]biphenylene and dibenzo-biphenylenes by the dehydrohalogenation of suitable intermediates are described. 2-o-Chlorophenyl-2-phenylpropionitrile with potassamide in liquid ammonia failed to give 8-cyano-7-phenylbicyclo[4,2,o]octa-I,3,5-triene, while diethyl 2-bromobenzylphenylmalonate with sodium in dry ethanol yielded I-phenylisochroman-3-one after hydrolysis. Bromination of 3,3′,4,4′-tetrahydro-2,2′-binaphthyl was accompanied by spontaneous dehydrobromination to yield 2,2′-binaphthyl, and interaction of phenyl-o-chlorophenylbromomethane with phenyllithium followed by chloracetic acid gave 1,2-di-o-chlorophenylethane.
IV.—On the Integrals of Hua and James.
Authors: Jack Henry
Published: July 2016

Synopsis

Recently a power series representation of Hypergeometric functions with matrix argument has been established. This representation involves a special type of spherical function from the theory of semi-simple Lie groups, called the zonal polynomials. A general theory of these polynomials is well established; however an explicit representation of them is lacking. This paper considers two integrals which are related to this explicit representation. The final paragraph considers a third integral which gives an application of a result from a previous paper of the author.
XVIII.—A Theory to Predict the Transport and Relaxation Properties of a Turbulent Fluid
Authors: Tyldesley J. R.
Published: July 2016

Synopsis

A new approach to the analysis of transport processes in a turbulent fluid is presented In this approach a model is used to represent the detailed fluid behaviour and it is shown that the model has similarities with a Fourier integral representation of the flow field. The model assumes that the turbulent motions can be represented by fluid entities of random size, shape and velocity, and that the large-scale transport processes are the consequences of the creation, decay and mutual interaction of the individual entities. The effects of this are analysed and it is shown how the diffusivities for vector and scalar quantities can be determined in terms of properties of the turbulence. The theory is applied in both bounded and free turbulent flows and it is shown that the predicted diffusivity ratios compare favourably with experimental data. Relaxation phenomena are also investigated and the memory function for stress and thermal relaxation is determined. It is concluded that the model provides a most useful framework for the analysis of turbulence phenomena and that its diverse and accurate predictions make it a powerful research tool.
VI.—The Stress Intensity Factors for a Griffith Crack in an Elastic Body in which there is an Asymmetrical Distributtion of Body Forces
Authors: Sneddon I. N. , Tweed J.
Published: July 2016

Synopsis

Formulae for the calculation of the stress intensity factor at the tip of a Griffith crack and for the normal component of the surface displacement are derived for a stressfree crack in an elastic solid in which there is an asymmetrical distribution of body forces. Particular distributions of point forces are considered in detail.
9.—Plant Cell—Water Relations: The Elasticity of the Cell Wall
Authors: Dainty J.
Published: July 2016

Synopsis

The elastic properties of plant cell walls are major factors controlling the swelling and shrinking of plant cells under conditions of varying water stress. The importance of these properties for the adaptation of plants to the changing water stresses they encounter is discussed.
13.—A Search for the Quark in Extensive Air Showers, using a Counter-controlled Cloud Chamber
Authors: Evans G. R. , Fancey N. E. , Muir J. , Watson A. A.
Published: July 2016

Synopsis

A search is reported for the relativistic e/3 quark among the cores of Extensive Air Showers initiated by primaries with energies greater than 1014 eV. The detector is a high-pressure cloud chamber filled with helium at 28 atmospheres, and is counter controlled. The experimental conditions avoid the criticisms levelled at the McCusker experiment and are such that the tracks of e/3 quarks cannot be simulated by singly charged shower particles either through statistical variations in primary ionisation or otherwise. The primary ionisation density, measured using a gap-counting technique on post-expansion electron and muon tracks, is compared with predictions from the theory of Budini et al. (1960). The agreement achieved shows that the theory is a reliable foundation for methods of identifying quark candidates, and measuring charges. The experiment has been running for 5000 hours. No quark candidates have been found. With an acceptance angle of 0·3 sr and an area of 140 cm2, this sets the upper limit of flux of e/3 quarks at 4 × 10−9 cm−2 sec−1 sr−1 with 95 per cent, confidence. The experiment is being continued.
22.—Organic Scintillators with Improved Timing Characteristics.
Authors: Birks J. B. , Pringle R. W.
Published: July 2016

Synopsis

Theoretical and experimental studies have been made of the scintillation pulse shapes of organic scintillators. In a unitary crystal the pulse shape is characterised by the scintillation decay timeτs. In solution scintillators additional parameters are required to describe the pulse shape: Δt, the pulse width (FWHM);tm, the time at which the intensity reaches a maximumpmax; andt½, the time at which the intensity reaches ½pmax. General relations are derived for τs, Δτ,τm,τ½, andpmaxfor binary liquid solutions in terms of molecular parameters, and the corresponding expression is given for the scintillation pulse shape of a binary plastic solution.

The scintillation pulse shapes of 4 binary liquid solutions and 12 binary and 15 ternary plastic solutions were measured using a single-photon sampling fluorometer. The results confirm the theoretical analysis. A new plastic scintillator (NE 111) with improved timing characteristics has thus been developed, and some of its applications in nuclear physics are briefly discussed. The time association of nuclear events can be measured to within 130 ps with this scintillator, the limiting factor being the time jitter of the photomultiplier itself.
24.—Eigenvalue and Eigenvector Solutions of a Wave System in a Non-Linear Dissipative Medium
Authors: Ross M. A. S. , Corner D. F.
Published: July 2016

Synopsis

This paper gives an account of some numerical methods which have been applied to solve the equations of second order stability theory in the flat plate boundary layer.
26.—Recent Light on Optical Interference
Authors: Sillitto R. M.
Published: July 2016

Synopsis

The interpretation of optical interference experiments at low light intensities and with independent light sources is discussed. A new experiment on interference between modulated light beams is described briefly, and its significance is indicated. There are two appendices, one a fuller discussion of the conditions under which interference and intensity correlation may be produced, the other a comment on one aspect of Jánossy and Nagy's discussion (1956) of the feasibility of the alternating slit interference experiment.
3.—Some Structure Semigroup Results for Arens-Singer Semigroups
Authors: McKilligan Sheila A.
Published: July 2016

Synopsis

In this paper we discuss the structure semigroup of the L1-algebra of an Arens-Singer semigroup. Arising from this study we provide a complete and rather unexpected description of a nontrivial structure semigroup. We then link the above ideas with that of the almost periodic compactification of the semigroup.
9.—On Relatively Bounded Perturbations
Authors: Brown K. J.
Published: July 2016

Synopsis

In this note it will be proved that any small relatively bounded perturbation of a self-adjoint operator with discrete spectrum also has discrete spectrum.