bluuebunny/crossref_metadata_2025 huggingface dataset:
Actors—The Image of Their Era
Authors: Clurman Harold
Published: January 2007

In the theatre this is the time of prizes and awards. The less theatre we have, the more prizes are awarded. Perhaps that is our way of compensating through honor and esteem what we cannot supply in substance. It is certain that among devoted playgoers, the prizes for acting—even more than those for plays—create jubilation, discussion, even dispute. In any case, a good deal of genuine sentiment is expended on the occasion of the various awards.

The most awarded actress of the past season is unquestionably Shirley Booth. Miss Booth (Motion Picture Academy Award for her performance in Come Back, Little Sheba; Antoinette Perry Award for The Time of the Cuckoo) didn't steal it, as the French say, when they mean that someone got what was deserved.
Comedy
Authors: Fry Christopher
Published: January 2007

A friend once told me that when he was under the influence of ether he dreamed he was turning over the pages of a great book, in which he knew he would find, on the last page, the meaning of life. The pages of the book were alternately tragic and comic, and he turned page after page, his excitement growing, not only because he was approaching the answer but because he couldn't know, until he arrived, on which side of the book the final page would be. At last it came: the universe opened up to him in a hundred words: and they were uproariously funny. He came back to consciousness crying with laughter, remembering everything. He opened his lips to speak. It was then that the great and comic answer plunged back out of his reach.
Mystery in the Plays of Christopher Fry
Authors: Lecky Eleazer
Published: January 2007

“There is always something new under the sun,” Christopher Fry has said, “because a mystery never ages.” The remark, set apart like this, itself may seem mysterious, but, when added to Fry's plays, it usefully annotates them. It redirects attention to the presence there not just of mystery but of kinds of mystery which affect the dramatic value of the plays.

I do not wish to exaggerate the differences, but when Fry speaks of mystery, directly in his essays or indirectly in the plays, the word may have one of several meanings. (1) Sometimes he (or the speaker) is saying of a particular moment of experience that, like any other moment, it is unique. It has, besides the familiar qualities that language can codify, an indefinable quality of its own, for, literally, “There is always something new under the sun.” It is as if creation were an infinite series of special creations or “miracles.” No event, therefore, is fully explicable. In uniqueness, there is mystery.
W. B. Yeats: A Poet Not in the Theatre
Authors: Sharp William L.
Published: January 2007

Yeats’ difficulty in becoming a successful playwright is not surprising or unexpected. His own views on the public theatre precluded success, and it would have surprised Yeats as much as anyone if at any time in his career he had achieved much widespread popularity. His growth as a playwright was always away from the “pit” and the appearance of Four Plays for Dancers, The Only Jealousy of Emer, At the Hawk's Well, The Dreaming of the Bones, and Calvary (the first of which was produced in 1916), is in many ways a predictable outcome of much of his opinion of what drama should be. In a note to At the Hawk's Well in 1916 he had written:
Fuenteovejuna: Form and Meaning
Authors: Casalduero Joaquín
Published: January 2007

One of the leading Spanish scholars of the past hundred years, Menéndez y Pelayo, had this to say of Fuenteovejuna: “Peribáñez and El mejor alcalde, el rey . . . have to do with personal justice or private vengeance. In Fuente Ovejuna what we witness is the vengeance of a whole town; there is no individual protagonist; there is no hero but the demos, the town council of Fuente Ovejuna: when the Royal power intervenes, it is only to sanction and consolidate the revolutionary deed. There is no more democratic play in the whole Castilian theatre” (Vol. V, p. 198). “A drama which is reality itself, brutal and throbbing, but magnified and exalted by the historical genius of the poet… . In Fuente Ovejuna the soul of the people found expression without danger, thanks to the.happy state of political unconsciousness in which the poet and his public lived.
All Aboard the Seesaw
Authors: Trilling Lionel
Published: January 2007

William Gibson's The Seesaw Log is a book about the theatre in, as it were, its very essence, and it seems to me that it is as interesting as such a book could possibly be.

Now that I have set down that statement, I see that it may sound ambiguous, and that it may suggest ambivalence on my part, but I let it stand as representing the division of my feelings, not about the book but about the theatre. I was the boy who refused to wave his handkerchief to keep Tinker Bell from dying, even though it was Maude Adams who pleaded, and I despised the children who did wave, and also envied them, and was glad they could help make so moving an event by their silliness.

Some part of me is repelled by the theatre. The histrionic personality bores me (after the first half-hour, in which it is usually charming).
The Madrigal in the Garden
Authors: Weales Gerald
Published: January 2007

Small ironies are the particular delight of those newspaper columns that deal in news and gossip about Broadway and its theatrical ventures; so it was natural that the most piquant tidbit of the 1955-56 season should have been the fact that Enid Bagnold’s The Chalk Garden, a play which managed at least the success of a five-month run in New York, had been turned down by every major London management before Irene Mayer Selznick decided to produce it here. The real surprise, however, was that Miss Bagnold’s lovely play should have been a success at all, even in a season unusual enough to list Giraudoux and Anouilh among its hit playwrights. The Chalk Garden is too many things that a Broadway hit is not. It is, first of all, primarily verbal, using language with a delight and a delicacy that is foreign to even our most serious playwrights.
Tennessee Williams: The World of His Imagery
Authors: Vowles Richard B.
Published: January 2007

In spite of his undeniable stature at home and abroad, Tennessee Williams has met with slight critical approbation. If not actively contemptuous, the little magazines have been cold. The acceptance of the ephemeral press, admittedly a mixed dish, has been succeeded by querulous denial, irritability, and, more frequently, silence from literary quarters. The reasons are not far to seek.

Mr. Williams has been too successful, and success on Broadway has come to be equated with the slick masquerading of the shoddy. Granted that Eugene O’Neill, too, has had his recent Broadway successes, but we may flatter ourselves that these amount to belated recognition of a “high seriousness” wanting in Tennesse Williams. After all, O’Neill had a tragic sense and a “daemon” (now inflated into myth), while all is negation in Williams. Or so Mr. Krutch would have us believe.
On Noh Drama
Authors: Kaula David
Published: January 2007

The current popularity of the Japanese arts in this country has extended only in a very limited way to what is perhaps the most beautiful of those arts: the Noh drama. The reasons for this are simple. One is the inaccessibility of the Noh. Unlike the Kabuki, it has never been performed in this country and probably never will be, at least in its pure form. Only once in its history, in fact, has the Noh been performed outside of Japan, at an Italian drama festival in 1954. Another reason for this relative neglect is the esoteric quality of the Noh. A Noh play is about as difficult for a Westerner unversed in Japanese culture to understand as, say, a medieval mystery play or Jacobean court masque would be for a Japanese who knew no English.
Molière the Indignant Satirist: Le Bourgeois gentilhomme
Authors: Falk Eugene H.
Published: January 2007

In a reference to Pascal, Ernst Cassirer wrote in his book An Essay on Man that:

what characterizes man is the richness and subtlety, the variety and versatility of his nature….Rational thought, logical and metaphysical thought can comprehend only those objects which are free from contradiction, and which have a consistent nature and truth. It is, however, just this homogeneity which we never find in man. The philosopher is not permitted to construct an artificial man; he must describe a real one. All the so-called definitions of man are nothing but airy speculation so long as they are not based upon and confirmed by our experience of man. There is no other way to know man than to understand his life and conduct. But what we find here defies every attempt at inclusion within a single and simple formula. Contradiction is the very element of human existence. Man has no ‘nature’—no simple or homogeneous being.
Marlowe Today
Authors: Levin Harry
Published: January 2007

On his four-hundredth anniversary, as at all other moments of critical judgment, it is Marlowe's peculiar destiny to be reconsidered in a Shakespearean context. His strongest claim is bound to be the fact that he did so much more than anyone else to bring that context into existence. This was the high point of A. C. Swinburne's eulogy in the Encyclopaedia Britannica: “He is the greatest discoverer, the most daring and inspired pioneer, in all our poetic literature.” Yet even Swinburne qualified his superlatives: “The place and the value of Christopher Marlowe as a leader among English poets it would be almost impossible for historical criticism to over-estimate.” The implicit qualification is underlined by our realization that the Victorian poet was far from being a historical critic. Marlowe must abide the question of history, which Shakespeare has all but outflown.
Five-Act Structure in Doctor Faustus
Authors: Hunter G. K.
Published: January 2007

The original and substantive texts of Marlowe's Doctor Faustus (the Quartos of 1604 and 1616) present the play completely without the punctuation of act division or scene enumeration. This is common enough in the play-texts of the period. Indeed it is much the commonest form in plays written for the public theatres. Shakespeare's Henry V and Pericles are without divisions in their quarto texts, but we know that they were written with a five-act structure in mind—the choruses tell us that.

What is exceptional in the textual history of Doctor Faustus is not the lack of division in the original texts; it is rather the reluctance of modern editors to impose an act-structure on the modern texts. This is curious, but it seems possible to discern why the reluctance exists and a survey of the modern editions of Faustus throws some interesting light on critical attitudes to the subject matter of the play.
The Art of Acting: Part II. “What's Hecuba to Him?”
Authors: Schyberg Frederik
Published: January 2007

In the eighteenth century a theory of acting is formulated for the first time. We have just traced the development of the art form from its obscure origin up to its new maturation in connection with the appearance of the geniuses Shakespeare and Molière. The art is liberated from dilettantism; new relationships are developed with society on the one hand, and with literature on the other! The person who play-acts is first of all an amateur—and can become a dilettante—then a professional actor, and finally becomes an artist. If we must set a date for the complete transformation it is the year 1750. About this time two books appear in Paris, epoch-making for the theatre and consequently for the new style of acting.
An Unfashionable View of Tennessee Williams
Authors: Sharp William
Published: January 2007

The fashionable view of Tennessee Williams at the moment is to see through him, to be above his sort of thing. Miss Signi Falk strikes the note in a recent article in Modern Drama when she says of his characters, “Most of them according to discriminating critics have been more deeply affected by the theatre than by life.” This position is an easy one just at present for two reasons. It has a certain degree of truth, and it has the support of most contemporary critics, discriminating or otherwise. Its danger, the danger of most easy positions, is that it tends to simplify Williams and make of him not a serious writer at all but a sensation monger. Henry Popkin would go so far as to say that he discloses only “the monstrosities of the nightmare, embellished by the playful ingenuity of a Gothic temperament.”
Guiscard and Oedipus
Authors: Stahl E. L.
Published: January 2007

In Kleist's Robert Guiscard there appear to be three main centers of interest: Guiscard himself, his army, and the members of his family. Undoubtedly Guiscard was to occupy a dominating position in the dramatic action; the fortunes of his family and of his army were to be of secondary importance compared with his own. Nevertheless, the army and the family were not a mere background of the tragic action, they were an essential part of it. This is shown by the vivid and emphatic description of the army surging around Guiscard's tent like the tempestuous sea around a rock, and by the clear-cut characterization of such figures as the old warrior, Abelard and Guiscard's son Robert.
Euripides’ Medea: Mythic Context and the Sense of Futurity
Authors: Brockett O. G.
Published: January 2007

Despite the high praise it has received from critics and the interest it has inspired in nearly every age, Euripides’ Medea offers certain problems in interpretation which have never been satisfactorily resolved. It is rather paradoxical, in fact, that a play of such enduring vitality should so often have been found unsatisfactory in one aspect or another. Adverse criticisms generally have been directed at three problems: the interpretation of the character of Medea, the purpose and relevance of the scene with Aegeus, and the resolution of the play. The first source of difficulty, a certain ambivalence in Euripides’ characterization of Medea, has evoked contradictory claims: that she is “one of the most tragic figures of the tragic stage,” but that she arouses no tragic pity in the spectator; that she is a brilliant achievement in humanizing a legendary figure; that, on the contrary she is not intended to appear human but primarily supernatural and demonic.
The Juggernaut of Production
Authors: Rogoff Gordon
Published: January 2007

In the autumn of 1958, Lee Strasberg told the members of The Actors’ Studio that he was feeling worried and belligerent about the emphasis on individual excellence that seemed to have become the entire raison d'etre of the Studio, an emphasis which he considered to be taken at the expense of the concept of the ensemble. “We lose the sense,” he said, “of serving the theatre.” His worry, seen then or now, could be easily understood by the most casual observer of the American theatrical scene. His belligerence, then and now, can not be so easily understood, since it is not readily apparent to the naked—or should I say hungry?—eye.

Belligerence implies the will to change, and in the case of those who would lead American theatre, the will to do more than change a way of work. The word belongs to the vocabulary of war.
Problems of the Theatre
Authors: Duerrenmatt Friedrich
Published: January 2007

Behold the drive for purity in art as art is practised these days. Behold this writer striving for the purely poetic, another for the purely lyrical, the purely epic, the purely dramatic. The painter ardently seeks to create the pure painting, the musician pure music, and someone even told me, pure radio represents the synthesis between Dionysos and Logos. Even more remarkable for our time, not otherwise renowned for its purity, is that each and everyone believes he has found his unique and the only true purity. Each vestal of the arts has, if you think of it, her own kind of chastity. Likewise, too numerous to count, are all the theories of the theatre, of what is pure theatre, pure tragedy, pure comedy.
The Dramatic Philosophy of Jean-Paul Sartre
Authors: Jarrett-Kerr Martin
Published: January 2007

I USE this title, because not only is Sartre a philosophical dramatist, but he is also a dramatic philosopher. I mean, that when he philosophizes he dramatizes his philosophical concepts. You cannot fully understand his philosophical drama unless you have an inkling of his dramatic philosophy. That is why when “existentialism” was all the rage in France (and elsewhere) about eleven years ago, but of course nobody had read L'Etre et le Néant, it was possible to get such a totally wrong idea of what Sartre was trying to do. (You will remember the story he himself tells of the young woman who utters a rude word and then exclaims “Ah, je crois que je deviens existentialiste.“) I must start, therefore, with the briefest account of his philosophical system, for the sake of those unfamiliar with it.
The Theatre of Edward Albee
Authors: Baxandall Lee
Published: January 2007

Edward Albee’s theatre continues to be controversial. The discussion centers around two questions: one has to do with truth, and the other with dramatic structure. The first runs as follows: is the image of human relations in America which Albee presents justifiable because it is in some sense realistic, or is his an essentially flawed and perverted point of view? The second is: are there valid grounds for the invented child in Who’s Afraid of Virginia Woolf and the confused events which lead to Julian’s death in Tiny Alice, or is Albee artistically callow and unable to structure a play properly?
A Note On Theatre
Authors: Genet Jean
Published: January 2007

So you need a foreword. But what is there to say about a play from which I felt detached even before it was finished? To speak of its composition would be to evoke a world and climate without grandeur. But I would rather say a few words about the theatre in general. I dislike it. One will gather as much from reading this play .What I have been told about Japanese, Chinese, and Balinese revels and the perhaps magnified idea that persists in my brain make the formula of the Western theatre seem to me too coarse. One can only dream of an art that would be a profound web of active symbols capable of speaking to the audience a language in which nothing is said but everything portended.

But any poet who tried to realize this dream would see the haughty stupidity of actors and theatre people rise up in arms.
The Balcony and Parisian Existentialism
Authors: Nelson Benjamin
Published: January 2007

The central theme of Jean Genet's extraordinary play, surely one of the major works of the twentieth century, is best expressed in two phrases about the nature of the cosmos we may take the liberty of adapting from two famous philosophers, Gottfried Wilhelm Leibnitz (1646-1716) and Cardinal Nicholas of Cusa (ca. 1400-1464): the identity of indiscernibles and the coincidence of opposites.

The ordinary man fancies that the solid realities of respectable society and the contrived illusions of the brothel are as far apart as are life and death. The play declares another message having only an incidental connection with the brothel setting: Reality and illusion are, strictly speaking, indistinguishable from one another, as indistinguishable as are dying and living.

In fact, Genet goes a giant step farther in his non-Euclidian geometry.
Genet's New Play: The Screens
Authors: Pierret Marc
Published: January 2007

In Jean Genet's The Screens the revolt of the Algerian Arabs against their French colonizers is not characterized by the emancipation of human beings. Although the colonizers are described as oppressors inflated with their own power, the misery and the intolerable condition of the oppressed are not denounced in order to promote the liberation of the colonized people. On the contrary, these misfortunes are exalted so that the humiliated individual has the opportunity to make his misery the occasion for an inner experience based on the absolute contrast and conflict between his values and those of the Other—an unceasing contestation through which Saïd achieves a sovereignty which no action founded on the hope of a more just world could yield. For hope can take root only in this world, and the hope of claiming one's rights is lost in the desire to become the Other. The subjective, ascetic, and tragic experience of Saïd has indeed no political value.
Notes On My Theatre
Authors: Ionesco Eugene
Published: January 2007

I have never succeeded in becoming completely used to existence, neither to that of the world, nor to that of others, nor above all to my own. I sometimes feel that forms are suddenly emptied of their content, reality is unreal, words are only noises stripped of all meaning. These houses, the sky, are only facades of nothingness; people seem to move automatically, without any reason; everything seems to evaporate, everything is threatened—including myself—by an imminent, silent sinking into I know not what abyss, beyond day and night. By what sorcery can all this still exist? And what does all this mean, this appearance of movement, this appearance of light, these kinds of things, this kind of world? And yet, I am here, surrounded by the halo of creation, unable to grasp the smoke, understanding nothing, disoriented, torn away from I know not what which makes me feel that I have nothing.
Ionesco and the Creative Dilemma
Authors: Esslin Martin
Published: January 2007

One of the principal, and most persistent, sources of error that tends to bedevil a considerable proportion of contemporary literary analysis is the implicit assumption that the writer's creative process is a wholly conscious and purposive type of activity. Few critics stop to inquire into the psychological basis and the mechanism of the creative process itself; hence their tendency to approach a work of art in terms of the author's intentions. The excellence of a work can then be deduced from an examination of the intentions in the mind of the writer (whether they are relevant and important) and of the degree to which these intentions have been realized. And even if the complexity of the creative process is realized by a critic, once he has started to analyze, say, the imagery of a poem or play the effect on the reader will tend to be an impression that the given author deliberately chose the metaphors or images concerned rather than following a semiconscious urge to express his intuition in these, and no other, terms.
Stanislavski and America: A Critical Chronology
Authors: Gray Paul
Published: January 2007

June, 1897. At a historic eighteen-hour session in the Slavic Bazaar, a restaurant in Moscow, Stanislavski and Nemirovich- Danchenko agreed to pool their acting companies and form the Moscow Art Theatre (MAT). Stanislavski wrote:

He, like me, thought the theatre's situation hopeless, for the brilliant traditions of the past had degenerated into a plain collection of easy technical devices… the theatre was in the hands of dilettantes and bureaucrats…
Lee Strasberg: Burning Ice
Authors: Rogoff Gordon
Published: January 2007

If the symbol was a hard nut for Stanislavski to crack, so is Lee Strasberg, symbolically and literally, a hard nut for anyone, friend or foe, to crack. Certainly it is easy to take an emotive view of him whether you admire him or not. In a most remarkably simple-minded way, his friends and disciples adore him while his enemies detest him. He is one of those figures who, like a supreme politician as opposed to an expert statesman, invites no middle ground, no neutral view. He suggests, as much by his nodding silences as by his little attentions, a classically formed love-hate relationship. But when the nut is there to be cracked, it almost always comes out melting love or towering hate, rarely both together.
Notes for Each in His Own Way
Authors: Squarzina Luigi
Published: January 2007

… The drama of modern art and its public, Everyman after Hiroshima faced with the debris of Dubuffet, the chromatic tumors of Wols, the burlap canvasses, Burri's industrial red-lead on shards of sheet metal, the orchestral blasts of Nono, the “what cannot be said is better left unsaid” of Wittgenstein's anti-philosophy; a drama already dated, if it is true that the levelling-off of taste, the techniques of psycho-control, the establishment of the marketplace in the cultural sphere all threaten to deprive Everyman (and his artist) of any right to tragedy. In this respect Each In His Own Way can be presented, today, not at all as a manifesto of Pirandellism, but rather as nothing less than a lyrical consummation without a trace of discursive reasoning, a poetics that is poetry. For someone working in the theatre it has the same value as a page by Mallarmé on poetry would have for a poet.
State of Play
Authors: Marowitz Charles
Published: January 2007

Ten years after Look Back in Anger, what has the English theatre got? In the order that it impinges upon my consciousness at the moment, I would make up the list as follows:

1.

The high esteem of America and the continent.

2.

Two well-honed, semi-permanent companies: the National Theatre and the Royal Shakespeare.

3.

Three major playwrights: John Osborne, Harold Pinter, and John Arden.

4.

A host of lesser lights ranging from the steady beams of Wesker and Bolt to the firefly-flickerings of Campton and Simpson.

5.

A chrestomathy of spot-on criticism by one drama critic: Tynan.

6.

Jennie Lee, recently-appointed Minister of Culture responsible for drumming the arts into the national consciousness, and directly responsible for a sizeable increase in the Arts Council appropriation.

7.

A few murmurings in the provinces; mostly audible at Nottingham and Stoke-on-Trent, but as yet nothing to write home about.
Notes for the Open Theatre Production
Authors: Feldman Peter , Walter Sydney S.
Published: January 2007

Keep Tightly Closed began as an actors’ project of the Open Theatre. Three of them rehearsed it for about a month under the supervision of one of our actresses. The work stopped for the next month, because of a busy production schedule. At that point I was asked to direct the play, only two weeks and a few days before the scheduled opening, with one cast change necessary. The actors’ morale was low because of the delays, the time limitations (some of us had day-time jobs and could only rehearse at night), the problems which had not been solved. The preliminary work they had done was very useful, but necessarily limited.

I began by having the actors work on improvisations for basic character and situation. These were of an abstract nature, dealing with dependency, enclosure, and isolation, and they threw the actors off guard.
Allan Kaprow's Eat
Authors: Kirby Michael
Published: January 2007

Eat, an Environment by Allan Kaprow, was presented during the mornings and afternoons of the two last weekends in January, 1964. Prospective visitors made reservations through the Smolin Gallery and were given directions on getting to the caves in the Bronx in which the Environment was created. Only twenty reservations were made for each one-hour period in an attempt—almost always successful—to forestall overcrowding and keep free circulation in the space.

After entering an old building that fronted low cliffs, the visitor walked through several corridors and doorways and finally came to the Environment. The rock from which the caves were carved had been somewhat incompletely covered with white paint—the place had once been used by the Ebling Brewery—and age and seeping water had created a sense of decay. Black charred wooden beams stood propped against the walls in several places.
Notes on Dance
Authors: Morris Robert
Published: January 2007

My involvement in theatre has been with the body in motion. However changed or reduced the motion might have been or however elaborate the means used might have been, the focus was this movement. In retrospect this seems a constant value which was preserved. From the beginning I wanted to avoid the pulled-up, turned-out, anti-gravitational qualities that not only give a body definition and role as “dancer” but qualify and delimit the movement available to it. The challenge was to find alternative movement.

I was not the first to attempt such alternatives. Simone Whitman, together with others, had already explored the possibilities inherent in a situation of “rules” or game-like structures which required the performer to respond to cues which might, for example, indicate changes in height or spatial position.
The Principles of Probability and Approximations in Arithmetic
Authors: Hope-Jones W.
Published: January 2007

To find the probability that if two quantities chosen at random are measured correct to n figures, their product so obtained is correct to n figures.
The Relative Abilities in Mathematics of Boys and Girls
Authors: Sandon Frank
Published: January 2007

In the Memorandum from the Girls’ Schools’ Committee of the Mathematical Association, published on pages 13-15 of the Mathematical Gazette for January, 1926, we are told that the Committee deprecates the use of the term “inferiority” as applied to girls’ mathematical work by the Report on the Differentiation of Curricula between the Sexes. Further, the Girls’ School Committee says: “Where boys and girls are given equal opportunities, as in some mixed schools, the consensus of opinion is that very little difference in capacity between boys and girls is shown in work up to Matriculation standard….” It seems desirable that the question should be put on a sound basis, and with this in mind the writer has endeavoured to draw on material available to him for a statistical inquiry into the points involved. For the last two years he has been engaged in teaching in a mixed school where the boys and girls are taught mathematics together by the same teacher in the lowest two forms, and the forms are chosen on a basis of general standard in school work. The marks are given below. In each case the marks are those obtained by equating the quartiles (by a modification of a method due to Prof. Nunn and given by the writer in the Forum of Education in papers in 1924 and 1925) to 40 and 60, in homework, weekly tests, and terminal exams. The two marks given are those obtained at the ends of the Christmas and Midsummer terms.
The Neglect of Arithmetic in
Schools
Authors: Steggall J. E. A.
Published: January 2007

For many years it has been my custom to
take the junior students, that is to say the
lowest class, in Mathematics for one hour a week:
and a part of the session has been given to what
may be called the simpler treatment of the
principles of Arithmetic. No attempt has been made
to touch the more difficult parts of this subject:
no effort has been made to base, for example, the
idea of fractions upon a purely abstract
foundation.
Presidential Address
Authors: Whitehead A.N.
Published: January 2007

When I had the honour of being made President of the Mathematical Association, I did not foresee the unusual responsibility which it entailed. It was my intention to take as the theme of a presidential address the consideration of some aspect of those special subjects to which my own researches have principally been directed. Events have forced me to abandon that intention. It is useless to discuss abstract questions in the midst of dominant practical preoccupation. We callnot disregard the present crisis in European civilization. It affects every function of life. In the harder struggle for existence which lies before the nation, all departments of national effort will be reviewed for judgment. The mere nccessity for economy in resources will provoke this reformation.
The Theory of Order, as Defined by Boundaries
Authors: Dixon E. T.
Published: January 2007

So much for preliminaries. We come now to the formulation of a postulate which may be compared to Euclid's “Let it be granted that a straight line can be drawn from any point to any other point ”; a postulate, by the way, whose significance has been much underrated by later geometricians. To explain fully the closeness of the analogy would involve the discussion of the cataloguing of groups higher than the first, for which I have not space here, but I may indicate its general nature, to those familiar with the subject, thus: In “projective” geometry the existence of straight lines is assumed, and from them, by means of the Quadrilateral Construction, we obtain an unique method of determining any number of points in a straight line, with reference to three given points in it. My procedure is the exact converse of this. I assume what corresponds to an unique method of determining any number of points in a straight line, with reference to any three of them, and from that I deduce a method of drawing other straight lines, that is, if I am given a plane to draw them in.
Mathematics for Evening Technical Students
Authors: Piaggio H. T. H.
Published: January 2007

There is a large and well-defined group of students, in polytechnics and elsewhere, taking a course of mathematics which is very different from that given in schools. Practical Mathematics, as the subject is usually known, is regarded very unfavourably by many mathematicians, and no doubt it has many defects. However, it is possible that some of its critics have failed to realise the difficulties that occur in connection with evening classes. The present article is intended to show that Practical Mathematics meets a real need, and that it may be made really educational. No attempt will be made to conceal the grave weaknesses that often occur in the actual working of the classes. Some suggestions for improvement will be given, and it is hoped that those with experience of the work, either as teachers or inspectors, will give their views on the subject. Ultimately the Mathematical Association may be able to issue a report that will incorporate the most helpful suggestions received.
The Nature of an Algebraic Curve at Infinity and the Conic of Closest Contact at Infinity
Authors: Smart E. H.
Published: January 2007

The recent discussion in the Gazette on the subject of asymptotes to algebraic curves has tempted me to offer a short account of a method of treatment which I have found useful in my teaching, in forming clear conceptions of the nature, not only of the contact of a curve with its asymptotes, but also of such singularities at infinity as the curve possesses. Incidentally the method affords an expeditious means of determining conies of closest contact at infinity—a subject upon which most text-books are discreetly silent—including parabolic asymptotes as a particular case.
Geometry Teaching: The Next Step
Authors: Godfrey C.
Published: January 2007

I draw your attention to two dates of some importance in the teaching of Geometry. In 1903 Cambridge ruled that “Any proof of a proposition will be accepted that appears to the examiners to form part of a systematic treatment of the subject”; in 1909 the Board of Education issued Circular 711. These two dates determine three periods of time.
A Formula in Inequalities
Authors: Lob H.
Published: January 2007

If particles of positive mass lie on a continuous curve whose concavity is always upwards, their centroid clearly lies above the curve and below the chord joining the extreme particles.

This obvious property gives a simple formula which includes several of the standard inequalities of the Algebra text-books.
An Application of Bessel Functions to a Problem in Optical Resolution
Authors: Buxton Arnold
Published: January 2007

Whatever theory is finally adopted for the propagation of light, there will always remain the interesting fundamental problem as to how far an object is exactly reproduced by an optical system. In this paper, the enquiry will be considered in its simplest form, and only the simplest types of objects can be considered. Taking the wave theory, let us consider the reproduction of an infinitely distant self-luminous point source, such as a star, through an optical system, such as a telescope. Sir George Airy investigated this case in 1834 ; he shewed what W. Herschel had recorded in 1782, that the image in the focal plane f of the optical system consisted of a central concentration of light, surrounded by light rings of rapidly diminishing intensity (see Fig 2), and gave formulae to shew the falling off in intensity of the light away from the centre of the image. This disc of light, then, is the approximation to the point-image of geometrical optics. The deformation is due to the distortion of the sphericity of the light waves making the image by diffraction at the aperture of the system. As in the propagation of wireless waves, however, diffraction is not the only cause of distortion.
Illegitimate Differentiation
Authors: Bryan G. H.
Published: January 2007

It has been my experience, and probably that of most teachers, that even advanced students who ought to know better cannot differentiate the simplest algebraic and trigonometric functions without indulging in an extravagant luxuriance of infinite series and making a number of illegitimate assumptions.
Nomography
Authors: Brodetsky S.
Published: January 2007

The algebraic solution of any problem formulated in mathematical symbols takes one of two forms: it is either given in the explicit form x=f(a, b, c,...), where → is some functional form of a, b, c, ... , which are supposed known in any particular case, or the solution required is to be found from an equation F(x, a, b, c, ...)=0, where F is a known functional form of the unknown x and of the quantities a, b, c, ... . The mathematician is generally concerned on the one hand with reducing f(a, b, c, ...) into its simplest, often its “prettiest” form, and on the other hand with investigating what method, if any, exists for “solving” the equation F(x, a, b, c, ...) = 0, i.e. finding x in terms of a, b, c, ... . The course included in any text-book of algebra consists principally of the former, since the latter is distinctly more difficult.
The Geometric Interpretation of Homographic Equations and their Application to loci and Envelopes
Authors: Milne John J.
Published: January 2007

If two lines are divided in such a way that any point on one corresponds to one and only one point on the other, the lines are said to be divided homographically, and any relation between the segments which gives the variable point on one corresponding uniquely to a variable point on the other is a homographic equation.

These equations are of two types:

(α), which contains the term xx', may be said to be of the second order, and (β), in which the term xx' is wanting, may be said to be of the first order.
Mathematics and Commerce
Authors: Shimmin A. N.
Published: January 2007

My first duty in approaching this subject is to make it clear that I am not a mathematician seeking to demonstrate the application of mathematical methods in the field of economics. My aim is to indicate the phases of the general economic problem which demand the co-operation of mathematician and economist as the only means of arriving at sound judgments and giving the scientific study of industry and commerce a value which will command increasing respect and attention.
The Teaching of Euclid
Authors: Russell B.
Published: January 2007

It has been customary when Euclid, considered as a text-book, is attacked for his verbosity or his obscurity or his pedantry, to defend him on the ground that his logical excellence is transcendent, and affords an invaluable training to the youthful powers of reasoning. This claim, however, vanishes on a close inspection. His definitions do not always define, his axioms are not always indemonstrable, his demonstrations require many axioms of which he is quite unconscious. A valid proof retains its demonstrative force when no figure is drawn, but very many of Euclid’s earlier proofs fail before this test.
Notes on the Radix Method of Calculating Logarithms. (Continued from p. 150.)
Authors: Lupton Sydney
Published: January 2007

A somewhat obvious simplification of Briggs’ logarithmic process was-discovered and given as one of three methods by Robert Flower in a rare small quarto tract, The ‘Radix a new way of making Logarithms, published in London by J Beecroft in 1771. Several tables of radices are given, the largest extending from r = 1 to 9 and n from 1 to 12 to twenty-three places.

Flower divides the given number, if necessary, by a power of ten and a single digit, so as to reduce the first figure to *9, and then multiplies by a succession of radices until all the digits become nines. The complement of the sum of the logarithms of the radices to the logarithm of the divisor gives the required logarithm. In some cases it is more convenient to multiply than to divide by a digit, the logarithm of the digit is then added to those of the radices and the complement to 1 taken.
Mathematics and the Pivotal Industries
Authors: Milne William P.
Published: January 2007

The Mathematical Association existed first of all as a society for the improvement of geometrical teaching in the schools, and had as its avowed intention the infusion of a spirit of sweet-reasonableness into abstract geometry. Whether the Association aimed in the first instance at the unconditional abdication of Euclid is difficult to say, but at all events such was the final result. So successful were the labours of the Association in the realm of geometry that it resolved to extend its activities into the domains of Arithmetic and Algebra. To these were quite recently added the Calculus and Mechanics; but, broadly speaking, it must be said that its activities have been almost entirely confined within the somewhat narrow limits of the Secondary Schools. The contention of this communication is that great and clamant opportunities of service lie outside the walls of our more academic Secondary Schools, and it is proposed to deal with some of those newer spheres of activity.
Introductory Theorems in Geometrical Conics
Authors: Lawrence B. E.
Published: January 2007

1. Nowadays the beginning of conics is a blend of pure and coordinate geometry, but the starting point is generally the focus-directrix definition. From this the standard equations and properties are deduced, but a good deal of time is taken before some of the more powerful methods can be applied.

The object here is to indicate compact proofs of some well-known results, and to obtain, at an early stage, such results as Newton’s Theorem and the cross-ratio property from the focus-directrix definition.
Euclid (I, 4) and Time-Space Theory
Authors: Dixon E. T.
Published: January 2007

May I be permitted to make some comments on the interesting paper by Dr. Robb in the July number of the Gazette? The point he raises is indeed interesting; though, without his having said so, I should have been surprised to find that it was not generally known; that the Time-Space Theory may, in a limiting instance, be incompatible with Euclid’s (I, 4). My comments must in a sense be critical, though I have nothing to say against his mathematics, so far as it is “pure,” or merely symbolic; for even though we might not, with Macaulay, say that it is well known to every schoolboy, or was even known to Macaulay himself, it would be obvious enough to every modern-side schoolboy who has got as far as “conic sections”; provided he was willing to take some of Dr. Robb’s technical terms in a more or less Pickwickian sense.
Some Missing Figure Problems and Coded Sums
Authors: Dudley Langford C.
Published: January 2007

It sometimes happens that teachers want missing figure problems and coded sums, for instance, at the end of term. These given here may be of use in saving teachers from having to make them up themselves. To save space, the missing figure problems are given as a whole, with the data printed in clarendon type. In setting these problems to a class the exact position of every missing digit must, of course, be indicated : this applies to remainders as well as to the main sum.
The Congress at Zürich
Authors: G. N. W.
Published: January 2007

A not unnatural consequence of my having complied with a request to act as a Delegate of the Mathematical Association at the International Congress of Mathematicians, which was held at Zürich during the week September 4-12, is that I have been asked to write a short account of the Congress for the Gazette. It is a little difficult to avoid giving merely an epitome of the official programme; and my difficulties are somewhat increased by my having, like many others, deliberately abstained from attending the Congresses at Strassburg and Toronto in 1920 and 1924, for reasons which are now, happily, a matter of past history, and by my having been unavoidably prevented from going to Bologna in 1928; in fact my only previous experience of a Congress was gained at Cambridge in 1912.
Theorems Connected with Focal Chords of a Conic
Authors: Lewis E. P.
Published: January 2007

1. PSQ is a focal chord of an ellipse and the normals at P and Q intersect at U.

Theorem I. The locus of the foot of the perpendicular from U to PSQ is a similar coaxal conic.

Let the tangents at P and Q meet at T: then T lies on the directrix and TS is perpendicular to PSQ. Draw UH perpendicular to PSQ and AR parallel to PSQ to meet the given conic at R and CVT at W Since TU is the diameter of the circle TQUP, and UH, TS are perpendicular to PQ, V, the mid-point of PQ is also the mid-point of SH But W is the mid-point of AR and hence C, H, R are collinear. Hence CH/CR = CS/CA = e, the eccentricity
The Eternal Triangle
Authors: Gibbins N M.
Published: January 2007

The title of this paper is “The Eternal Triangle” ; but titles, like politicians, are sometimes misleading. Only last year, for example, you, Mr. President, skilfully cloaked an address on elliptic arcs under the beguiling title of “The Marquis and the Land Agent : a Tale of the Eighteenth Century”. And so now, Ladies and Gentlemen, any hopes you may have entertained of hearing a new solution of an age-old problem must be abandoned. I cannot even say with George Canning.
The Slide Rule in the Teaching of Logarithms and Indices
Authors: Atkinson E.J.
Published: January 2007

A Logarithm as generally understood and used by the ordinary student is the expression of a number as a power of 10. In order to multiply two numbers together he adds the logarithms of these numbers and takes as the result the anti-logarithm of this sum. Similarly for division he takes the anti-logarithm of the difference of the logarithms of the two numbers.
A Chapter on Limits
Authors: Gibbins N. M.
Published: January 2007

The course of study pursued by very many boys in secondary schools who take an advanced course after matriculation is governed by the syllabus of the intermediate examination of a degree in a university other than those of Oxford and Cambridge. In London those boys who intend to specialise in mathematics generally take physics and chemistry as well. It is clear that physics is a valuable complementary study for the mathematical specialist, but it is not so clear that chemistry is. It is a pity that the intermediate qualification cannot be obtained on a syllabus in mathematics a good deal more advanced than the present one, coupled with the present syllabus in physics.
On Geodesic Ellipses and Hyperbolas
Authors: Weatherburn C. E.
Published: January 2007

The following approach to the study of geodesic ellipses and hyperbolas is instructive, and leads to a generalisation in Riemannian geometry.
Notes on the Place of Similarity in School Geometry
Authors: Nunn Percy
Published: January 2007

The principles underlying my proposals with regard to this matter were published in an article in the Mathematical Gazette (May 1922). They may be briefly restated as follows.

The first principle is that school geometry should be organised not as a purely logical system but rather on the lines of the natural sciences. This means that it should be based explicitly upon the pupils’ spatial experiences, which it should seek to extend, to make precise, to analyse and to co-ordinate. Under this description one includes the important field in which geometrical observations and conclusions have practical utility.