bluuebunny/crossref_metadata_2025 huggingface dataset:
Doctor Faustus in Poland
Authors: Grotowski Jerzy
Published: January 2007

In 1963, Jerzy Grotowski's Theatre Laboratory in Opole, Poland— an industrial town of 50,000 some sixty miles from Auschwitz— produced Marlowe's Doctor Faustus. Not one word was changed in the script, but the text was reordered into a “montage,” as Grotowski calls it, drawing on all the Quartos and rearranging the sequence of scenes, creating new ones and eliminating some others. We are printing the program notes to this production, including the sequence of scenes as Grotowski conceived them,. Although the play was performed in Polish, Grotowski wrote the program in French. The Theatre Laboratory is small, seating only sixty, and productions are mounted only when they are ready. For Faustus the long, low theatre room—about forty by fifteen feet—was painted black, and the set consisted of two long tables running the length of the room and one smaller table at one end of the room. In a future issue, we shall have an article about the Theatre Laboratory's work and an interview with Grotowski by Eugenia Barba, who spent some months in Poland with Grotowski's company. We would like to thank Mr. Barba for sending us the program and photographs printed below. —The Editor
Georg Büchner's Danton's Death
Authors: Baxandall Lee
Published: January 2007

Danton's Death is the first play of a twenty-one year old German revolutionary who died before he had lived another three years. Written in secrecy during five weeks of 1835, it may well be the most remarkable first play ever composed. It breaks through prevailing patterns of dramaturgy to a new form, creates the first passive hero in the history of tragedy, and strikingly foreshadows surrealism, expressionism and naturalism. Its author, a youth who short weeks previously had barely escaped arrest for his own revolutionary writings and organizational activities, proceeded to concentrate, in this study of the decline of the French Revolution during Danton's last days, on the antinomy of his passionate desire for social change and his calm knowledge that revolution could not succeed in Germany in his time.
Dispatches from the Prince of Ostrelande
Authors: Hauger George
Published: January 2007

Although the idea of publishing the letters Michel de Ghelderode wrote to me during a correspondence lasting some years is very attractive, it is an idea I strongly resist. The time I would need to translate and annotate the letters could be made available, but the pressing claims of tact and modesty would still prevail. Publication must wait until the years have afforded a perspective that no amount of present-day explanation can provide. Nevertheless, it seems to me that some of Ghelderode's comments in these letters would be of interest to those who are aware of his plays and stories, and I have assembled a small selection of such statements which I feel are not liable to misinterpretation when removed from their contexts.
The Theatrical World of Michel de Ghelderode
Authors: Weiss Auréliu
Published: January 2007

The recent death of Ghelderode has awakened renewed interest in his drama. One of the most astounding figures in the contemporary theatre (a theatre full of astounding figures), his work is characterized by such bizarre aspects as fetishism, living dead men, leaps through time, devils, sorcerers, ghosts, grinning buffoons, legendary heroes stubbornly destroying their legend, historical characters denying the facts of their history, philosophical drunkards, and death as a character in farce.

Obsessed by a universe of dark forces in endless ferment, he saw evil and damnation everywhere. Plagued by them, it did not occur to him to attack them with righteous wrath, as did Calderón and Tirso de Molina, the priest-playwrights of the Golden Age of Spanish drama. In Ghelderode's works the devil is alive and active. Moreover, if one probes beneath his anxiety, one finds a certain satisfaction, a feeling of tenderness and amusement.
The Cat has Nine Lives
Authors: Dukore Bernard F.
Published: January 2007

Beneath a hot roof, on an oppressive summer's day, in a roasting room, Brick and Margaret Pollitt face each other. Brick, heated and hardening in this oven-like bedroom, turns his thoughts toward the liquor cabinet. Margaret, wanting a child by her husband (“in the oven,” as father-in-law Big Daddy would say), and tense (as nervous as a cat on a hot tin roof) because of enforced continence, turns her thoughts toward the bed.

Indeed, the two most prominent scenic elements of Cat on a Hot Tin Roof—elements which fulfill the needs both of the world on stage and the box office in the lobby—are a liquor cabinet and a bed. The former is a “monument,” and the latter is “slightly raked to make figures on it seen more easily….”
Regression-Progression in Ugo Betti's Drama
Authors: Rizzo Gino
Published: January 2007

When Betti's Time of Vengeance was given its off-Broadway production, Harold Clurman wrote (The Nation, Jan. 2, 1960) that the central theme of the play is “evil as a means to satisfy a need for good of which the besmirched mortal does not seem capable.” This is true not only of this particular play but of all the “serious” plays Betti wrote. There is still, however, the task of clarifying the paradox contained in such a statement—a task which until now has been shirked by Betti's critics both in his native Italy and abroad.

The paradox is a faithful reflection of Betti's notion of life's absurdity, or “incongruity.“ In fact, he revealed his own awareness of this paradox and suggested that it stands at the core of his drama:

We are all poor, restless creatures, and we would like at least to understand the tremendous, bewildering incongruity that we see between our existence and what it ought to be according to the aspirations of our soul; to understand why life is the marvelously tranquil iniquity that it is.
Theatre for Learning
Authors: Brecht Bertolt
Published: January 2007

When anyone spoke of modern theatre a few years ago, he mentioned the Moscow, the New York or the Berlin theatre. He may also have spoken of a particular production of Jouvet's in Paris, of Cochran's in London, or the Habima performance of The Dybbuk, which, in fact, belonged to Russian theatre since it was directed by Vakhtangov; but by and large, there were only three capitals so far as modern theatre was concerned.

The Russian, the American and the German theatres were very different from one another, but they were alike in being modern, i.e., in introducing technical and artistic innovations. In a certain sense they even developed stylistic similarities, probably because technique is international (not only the technique directly required for the stage, but also that which exerts an influence on it, the film, for example) and because the cities in question were great progressive cities in great industrial countries.
Recollections of Brecht
Authors: Frisch Max
Published: January 2007

My association with Brecht, taxing as any such association with a reflective person always is, has lasted now for half a year, and the attempt simply to avoid such association is oftentimes not a trifling one.

It is Brecht who always telephones or who, always friendly in his dry and somewhat restrained manner, inquires on the street if one has an evening free. Brecht seeks out conversation wherever he can find it. For my part, I gain the least from our conversations when Brecht thwarts them with his dialectic. One is defeated but not convinced.

On my way home at night, reflecting on his sarcastic comments, I often lose myself in an exasperated monologue: What he says just doesn't all agree! It is only when I hear his verbal discharges again from my own mouth, in the third person, spoken in a similar manner, just as frivolously, often even as spitefully, that I feel the need to cycle back again to Herrliberg.
Bertolt Brecht in New York
Authors: Schevill James
Published: January 2007

Early in 1946, when I met Brecht, he was living in a spacious studio apartment in New York. I had to walk up several flights of stairs to reach the apartment which was on the top floor. Through the door, as I waited, I heard the squabble of pontifical radio voices. A short, wiry man in his shirtsleeves, with close-cropped hair, opened the door. Grinning broadly, he pointed to the radio and said: “That's the best theatre in America. Marvelous, the way they stutter around, go forward a little, go back then forward, then back some more.” Confused for a moment, I began slowly to make out that the radio voices were representatives of an UNRRA conference at the United Nations. Listening intensely, Brecht gesticulated and acted out with his body the invisible UNRRA delegates “stuttering” and “going forwards and backwards,” as he repeated with glee.
Theatres—Not Theatre
Authors: Mee Charles L.
Published: January 2007

Ideals are fine. In most of the pages of this issue the writers are concerned with ideals. These pages are concerned with something more tangible: money.

The fact is, as we all know, today's theatre is run with money. Tomorrow's theatre, such as it may be, must also be solvent. I am not concerned, in the following paragraphs, with dreams or aspirations. I am concerned with certain economic facts of the present, certain economic trends that will shape the theatres of the future.

Who pays for the theatre in America? The audience. What is our audience today in America? First: what is our present Broadway audience?

The present Broadway audience, according to a survey made by Playbill magazine, consists of eleven million people. That is, the Broadway theatres fill about eleven million seats in a given season—sometimes the same people fill the same seats.
For Everyman, A Theatre
Authors: Miller James Hull
Published: January 2007

I suppose the most beneficial result of your letter is the actual analysis on my part of what it is I am really doing. For many years I have been pulling better designs than the next fellow out of the hats of clients in financial corners. I can boast of never having had a rich client. I live at the top of my class but my work was at the bottom of the theatre world. I thought Izenour's theatres monstrously top-heavy, but had to admit he was more popular with the well-heeled lads and the conformists. Then someone pointed out to me the other day that perhaps I was building more theatres than he. On the other hand, your letter seemed to stigmatize my experimentation in actual “bricks-and-wood” and encourage, rather, flight-free drawings.

Finally I decided to stay with the “bricks-and-wood” and try to bring you around to a realization of what is actually going on in my world.
The Actor as Private Man
Authors: Rogoff Gordon
Published: January 2007

If, as I suspect, we are pausing for prophecy, then we might as well admit that, where dreams for the theatre in America are concerned, we must be so many Cassandras. The timbre of our pessimism need not ring with the old lugubrious echo of the original tragic Greek; to be fair to our time, when we have to believe that we control our fate, the echo can be taken from the Giraudoux Cassandra, ironic, bemused and mad only to those who are madder than we are. The question should not be, “What's next in theatre?” but rather, “What ought to be in theatre (and when, if ever)?” “What's next” bears the misleading implication that we have truly been somewhere in theatre and that there are signs, people, and forces clearly leading us somewhere else.
Tragedy, Genet and The Maids
Authors: Pucciani Oreste F.
Published: January 2007

The Maids, produced for the first time in 1946 by Louis Jouvet at the Thèâtre de l'Athènèe, marks perhaps the beginning of “anti-theatre” in France. Certainly we are aware for the first time in The Maids of a strange new consciousness of theatre as in the same year Nathalie Sarraute in Portrait of a Man Unknown made us aware of a new concept of the novel. Sartre wrote of Nathalie Sarraute's “anti-novel”: “We live in an age of reflection and the novel is in process of reflecting on itself.” One might say with equal validity of Genet that his plays are theatre reflecting on the nature of theatre. It is this fact that makes his plays difficult to understand in any normal sense of the word. Nor are his plays “theatre within theatre” as Hamlet contains a play within a play.
The White Mask Falls
Authors: Taubes Susan
Published: January 2007

What makes The Blacks an entirely unique, entrancing, and disturbing theatrical venture is that the very ground of theatrical experience—the community of understanding and sympathy between the people in the audience and the humanity represented on the stage—seems to be pulled out from under our feet. Instead we become parts, both as objects and participants, of a “black” rite of murder and exorcism. The actors inform us at the opening of the play that there can be no relation between us and them other than hostility and contempt. They assure us, moreover, that they shall have the decency to make real communication between us and them impossible. The Negro (Diouf) who tries to adopt a conciliatory tone, who hopes to come to an understanding by engaging our sympathy, is promptly denounced by the group as a traitor; his place is in the ranks of the white spectators.
Towards the Poor Theatre
Authors: Grotowski Jerzy
Published: January 2007

I am a bit impatient when asked, “What is the origin of your experimental theatre productions?” The assumption seems to be that “experimental” work is tangential (toying with some “new” technique each time) and tributary. The result is supposed to be a contribution to modern staging—scenography using current sculptural or electronic ideas, contemporary music, actors independently projecting clownish or cabaret stereotypes. I know that scene: I used to be part of it. Our Theatre Lab productions are going in another direction. In the first place, we are trying to avoid eclecticism, trying to resist thinking of theatre as a composite of disciplines. We are seeking to define what is distinctively theatre, what separates this activity from other categories of performance and spectacle. Secondly, our productions are detailed investigations of the actor-audience relationship. That is, we consider the spiritual and scenic technique of the actor as the core of theatre art.
Moliere Our Contemporary
Authors: Kott Jan
Published: January 2007

In a Tunisian production of L'Ecole des Femmes, Arnolphe wore a red tarboosh with a green band around it. The green band meant he had made a pilgrimage to Mecca. Arnolphe was full of dignity and refinement, rarely flew into a rage, and only on one or two occasions leveled at his servants a long black stick with a bent silver handle. For the most part he was smiling, ironical, had an air of superiority, was certain of his absolute rights. He was a merchant—an honest and experienced merchant. Agnes was his property: he had bought her as a child, was maintaining her and bringing her up to be his wife. She should be obedient. She must not know too much.
Beckett's Purgatory of the Individual or the 3 Laws of Thermodynamics: Notes for an Incamination towards a Presubluminary Exagmination Round Beckett's Factification
Authors: Suvin Darko
Published: January 2007

A critic of modern dramaturgy with a bent for Brecht and O'Casey, the TNP and the Berliner Ensemble, Morgan and Frazer, Marx and Bloch, has one outstanding difficulty to come to terms with, if he is to be sincere to his trade and himself: Samuel Beckett. If the chief measure of a major dramatist is a happy union of relevance and consistency of dramatic vision, there is little doubt that in our cultural circle—middle and western Europe, based on the Mediterranean, with the massive wings of the Soviet Union and North America—the two major dramatists since World War II are Brecht and Beckett. Yet it is rare for a critic devoted to Beckett seriously and knowledgeably to face Brecht. I can think of only one such comprehensive effort—Martin Esslin's—and that one, to my mind, is finally unconvincing. Conversely, however, I can think of no critic of the Brechtian bent who has attempted a comprehensive study of Beckett.
Pirandello and Possibility
Authors: Herman William
Published: January 2007

For it is ultimately the function of art, in imposing a credible order on ordinary reality, and thereby eliciting some perception of an order in reality, to bring us to a condition of serenity, stillness, and reconciliation; and then leave us, as Vergil left Dante, to proceed toward a region where that guide can avail us no further.

—T. S. Eliot

III. The lowest class of funeral carriage, the one for the poor. Naked. And let no one accompany me, neither relatives, nor friends. The carriage, the horse, the driver, and that's all.

IV. Burn me. And let my body, as soon as it has been consumed, be dispersed, because I want nothing, not even my ashes, to be left of me …

—Luigi Pirandello (from his Will)
A Note on Beckett's Realism
Authors: Kott Jan
Published: January 2007

Winnie is buried up to her waist. Happy Days opens with the terrifying sound of a bell. A moment later the bell rings once again. Winnie wakes up, raises her head, opens her eyes. What does this bell mean? Winnie talks about it often, and throughout the entire first act she waits for it to ring. The bell rings when it is time to get up and when it is time to go to sleep. When I was in the hospital, there was no bell; the nurses woke us up and turned out the lights at night. But there was a bell when I stayed in a nursing home. The bell had a horrifying sound and woke us up every morning. The bell rang also at night, and when it had rung, we were not allowed to have the light on.
Review of the Pitoёff production of Six Characters at the Théâter des Champs Elysées in 1923, Found in our files too late for entry in the table of contents.
Authors: Artaud Antonin
Published: January 2007

Life goes on as before. Without any show.

Our eyes are drawn to the very back of the stage. The curtain has gone up. And the whole theatre is a vast hall where the audience is about to watch a rehearsal in progress. But a rehearsal of what? There is no play. We are about to see theatre made before our eyes. Everyone is occupied with his own trivial affairs. After a while, however, the actors come together. Then a family in mourning steps out of the Théâter des Champs Elysées’ elevator; their faces are ashen white, as if started out of dreams.

These are the Six Characters in Search of an Author. Now these Six Characters want to come alive. They want to take part in drama. They are more real than you, stage manager, or you, barn-stormers. They are real and they are about to prove it.
Brecht and the English Theatre
Authors: Esslin Martin
Published: January 2007

That future historians of English drama will describe the period since 1956 as an era of Brechtian influence is quite possible. If so, the phenomenon will be an illustration of the quirks and ironies of cultural diffusion between nations: for that Brechtian era had a great deal of talk and discussion about Brecht and what he was thought to stand for, but few valid productions of Brecht, little genuine knowledge about Brecht, and hence little evidence of any influence of Brecht's actual work and thought. The “Brechtian” era in England stood under the aegis not of Brecht himself but of various second-hand ideas and concepts about Brecht, an image of Brecht created from misunderstandings and misconceptions.
The Living Theatre in Exile: Mysteries, Frankenstein
Authors: Gottlieb Saul
Published: January 2007

The Living Theatre Company of New York has been playing Europe, in voluntary, self-imposed exile, since September, 1964. During this period, despite extreme physical and financial hardship, they have created and produced two astonishing new works, Mysteries and Smaller Pieces and a new version of Frankenstein, both of which have had an enormous impact on critics and large audiences in Europe. Both are remarkable in that they are the result of the collective authorship of an entire company working deliberately with the concepts of Artaud. Each has a freedom of movement, an imaginative inventiveness, and lyric qualities that transcend Artaud. Each has a unity of form and content, fusing the political and aesthetic directions in which the Living Theatre had been groping for many years.
The New Theatre
Authors: Kirby Michael
Published: January 2007

Since the turn of the century, most art forms have vastly expanded their materials and scope. Totally abstract or non-objective painting and sculpture, unheard of in 1900, is practiced by many major artists today. Composers tend to discard traditional Western scales and harmonies, and atonal music is relatively common. Poetry has abandoned rhyme, meter, and syntax. Almost alone among the arts, theatre has lagged. But during the last few years there have been a number of performances that begin to bring theatre into some relation with the other arts. These works, as well as productions in other performance-oriented fields, force us to examine theatre in a new light and raise questions about the meaning of the word “theatre” itself.

In discussing this new theatre, new terms are needed. A few have already been provided by public usage, although they need clarification and standardization. Others will have to be created. Accurate nomenclature is important—not for the sake of limitation but to facilitate easy, accurate, and creative exchange among those concerned with the work and its concepts.
Washes
Authors: Oldenburg Claes
Published: January 2007

Creation of Washes followed the procedure established in previous pieces:

A period of about two weeks, of priming myself with possibilities—practical and impractical—for a pool piece, recording these in a book, and writing a number of script drafts.

Familiarizing myself with the particular place. In this case by signing up for massage etc., at Al Roon's. Noticing the importance of sound in the hall, the impossibility of any rapid action. Details of the normal activity of the Health Club.

Recruiting the cast from volunteers, some new and some familiar from past performances. Setting up schedule of rehearsals. First meeting.

Purchase of objects and costumes. In this case mostly from Canal Street stores, Avenue C used clothing stores, several “thrift” shops, swimming pool suppliers, and sporting goods stores.

First three rehearsals, combining prepared ideas, actual place, individuals in cast, and objects and costumes. Confusion and numerous trials and errors.
Combination Wedding and Funeral
Authors: Ashley Robert
Published: January 2007

All members of the cast dress conventionally, and with the dignity and style that is appropriate to a wedding ceremony.

The Bride wears a bridal gown, etc., but her face and hands are made up with thickly matted hair so that she appears to be some sort of animal. She is shackled with white ribbons to the frontside of an open box (6’ long, 2’ wide, 1’ deep, with carrying handles on either side) which rides upright on, but not attached to, a small, caster-wheel dolly. The open side of the box (facing toward the audience) is curtained with an opaque veil that can be lifted aside. The nude girl (the “cake”) rides inside of the box, hidden from the audience. At the entrance of the Bride in the wedding ceremony the Father of the Bride pushes the rolling structure with the two girls into position in front of the minister.
Happenings
Authors: Schechner Richard
Published: January 2007

Art and politics have long been bad bedfellows. Politicians have converted art into propaganda and artists have welcomed alienation from bureaucratic societies. It very well may be that the modern nation is inimical to art, knowing at best how to “tolerate” it and at worst how to “suppress” it. In which case, my discussion is ended. But if art and politics are not oil and water; if, indeed, perception is basic to “social action,” we may develop a rapport whose possibilities should make both artist and politician stop and think.
Artaud and Film
Authors: Virmaux Alain
Published: January 2007

Since his death eighteen years ago, Artaud's fame has steadily increased. Everyone claims him as predecessor; literary magazines and theatre programs propagate his name; he is quoted as having said things which he never said and he is used as a front for the worst eccentricities. After the Rimbaud myth we have the Artaud myth; to expose the hoax we need a new Etiemble.

In the meantime, Gallimard's careful publication of Artaud's complete works puts into our hands an objective tool to evaluate texts which have been distorted by faddism. The six volumes published so far have already set straight a number of wrong judgments. Volume III revealed Artaud's creativity in cinema; until then, film historians knew Artaud only as an actor. They barely mentioned the one film he had directly inspired, The Shell and the Clergyman [see p. 173], and dismissed it as unimportant.
Two Lectures
Authors: Meyerhold Vsevolod
Published: January 2007

The reconstructed theatre, using every technical means at its disposal, will work with film, so that scenes played by the actor on stage can alternate with scenes he has played on screen. Going further, a dramatic production could become a kind of revue in which the actor uses dramatic, operatic, and film methods, as well as those of the ballet dancer, acrobat, gymnast, clown. And, of course, the play's division into acts, the inflexibility of conventional dramatic structure, must be superseded by episodes after the model of Shakespeare and the dramatists of the old Spanish theatre, making it possible to abandon the antiquated pseudo-classical unities of time and action. We are entering upon a new phase of playwriting. We are creating a new kind of play.
The Division of the Circle
Authors: Manzitti Camillo
Published: January 2007

The possibility of solving the problem of the elementary division of a circumference into equal parts was known to the ancients for the cases

n = 2p, n = 3, n = 5, and their products.

Gauss in his Disquisitiones Arithmeticae proved the possibility of solving the problem by quadratics, and therefore geometrically with ruler and the compass, for all the prime numbers of the series

n = 22p + 1.
Mathematics and Morals
Authors: Cunningham E.
Published: January 2007

The title of this paper was chosen before I had put my thoughts together, and even before I had considered thoroughly whether it were possible to make any general conclusions at all. I hope I shall not be accused afterwards of making something out of nothing, or of seeing connections where none exist. Perhaps it will be that, instead of having a vague notion that mathematics and morals are strangers or opposites, we may arrive at the end of the evening with a reasoned conviction that they are indeed so. But that the subject is not unprofitable to discuss I am strengthened in believing by noticing that Henri Poincaré, perhaps the greatest mathematician of the last fifty years, in the closing years of his life wrote an essay on the “Relations of Morals to Science,” which is included in the volume of his last thoughts.
Note on the Sphero-Conic
Authors: Morley Frank
Published: January 2007

(i.) A quadric cone is a cone having any conic for base, and a point O on the line perpendicular to the plane of the conic through the focus for vertex.

(ii.) A sphero-conic is the curve in which any quadric cone cuts a sphere whose centre is the vertex of the cone.

In an introductory course on space-geometry, where only a passing mention of sphero-conics seems possible, I have found it useful to show directly the fundamental property that the sum or difference of the focal distances is constant, instead of following the classical method, which consists in deducing the property by the use of infinitesimals, from the fact that these focal distances make equal angles with the curve; this latter fact being in effect a direct consequence of Desargue’s theorem.
The Postulate of Parallels
Authors: Hill M. J. M.
Published: January 2007

I desire to suggest to those of your readers, who are giving instruction in the Elements of Geometry, that they should try an experiment when they arrive at the stage in which it is necessary to introduce the Postulate of Parallels.
A Certain Dissection Problem
Authors: Brill J.
Published: January 2007

To cut up an isosceles triangle so that the parts may be put together to form two triangles similar to the original triangle.

Let ABC be the triangle, having the angles at B and C equal, and let D be the middle point of the base. Draw a circle, passing through A, having its centre on AD, and cutting AB and AC in E and F. Join DE, cutting the circle in G.
Director Circle of a Conic Inscribed in a Triangle
Authors: Rouse E. P.
Published: January 2007

Let TP, TQ (Fig. i.) be tangents to a conic, C its centre, S, H its foci, 2a and 2b its axes. From S draw a perpendicular to TP and produce it to its image S′; then we know that S′T = ST, angle S′TP = PTS, and S′H = major-axis = 2a. Similarly with a perpendicular drawn from H to TQ and produced to its image H′. Thus the two triangles S′TH and STH′ are equal, and the angles S′TS, HTH′, and therefore the halves of these angles, are equal, that is, “the tangents from T are equally inclined to the focal distances of T.′
The Equation of Activity in Dynamics, and the Principle of Zero Activity in Statics.
Authors: Hassé H. R.
Published: January 2007

In spite of the great increase in the last fifteen years in the use of the Calculus in the higher forms of schools, and of its introduction into the Intermediate Examinations of many universities, it has not yet been used as much as it could be in the teaching of elementary Applied Mathematics.

It has, of course, long been realised that in the kinematics of the motion of a particle in a straight line we have some of the best examples of the ideas that are the basis of the Calculus, and the notation and machinery of the Calculus is now extensively used in dealing with this part of the subject.
The Teaching of Mathematics in English Public Schools for Boys
Authors: Godfrey C.
Published: January 2007

In the first place, the present paper refers to conditions prevailing in England only, to the exclusion of Scotland, Ireland and Wales.

Secondly, the term " public school" has, in England, a rather special meaning. A public school is generally understood to be an endowed secondary school of fair size, educating boys of the upper and middle classes, independent of state control except in so far as its income is supplemented from public funds. Public schools may be either boarding schools or day schools, but most of them belong to the former category.
A Proposal for the Unknown Digit
Authors: Bryan G.H.
Published: January 2007

In last year’s address I called attention to the need of some symbol to denote unknown digits in approximate numerical calculations. The present note is commuunicated in the hopes that the matter may be submitted either to the Council or to a special committee of the Association in order that some definite recommendation may be adopted.
A Plea for Teaching Probability in Schools.
Authors: Hope-Jones W.
Published: January 2007

In your Mathematical Gazette for last month you read that “the mathematical theory of Probability is practically dead”—and that from a real authority on the subject whose name is known and honoured wherever statistics are analysed and laws deduced from them.
The Complete Angle and Geometrical Generality
Authors: Picken D. K.
Published: January 2007

The very great importance to Elementary Euclidean Geometry of the figure intermediate between the Straight Line and the Triangle appears to have been missed: viz. of the plane figure formed by two intersecting straight lines, each unbounded both ways. For this type of figure we use the name “Complete Angle.”
On the Approximation to Irrational Numbers By Rationals
Authors: Heath A.C.
Published: January 2007

The problem of deciding whether a given number is irrational or not is frequently one of some difficulty, as in the proof that π is irrational. Several numbers which are very probably irrational have never been proved so, e.g. y, eπ. However, we have one quite simple test for deciding whether a number is irrational or not when we have the number expressed as a continued fraction, viz. if the continued fraction terminates, the number is rational; if not, irrational. In what follows we assume our irrational number given as a continued fraction :

or shortly
The Teaching of Indices and Logarithms
Authors: Dobbs W. J.
Published: January 2007

I propose to give you in outline the short course on Indices and Logarithms taken at the present time by the Upper Fifth Form at the Holloway County School. Soon I hope it may be attempted by the Lower Fifth Forms, and, later on, perhaps by kind permission of the examining authority, it may be found possible to include it in the work of the Fourth Forms.

§ 1. Index Notation.—Let a denote any positive numerical quantity, and n any positive integer. Then “ x a” means “ multiplied n times in succession by a.” “an” alone means “1 x an”, i.e. “unity multiplied n times in succession by a.” The index n tells us the number of multiplications.
Geometry and Relativity
Authors: Piaggio H. T. H.
Published: January 2007

Thus Euclidean geometry does not hold in the gravitational field even in the first approximation, if we conceive that one and the same rod independent of its position and orientation can serve as the measure of the same extension.

This quotation from Einstein is merely one of the many disturbing statements that a teacher of geometry may find in recent books on physics or even in the newspapers. It will not be long before some of our pupils will ask if it is worth while to continue the study of a subject of which the principal results are apparently contradicted by the latest discoveries. The object of the present article is to examine these apparent contradictions. To do this we shall trace the evolution of ideas concerning the nature of geometry and consider their relation to school work. The conclusion will be reached that certain changes in our teaching are desirable. Fortunately these changes will actually make school geometry easier as well as more scientific.
Notes on “A Treatise on the Rectilinear Motion and Rotation of Bodies.” By George Atwood, M.A., F.R.S. (Cambridge, 1784.)
Authors: Hall F. G.
Published: January 2007

This is a remarkable book in many respects, and well worthy of the attention of those teachers of mechanics who have not yet made its acquaintance at first hand. Though written in 1784, some of its pages are greatly superior to those in many of the text-books now in use in schools, and one is particularly impressed by the stress laid on experimental verification of the various laws of mechanics, and by the extreme care shown in the planning and execution of the experiments proposed. The following quotations from it and the notes thereon are given, because I feel sure that they will prove of use to those who want Mechanics to become a more interesting subject to their pupils and to stand for something more than what is usually covered by the name “Applied Mathematics.” I have added a few parentheses, but only, I hope, where they were necessary.
Elliptic Trammels and Fagnano Points
Authors: Harding P. J.
Published: January 2007

1. Giulio Carlo dei Toschi di Fagnano, Count and Marquis, was an Italian mathematician of the first half of the eighteenth century. He was one of the second generation of the followers of Leibniz, a generation rather pale and unimportant compared either with the first great founders of the Differential Calculus or with the third generation that dated from about the middle of the eighteenth century, of which Lagrange was the leading genius.

Several of the men of this second generation are known mainly for some one piece of work. This is particularly the case with Fagnano, who extended the application of the Integral Calculus to the rectification of curves in a way that may be regarded as the first germ from which afterwards sprang the Theory of Elliptic Functions.

Experiencing the well known difficulty of rectifying, by elementary integration, many curves whose equations seem, at first sight, easy to deal with, he showed that on some curves two arcs could be found whose difference was rectifiable ; although each separate arc presented the same difficulty as before.
Analysis and Projective Geometry
Authors: Durell C. V.
Published: January 2007

FEW branches of elementary mathematics have escaped reform in recent years; algebra, trigonometry, elementary geometry, statics, and the calculus have all been transformed to suit the practical needs of the time. But amid all this change, there have been few attempts to alter the methods employed in introducing students to the geometry of the conic. Dr. Filon, in his most interesting treatise on Projective Geometry published in 1909, points out that students learn the same facts about the conic practically three times over, (1) analytically, (2) through a course of what is called “geometrical conies” based on the focus-directrix definition, and (3) protectively ; and his book indicates a method of co-ordinating and uniting the last two systems of approach. Although it is undoubtedly the general custom in this country to start in the first place from the focus definition, it is worth while considering afresh whether this plan is really the most advantageous.

It is interesting to note that historically this was not the starting point of the early geometers. It is true that the focus-directrix property was known to Pappus, but so far from being regarded as fundamental, it was actually lost sight of altogether, until attention was called to it by Newton. The geometrical investigations of Apollonius were based on the conception of the conic as the plane section of a cone, the advantages of which plan may be enumerated roughly as follows:
On the Setting Out of Certain Easy Cubics
Authors: Edwards R.W.K.
Published: January 2007

If we wish to develop a race of geometers, I think we should begin by encouraging the habit of speculation. This we do nowadays by using squared paper for plotting graphs. Here, however, we place ourselves very much in the hands of the printer : and although ideas of geometrical shape are enlarged and systematised, the right angle plays too great a part in whatever knowledge of curves is acquired ; indeed a knowledge of curves is not the professed object in plotting graphs so much as a visualised representation of corresponding changes in related physical quantities.

In teaching elementary geometry there lingers an aversion from the use of dividers in pricking out equal distances : for the transference of distances is not recognised in the postulates of Euclid, and Euclid's influence remains.

Later on a study of the conics, carried on for a prolonged period, and the application of the theorems of Pascal and Brianchon, must exercise their fascination. Ideas about infinity become clarified : the use of parallels is seen to be necessary, to exercise the right accorded by Euclid's first postulate to join any given point to any other, even if one be at infinity. But the mind inevitably tends to become obsessed with the second-degree idea. Mere straight-edge methods are found to be so potent in the construction of conics that metrical properties are neglected. Primary notions about equal distances interfere with the whole scheme of a projective geometry confined to the conics ; and the bisection of a given finite straight line becomes a search for the harmonic conjugate of the point at infinity in its direction, with regard to its two ends.
Kinetic Energy, Divided into Molar Energy and Available, Internal, or Molecular Energy
Authors: Greenhill G.
Published: January 2007

The algebraical transformation

should be introduced into dynamical instruction at an early stage, and interpreted as the resolution or rearrangement of the left-hand side, the kinetic energy of two bodies, say railway trucks, of weight W1 and W2 tons, moving on the same line with velocity U1 and U2 feet per second, into (A) and (B) in the right-hand side.
Berkeley and Newton
Authors: Evans W.D.
Published: January 2007

In his interesting article on Newton in the July Gazette Dr. Rouse Ball had space only for a slight reference to Newton’s views on what we should now call the Foundations of the Differential Calculus. The subject “ involves,” as Dr. Rouse Ball has remarked, “ some awkward questions of philosophy which before Weierstrass’s researches were usually slurred over.” Some of the logical difficulties incident to Newton’s method of approach were clearly seen and pointed out by a contemporary, the celebrated Bishop Berkeley, in a tract which drew much attention at the time, and was followed by a considerable controversy.
Unicursal Plane Curves
Authors: Mathews G. B.
Published: January 2007

The theory of unicursal plane curves affords so many interesting exercises that teachers may like to have a short collection of formulae and theorems about these curves, reduced to the shape which appears to be most convenient for applications.
Vectors
Authors: Godfrey C.
Published: January 2007

Vectors in two dimensions are generally studied in schools; I do not suppose that the study is often pushed into three dimensions. But it is difficult to understand a modern book on electricity without some knowledge of three-dimensional vector notation.

The particular point that I wish to bring before you is that the two-dimensional case is often presented in such a way that its relation to the more general case is obscured.
The Durham Summer Course in Mathematics for Teachers in Secondary Schools
Authors: Westcott G. J. B.
Published: January 2007

Together with our fellow-students of the Courses in French, Geography and History, we assembled on the evening of the 30th July at the University Lecture Rooms, Palace Green, Durham, and were welcomed on behalf of the University by the Dean of Durham and Canon Cruiokshanks, who promised lis that everything should be done by the authorities to make our visit to their historic city a pleasant one, a promise which it is needless to say was amply fulfilled.
Recent Developments in Invariant Theory
Authors: Turnbull H.W.
Published: January 2007

I have been asked to write a short account of the present-day work in the algebra of invariants for the benefit of those who have not made a special study of the subject. A good summary account can be found in the various continental works of reference, and particularly in the Encyklopädie der Mathematischen Wissenschaften, Band III. Teil iv. 7, written by Dr. R. Weitzenböck, and brought up to about tho date 1920 with tolerable completeness, both in subject-matter and in references. Nothing has, however, been published in the last thirty years quite so good and readable as Meyer’s Bericht, which reviewed the first fifty years of progress from the time when Boole inaugurated the theory in the Cambridge Mathematical Journal, iii. pp. 1-20, of the year 1841. As things have turned out, and especially because of the impossibility of buying separate parts of the Encyklopädie without embarking on the whole section (Geometry in this particular case), it seems a pity that we have no machinery in England for the systematic issue of corresponding reviews, perhaps in the form of this Bericht, to cover by degrees the field of present-day mathematics.
A Geometrical Construction for epi- and Hypo-Cycloids
Authors: Piggott H. E.
Published: January 2007

In the Gazette for January, 1925, I gave a geometrical construction for a cardioid. Thé curve was obtained as the envelope of chords of a circle drawn to a certain rule. It has recently come to my notice that the rule can be extended to cover epi- and hypo-cycloids.
The Principles of Dynamics
Authors: Larden W.
Published: January 2007

(1)

We have, above, assigned an intelligible meaning to this expression if the body be considered as a member of a system. But, taken absolutely, it has no meaning.

(2)

If our shot, now considered separately, meet directly a target of mass M′ and there be inelastic collision, and if the relative velocity be U, then the velocity u′ of the shot relatively to the c.m. of this new system will be , and the velocity V′ of the target relatively to this c.m. will be .

The total internal energy of this system as measured by the heat given out will be , and of this the shot may with some reason be said to contribute the first term, and the target the second, in virtue of its K.E. [see VII., (3) and (4)].
The Integral Calculus Theorem
Authors: Picken D. K.
Published: January 2007

The following presentation of the fundamental theorem of The Integral Calculus has been evolved as the result of attempts to put § 31 of Whittaker’s “Analysis” before a University class. It is to be regarded as the first application of the Infinite Sequence Theory which has been the subject of articles in recent numbers of The Mathematical Gazette. It is in the details, making for stricter logical accuracy, that what is new will be found.
A Case of Three Rotating Lines and the Point “O.” (Continued.)
Authors: Taylor F Glanville
Published: January 2007

15. Let X1, Y1, Z1 be the second points in which AH, BH, CH meet the circle GH

Then GX1 ┴ HX, and hence ║ BC,

X1X =⅓AX;

tan PX1X= 3 tan PAX = 3 tan θ,

i.e. -PX1X= ø.

But OX1H = OGH= ø; 0X1P is a straight line.
The Laws of Dynamics, and their Treatment in Text-Books
Authors: Macaulay W. H.
Published: January 2007

In the preceding discussion of the Galileo-Newton theory, force has been introduced as measured by mass-acceleration, in accordance with the generally accepted procedure. The existence of laws, connecting force with the conditions accompanying it, has been referred to as a fundamental fact which makes the theory possible; though, as a matter of logical order, all details as to such laws have been put into a secondary position. The recognition of the fact that acceleration was the thing, which could be connected by laws with the conditions under which a body moved, has been mentioned as Galileo’s great achievement. This was historically the first and most important, and was probably the most difficult, step to be taken. There is no record of any suggestion of it before Galileo’s time, and no theory of motion of any value had been constructed on any other basis. Perhaps the nearest approach to such a theory was the study of the celestial motions on the basis of circular motion; and this was not capable of progressing beyond the empirical stage.
The Division of the Circle—Concluded
Authors: Manzitti Camillo
Published: January 2007

To establish the order of the locus we must note that besides the above mentioned n intersections with the circumference, the point D also belongs to the curve, so that the latter cuts the circle in n+1 points. The order of the curve is therefore Let n be even.

The ratio is not an integer, so that a complete rotation of the straight line BC must take place before the two generating straight lines can be in their initial mutual position; the line revolving round D will be, after a semi-rotation of BC, parallel to BC in DE, and we may say that all the loci for n = 2p are asymptotic in the direction BC, on account of the initial position of BC and DA.
Conjugate Diameters in Areals
Authors: Gibbins N. M.
Published: January 2007

Principles. 1. If K be the centre of a conic and P a point not on it, the diameter conjugate to KP is parallel to the polar of P.

2. Conjugate diameters form a pencil in involution. Hence if S=0 and S' =0 be the equations of two known pairs of conjugate diameters, the general equation is S + λS' =0.

The method then is to find the diameters conjugate to KA, KB, KC, where ABC is the triangle of reference, by means of 1, and then to write down the general equation by means of 2.
A Curious Property of Numbers
Authors: Ayyangar A. A. Krishnaswami
Published: January 2007

The difference between any number and another formed by reversing its digits has certain interesting properties, which, I believe, have not been explicitly noticed before, and these properties determine the necessary and sufficient conditions that a number may be expressed as such a difference.

To begin with, let us take a number having an even number of digits and denote it by

where ap, bp are the middle digits, b1 the units digit and a1>b1.