bluuebunny/crossref_metadata_2025 huggingface dataset:
Flickers of Incest on the Face of Honor: Calderon's Phantom Lady
Authors: Honig Edwin
Published: January 2007

The pastoral ethic is that set of ameliorative principles in La devotión de la cruz (Devotion to the Cross) and El alcalde de Zalamea (The Mayor of Zalamea) working to assuage the intolerable burden of fear and vengeance exacted by the autocratic honor code. These principles receive maximum dramatic range, with the happiest consequences, in The Phantom Lady. The issue is not so much the honor of a woman in danger of losing it, though this hazard is real and accounts for much of the play's dramatic interest. It is rather the clandestine yet clearly approved means by which a lady of rank asserts her rights as a woman in love. Without knowing the odierwise fatal role of honor in Calderonian drama, a casual reader would miss these positive implications of the theme so tfiat the play would seem little more than an auspicious forerunner of Restoration comedy, which indeed it influenced.
Cuchulain, Christ, and the Queen of Love: Aspects of Yeatsian Drama
Authors: Moore John R.
Published: January 2007

Yeats stands out among the poets of this century who have attempted poetic drama because of his life-long struggle to make the drama serve both his own and his country's purposes. From Vivien and Time (1884) to The Death of Cuchulain (1939) he labored at the often uncongenial task of giving voice (or mask) to conflicting attitudes within the scope of a dramatic action. The dramatic discipline he came to see as a necessity for his own development as a man and poet, and as a possible means of transforming the vulgar or sentimental patriotism he despised into a defense of the Irish heroic ideal which could arouse his countrymen and earn the respect of his literary friends and rivals too.
Our Man in the Sixteenth Century: Michel de Ghelderode
Authors: Abel Lionel
Published: January 2007

I am of the opinion that exaggerated estimates of an author often work against a continuing interest in him; thus I cannot but be sympathetic to certain of the criticisms M. Auréliu Weiss has made of Michel de Ghelderode. I want people to be interested in Ghelderode and in his plays; and I should like their interest to be lasting. So I shall not dispute M. Weiss's pejorative judgments of some of the dramatist's lesser works: Le Soleil Se Couche, La Mori du Docteur Faust, Don Juan, Sortie de L'Acteur, and Pantagleize, all of which have been overrated by Ghelderode's admirers. It is true to say, as M. Weiss does, that in these plays, as in others by the Belgian playwright, there are precious bits along with “capricious inventions, exaggerations, absurdities … platitudinous meditations, extravagances, esoteric obscurities.”
The World of Jonesco
Authors: Ionesco Eugene
Published: January 2007

The “society” I have tried to depict in The Bald Prima Donna is a society which is perfect, I mean where all social problems have been resolved. Unfortunately this has no effect upon life as it is lived. The play deals with a world where economic worries are a thing of the past, a universe without mystery, in which everything runs smoothly, for one section of humanity at least. I have no doubt that this is the world of tomorrow. In America, Russia, China, Africa, and so on, the march of science and industrialization must finally arrive at stability and social contentment.

In The Bald Prima Donna, which is a completely unserious play where I was most concerned with solving purely theatrical problems, some people have seen a satire on bourgeois society, a criticism of life in England, and heaven knows what.
“Madame Bovary” in Book and Film
Authors: Bluestone George
Published: January 2007

In her “Note on the Film” in Feeling and Form, Susanne Langer suggests that “… the novel lends itself more readily to screen dramatization than the drama. The fact is, I think, that a story narrated does not require as much ‘breaking down’ to become screen apparition, because it has no framework itself of fixed space, as the stage has…” But Miss Langer overlooks an essential similarity betwen the drama and the novel which, in a basic way, sets both media apart from the cinema: both are fundamentally composed of verbal forms. Hamlet can be grasped by an audience in a reading from the lectern, the actors immaculate in evening clothes; Thomas Wolfe can affect us in our own silent reading or in Charles Laughton's recitation. Both have existences apart from stage space, apart from vision, even.
Gestus in Music
Authors: Weill Kurt
Published: January 2007

In my attempts to arrive at a basic form for the musical theatre, I noticed several things which at first seemed to me to constitute entirely new insights but which after a closer look were revealed as but logical parts of the whole historical situation. While working on my own compositions, I constantly forced myself to answer the question: What occasions for music does the theatre offer? But as soon as I looked back at the operas written by myself and others, another question arose: What is the nature of music which is found in the theatre, and does such music have definite characteristics which label it music of the theatre? After all it has often been stated that a number of important composers have either never paid any attention to the stage or that they have tried in vain to conquer the stage.
Building For The Performing Arts
Authors: Izenour George C.
Published: January 2007

When we talk of the “performing arts,” we must talk about all of them: the spoken drama, musical theatre, opera, ballet, and concert music. Up until now it has been generally true in the majority of American communities that most all spaces that could seat anywhere from one hundred to ten thousand people have, at one time or another, been used for performances of every kind, size, and description. It was inevitable that the artist made compromises which lessened—sometimes almost to the vanishing point—his effectiveness as a performer. Space designed specifically as a theatre does not make a good concert hall, nor does space designed specifically as a concert hall make a good theatre. This is true visually as well as acoustically. We can demonstrate that certain transformations are possible within a single facility which will adjust both the performing and audience spaces to quite opposite and diverse uses.
The Theatre Of The Marvelous
Authors: Gray Paul
Published: January 2007

When I was young and easy—not so long before we really reached for the absurd—and when theatre was all the thunder and hooves of the Old Vic or, if you chose, that something wild and psychotic in Stanislavski New York, I became involved in a very curious circumstance. It was then that the possibilities of a theatre of the marvelous dawned upon me.

I was working at the time as a social investigator for the New York City Department of Welfare. My clients were the mentally deteriorating, the physically disabled, old people left alone to die, frustrated and inept unwed mothers, and last, but not by any means the least, children: in other words, people representing that large segment of our population who do not know the theatre and to whom America, itself, is one huge stage show. Indeed, when I studied their case records which read like epics, I realized that nothing in our modern theatre would be inspirational to them.
Who Killed Laius?
Authors: Harshbarger Karl
Published: January 2007

There are two versions of Laius’ murder in Oedipus Rex. First, there is the version that is current in Thebes and is expressed by Creon, Jocasta, the Chorus, and presumably the Shepherd if he were to talk about it. Second, there is Oedipus’ version.

The first version is essentially this: one day, not too long before the Sphinx came to terrorize Thebes, Laius set out—so he said—to Delphi. He did not travel as a king generally might with a great many soldiers, but with only four of his men, one of whom was a herald. Laius himself rode in a chariot. At a place where three roads meet, Laius was met by a group of robbers.
To end god’s judgment
Authors: Artaud Antonin , Corti Victor
Published: January 2007

In 1946, after nine years’ confinement, Antonin Artaud was at last allowed to leave mental hospital and he returned to live just outside Paris. He was in poor physical condition and, in consequence of this and his supposed insanity, he did not return to work in the Paris theatre. He nonetheless wrote with an energy which bespoke several years of forced literary inactivity. He gave some lectures and talks, one very notable one under the patronage of his friend, Charles Dullin. However, despite his personal liberation, not all Paris welcomed his return; some, such as André Breton and Surrealists, had little respect for his genius, others, perhaps a little more staid, were frankly scared by his intransigent attitude.
The Inner and the Outer Reality
Authors: Schechner Richard
Published: January 2007

Ionesco is the closest thing we have to an abstract expressionist in the theatre. His plays are plainly autobiographical and confessional. “I try to project on stage an inner drama (incomprehensible even to myself) telling myself, nevertheless, that since the microcosm is the image of the macrocosm, it may happen that this torn up, disarticulated inner world is in some way the mirror or the symbol of universal contradictions.” He discovers the astonishing in the banal, the unreal in the real, the new in the old, the fresh in the stale, and the archetype in the stereotype. His work is romantic and subjective, mirroring his own anguish and inner struggles, translating them into symbols and patterns that have been empathetically embraced by audiences throughout the world. But this empathy should not confuse us.
Stanislavski at School
Authors: Schechner Richard
Published: January 2007

First, acknowledge the talent of so many American actors. Why, then, is their acting so bad? Between talent and its expression on stage stands an Establishment which brutally uses its people, even while improving the theatre. Earlier still, the actor in training is confused and misled, over-worked and under-trained, frustrated and stunted. Training is so isolated, haphazard, and contradictory that it is hard to discuss it, almost impossible to evaluate it with anything but blanket condemnation. In no other profession is there so little agreement about standards and methods, so little active contact among those doing the work.
Calderón's Mayor: Honor Humanized
Authors: Honig Edwin
Published: January 2007

The ambiance of The Mayor of Zalainea (El alcalde de Zalainea) is free-flowing and quick-changing. Though many scenes take place in Crespo's house, the impression is that the out-of-doors predominates, that things are literally and figuratively out in the open. From the soldier Rebolledo's raucous expostulations against marching orders in the opening scene, to the crowds of farmers, soldiers, and officials listening to the banter of Don Lope and Crespo, Chispa and Rebolledo in the closing scenes, the play abounds with jaunty speech, the excited intermingling of classes, and rapid scene shifts which follow the intrigue and the conflicts of interests. Characters tend to pair off and move now toward and now away from other pairs as they reflect or mark off changes of situation: Rebolledo and La Chispa, his sweetheart; the captain Don Álvaro and his sergeant; the impoverished hidalgo Don Mendo and Nuño his servant; Pedro Crespo the mayor and Don Lope the commander; Crespo and his son Juan; Crespo and his daughter Isabel; and finally, Isabel and her cousin Inés.
The White Man's Burden
Authors: Schechner Richard
Published: January 2007

When questioned about the audience at Minneapolis’ Guthrie Theatre, a man who ought to know said, “Well, we're working out a deal with New York. They're going to send us 300,000 Jews and Italians and we're going to send them 300,000 Swedes and Norwegians.” The Guthrie started because Sir Tony wanted a regional theatre and Minneapolis came up with the best bid. Like starting an industry or relocating a plant. Three years have passed since the missionaries arrived. Sir Tony is leaving and his associate artistic director, Douglas Campbell, is replacing him. The theatre has developed into one of the two best in the nation (Washington's Arena Stage is the other). But something is missing—dialogue with the audience.

Sir Tony directed two plays last season, The Cherry Orchard and Richard III. The first was a museum piece of exquisite taste, the second a bold and bald exercise in condescension.
The Royal Shakespeare's “US”
Authors: Marowitz Charles
Published: January 2007

The artistic failure of the Royal Shakespeare Company’s Vietnam documentary US has been largely obscured by the controversies it has wittingly and unwittingly aroused. In London, at the present time, it is possible to convert almost any lukewarm entertainment into a box-office success by stirring it in the press. In the case of US, one had a subject which was already incendiary, and so it was relatively simple to work up the requisite hoopla. This is unfortunate whenever it happens, because it gives an audience the added difficulty of having to disentangle legitimate intentions and actual results from distortions perpetrated by the mass media. But in this case, Peter Brook’s production, devised collectively by the Company, is no innocent victim of circumstances. It seemed pre-disposed to vulgarization; almost intended for tabloid exploitation.
The Homecoming
Authors: Morris Kelly
Published: January 2007

Eliot, speaking of Jonson, said that poetry dealing with the surface of life requires great deliberateness and simplicity of effect. Pinter is a poet of the surface. His manipulation of performance conventions suggests the “comedy of manners” in its dependence on standard theatrical devices and tightly constructed exploitation of speech and gesture patterns, disabused of conscious causality and motivation data. He differs radically from most comic theatre in two important respects: his plays do not aim (or pretend) to reflect or represent society in a typical, satiric, or parodic way; and he effectively eliminates plot as even a structural element (which is one of his similarities to Beckett).
Approaches to Theory/Criticism
Authors: Schechner Richard
Published: January 2007

For the last hundred years or more, Greek tragedy has been understood as an outgrowth of rites celebrated annually at the Festival of Dionysus. Those rites have been investigated both in their relation to the god Dionysus and in their relation to the primitive religion of the Greeks. The result is a conception of Greek tragedy which is very different from that which prevailed from the Renaissance into the eighteenth century. The Renaissance humanists and their successors saw it in “civilized” and rational terms; in our time we see that much of its form and meaning is due to its primitive source, and to the religious Festival of which it was a part. This new conception of Greek tragedy has had a very wide effect upon our understanding of the sources of poetry in our tradition, and also upon modern poetry itself, including the theatre and music….
The Restless Intelligence of Tennessee Williams
Authors: Rogoff Gordon
Published: January 2007

That Tennessee Williams is presently in crisis probably goes without saying. There are reasons, however, why it should be said yet again; not the least of which is the need to name the crisis, place it, forget about it, and move on to more helpful abstractions. To name it, at least as it comes to us from the theatre page of the New York Times or the gossip columns of the New York Journal-American, all we have to ponder are those twin obsessions, money and sex.

The popular image of Williams is that of the Successful Playwright, man about many towns, suavely wearing a pencil moustache that seems to have been bought as an elegant accessory to his debonair tropical suit.
The First and Second Wilderness
Authors: Kirby Michael
Published: January 2007

During May 1963, the Smolin Gallery sponsored a month-long program of Happenings, Events, music, dance, chance theatre, etc. called the Yam Festival (“Yam” is “May” spelled backward). One of the many performances listed on the published calendar was The First and Second Wilderness, subtitled A Civil War Game. It was presented for one evening only—May 27.

When the spectator climbed four flights of stairs to the loft where the piece was being done, he found himself in a clean, freshly painted room about ninety feet long and twenty feet wide. Near the center of the space, the squares of a large game board had been laid out on the floor with tape. The usual rectangular grid pattern was extended by pyramids of squares at each end which ended in single squares marked “Washington” and “Richmond.” Blue and grey cardboard soldiers about two feet tall stood near the opposite ends of the board.
On a Symbolic Proof of Fourier’s Theorem
Authors: Filon L. N. G.
Published: January 2007

Some time ago, when attempting to generalise certain methods of solving differential equations by operators, the writer came across the following mode of deducing Fourier’s Theorem symbolically.

The method is so simple that it seems improbable that it should be unknown. The nearest approach to it known to the author, however, occurs in Oliver Heaviside’s Electromagnetic Theory, Vol. II. §§ 275 et seq., but the investigation there proceeds on somewhat different lines, and the interpretation of the operators used requires to be carefully defined.
The International Commission on the Teaching of Mathematics
Authors: Jackson C. S.
Published: January 2007

As a first result of the labours of the International Commission on the Teaching of Mathematics, appointed in 1908 on the initiative of Professor D. E. Smith, the distinguished author of Rara Arithmetica, some 9000 printed pages were presented to the International Congress of Mathematicians at Cambridge. It is obviously impossible to go into details: I can only hope to mention one or two facts, and to give a general impression of the problems raised.
The Work of a Local Branch
Authors: Hudson W.H.H.
Published: January 2007

We meet to-day to inaugurate a London Branch of the Mathematical Association. This is a step in a process of evolution.

The Mathematical Association is a continuation of the Association for the Improvement of Geometrical Teaching, commonly known as the A.I.G.T., founded in 1870.

I did not join the Association till 1883, but some of its earliest reports are in my possession; to thrse I shall refer

It owed its existence to a profound wide-spread dissatisfaction with the lack of geometrical knowledge, and still more the absence of geometrical power, displayed by students who had passcd through the ordinary school course of Euclid.
Projective Geometry
Authors: Macaulay F.S.
Published: January 2007

Projective geometry derives both interest and importance from the fact that it assumes only the simplest and most fundamental axioms. The following sketch of the first principles, and proof of the fundamental theorem, is taken from Prof. Federigo Enriques' Projektive Geometrie (B. G. Teubner, Leipzig, 1903, 8vo, pp. xiv, 374). This work is specially adapted for school teaching. The first (Italian) edition appeared in 1898, and the axioms on which it is founded were explained, four years earlier in the Rendiconti R. 1st. Lombardo, Vol. 27, pp. 550-567.

Projective geometry is the geometry originated by von Staudt in the Geometrie der Zage, of which an excellent account by Prof. C A. Scott has already been given in the Mathematical Gazette, Vol. I., Nos. 19, 20, 22, pp. 307, 323, 363. Russell's very original Foundations of Geometry is the only English work which treats the subject from a strictly logical standpoint, but is unfortunately very unreliable as far as the mathematics is concerned.
A Plea for a More General Use of Vector Analysis in Applied Mathematics
Authors: Weatherburn C.E.
Published: January 2007

That the advantage of using vector analysis in mathematical physics has met with so little recognition by British applied mathematicians must appear rather strange to those of other countries. There are probably not more than half a dozen among us who habitually use vector methods and notation, at any rate in published work. The fact is still more surprising when we recall the work of Maxwell and Heaviside, seeing that the former gave a sort of authority to the curl and divergence, while the latter had so much to do with the systematic development of the vectorial calculus.

Perhaps the chief reason why vector analysis has not come into more general favour with us is that our leaders in applied mathematics have not felt the need of it. It has often been remarked, and perhaps with some degree of truth, that nothing can be accomplished by vector methods that cannot also be done by Cartesian analysis ; and therefore, it is argued, the change is unnecessary and useless. If we had to deal only with minds of special mathematical ability and analytical insight, this conclusion might be accepted. But with the average student so much of his attention is occupied in dealing with the complex array of symbols of partial differentiation to which he is often led in Cartesian analysis, that he is unable to grasp the inner meaning of the work. It is difficult for him in many cases even to see exactly what is expressed in the formulae obtained, involving as they do the three components of a vector quantity in combinations not easy to visualise. And even if the student succeeds in following the argument it is often almost impossible for him to remember either the train of reasoning or the result arrived at. He does not perhaps see why his equations should be differentiated partially with respect to x, y, z and added, or with respect to z, y and subtracted.
Some Incidental Writings by De Morgan
Authors: De Morgan A.
Published: January 2007

Ser. v. 89. John of Halifax.—Since every country has its Holywood, and de Sacnbosco does not distinguish Holywood from Halifax, John of Halifax has been claimed both by Ireland and Scotland, and, if I remember right, by some foreign countries. The manuscripts of his works, as well as the earlier printed editions, call him Anglus or Anglicus; and he lived in a time at which the natives of the three countries were as distinct as Frenchmen, Spaniards, and Italians. Bale, quoting Leland, calls him Halifax; as does Tanner: Pits gives his birth to Halifax. He was buried in the Maturin convent at Paris, where his epitaph existed in the sixteenth century. Pits implies that it appears from the epitaph that he died in 1256: Maestlinus expressly affirms that it can be collected from the epitaph, in the Ad Lectorem of his Epitome Astronorniae. All the authorities believe him to be English; and Leland thought he traced him as a student at Oxford. But had the manuscripts called him anything but English, the other evidence would not have weighed them down; for there are plenty of Holywoods, and there was, notoriously, a press of foreign students to Oxford in the thirteenth century. But name and residence in England may come in aid of the manuscripts.
The Teaching of Easy Calculus to Boys
Authors: Knowles W.
Published: January 2007

The majority of the boys who enter the Technical Day School of the Borough Polytechnic Institute come from elementary schools, a few only come from secondary schools. The general age of entry is about 13 years, and the boys are about up to the level of the VIIth standard of a good Council School.

As far as we are able, we select for admission boys who have a mechanical or constructive bias. All the boys who enter are expected to take the full three-years' course of work. At the end of that time they go into engineering workshops.
On the Teaching of Indices and Surds
Authors: Genese R. W.
Published: January 2007

The object of the present paper is to invite discussion as to the safest lines upon which to proceed in the teaching of Indices and Surds. And firstly, I am inclined to think that the beginner would get a firmer grasp of the theory of fractional indices (with which alone I am concerned) if a short course of surds, or, at least, of surd-forms, were made to precede; the simple theorem

would suffice, as shown later: and it seems more intelligible than its rival
The Theory of Order, as Defined by Boundaries
Authors: Dixon E. T.
Published: January 2007

I propose in these papers to demonstrate, or rather to indicate the nature of the demonstration of, the proposition that—All Geometry, whether projective or metrical, may logically be regarded as merely a particular concrete application of the general theory of Order, as defined by Boundaries.

It is true that Geometry, as ordinarily understood, is something more than this; it is concerned with the actual subjective conceptions we entertain of Space, and so far provides matter of discussion to the Psychologist; and it is concerned with the actual objective measurements we make upon physical bodies in Space, and so far concerns the Physicist; while in both these respects it extends beyond the region of pure Logic into those of Epistemology and Philosophy generally. But so far as the pure Mathematician is concerned, every geometrical theorem is embraced in the Theory about to be discussed.
The Teaching of Limits and Convergence to Scholarship Candidates
Authors: Milne W. P.
Published: January 2007

1. The present paper is an attempt to sketch a mode of procedure for teaching Limits and Convergence to beginners. It is felt by many teachers that at present

(1) the subject is introduced too academically;

(2) that its Arithmetical foundation is not brought into sufficient prominence;

(3) that therefore pupils leave school with only a very hazy notion of what it is all about;
The Pseudo-Definition of the Straight Line
Authors: Halsted George Bruce
Published: January 2007

We recognise as decadence the substitution for Euclid’s theorem I. 20, “Any two sides of a triangle are together greater than the third side,” of the objectionable pseudo-axiom, “A straight line is the shortest line from one point to another.”

This phrase, as Hilbert has well said, is of necessity meaningless when the concept “length of a curve” has not been defined. Every book on elementary geometry which has introduced as axiom or definition of a straight line any phrase equivalent to “ A straight line is the shortest distance between two points,” every book which has at its beginning as axiom or definition of a straight line any phrase equivalent to “A straight line is the shortest distance between two points,” has been in error. We believe the advances in regard to the foundations of elementary geometry make timely the rejection of this piece of decay from the body of the elements, and that the time is ripe for the return at this point to the pristine purity of Euclid.
The Discussion of Certain Power-Series
Authors: Carson G. St. L.
Published: January 2007

The difficulties which arise in teaching the elementary power series appear to form part of a larger question, namely, the proper course of mathematical education after a sufficient knowledge of Elementary Geometry, Algebra and Trigonometry has been acquired. The question of Geometry is hardly germane to the present discussion, and I will only mention it so far as to say that I believe it is the hope of many teachers of mathematics that boys of 15 or 16 may in the future learn far more of Projective and Descriptive Geometry than is the case at present.
Some Theorems in Geometry and some Suggestions
Authors: Robinson R. T.
Published: January 2007

In a system in which we have given a circle and the relations between it and certain points and lines, certain changes take place in these relations in another system in which a conic takes the place of the circle. To enable these changes to be more easily seen and interpreted, the writer has found it very convenient to use certain modes of expression.
A Model for Figures in Three Dimensions
Authors: Green H. G.
Published: January 2007

Now that the value of models in the teaching of Geometry has received emphasis in the Report on the Teaching of Geometry in Schools, a great impetus may be expected in their development. This expectancy combined with the article by Mr. Langley (Math. Gazette, May 1924), has led the writer to think that some account of a device for three-dimensional representation may be of interest to readers. In its present form the model is so arranged that figures for very general straight-line problems can be built up in a very few munites. It has been in active use for about a year and has proved of valuable assistance both in trigonometrical and in pure geometry.
The Tracing of Conics
Authors: Neville E. H.
Published: January 2007

It is hard to understand why the problem of tracing a conic from its equation is usually subordinated to if not identified with the problem, intrinsically more difficult, of calculating axes, or why students are not encouraged to bring their knowledge of geometrical properties of the curve to the drawingboard. The essence of tracing a curve is to render the sketching of it as accurate as may be desired, and I venture to assert that for this purpose the discovery of axes and vertices is not worth a tithe of the labour which it demands. Prom the advice in some of our text-books one would imagine that the ellipse could be drawn accurately from its four vertices alone, the hyperbola from its vertices and its asymptotes, and the parabola from its axis and vertex and one or two other points. The truth is, that in any but expert hands these details are wofully insufficient; what is wanted is a multitude of points on the curve, and it matters little whether or not the vertices are included. The student finds satisfaction in drawing the curve from its equation and observing the symmetry that appears when the axes are inserted subsequently.
A First Practical Training in Arithmetic
Authors: Epps Frances
Published: January 2007

The following practical suggestions are offered as an answer to the question of ever-increasing interest, “How, when, where, shall the child begin arithmetic?”

The importance of the science of number, as a great teacher has shown, is enormous, not only in its relation to the study of abstract mathematics and in its dominance over the prosperity of nations, but in the fact that it is the “conclusive science which we have to apply all our days to all our affairs.”
On Higher Trigonometry: III. The Elementary Transcendental Fuctions
Authors: Picken D. K.
Published: January 2007

The following system of algebraic inequalities is of great value and of wide application:

for all positive proper fractional values of a,

for positive proper fractional values of α1, α2, αn, and value of k Such that 2k<n; ∑r denoting the sum of the r-products of the α’s.
Modern Theories of Integration
Authors: Francis E. C.
Published: January 2007

As the outcome of a short but occasionally painful experience of mathematical papers, I would suggest that such a paper, if it is to be of any interest at all to the majority of those to whom it is addressed, must necessarily be boring to some of them. It is therefore with this explanation that I am trying to put before you results which are not in any sense new, which are, indeed, the stock-in-trade of the present-day analyst, and therefore well known to many here, but which may interest some whose studies have not lain in this particular direction.
The Normal Law of Error
Authors: Jackson C. S.
Published: January 2007

The investigations of Professor Karl Pearson and his coadjutors on the applications of the theory of errors to statistics have greatly increased the importance and extent of the subject.

It is hoped that the following version of one of the methods of arriving at the so-called normal law of error may be of interest from an elementary point of view: affording, as it does, a simple application of the binomial theorem and some interesting graphical work.
Greek Mathematics and Science
Authors: Heath T. L.
Published: January 2007

It is, I think, of happy augury that it should have been found possible to arrange a joint meeting of members of the local branches of the Classical and Mathematical Associations, as well as members of the Yorkshire Natural Science Association, to hear a few words about Greek science. No doubt the classical or humane studies can stand by- themselves and so (in a way) can the study of science based only on good English: but I venture to think that they are both much stronger when they stand side by side and support one another. The idea that there is any necessary antagonism or opposition of interests between them is surely unfounded, and there is room for both in our system of education. It is a mistake to suppose that in our school education there is not time for the one or the other; the question is really one of using the time that there is to the best advantage. No doubt schoolboys in the past have wasted much time in the perfunctory learning of Latin and Greek. It has often been remarked that, while a boy was more or less continuously learning Latin and Greek from the age of nine or ten till he went to the University, a girl who only began Latin and Greek at, say, fifteen or sixteen managed to catch up the boy and take a place alongside him in Part I. of the Classical Tripos. It was therefore probably the inefficient or uninteresting way in which the boy used to be taught Greek and Latin that caused the waste of time. If the subjects were made sufficiently attractive and the bogey of compulsion were removed, there is no reason why the boy of good ability should not during his school years acquire a good working knowledge of both classics and science, as well as of the indispensable amount of modern languages. And, if the boy’s interest can be aroused sufficiently to make him take kindly to Greek and Latin on the one side and mathematics and science on the other, I am clear that each branch will help the other and be better done.
Cajori’s History of Mathematics
Authors: Halsted George Bruce
Published: January 2007

The extraordinary development, ramification, and specialisation which our generation sees in all science, but especially in the queen of sciences, mathematics, makes imperative a determined attempt to keep connected these new and growing fields.
Modern Examination Tendency
Authors: Williamson R.S.
Published: January 2007

(1) The institution of Local Education Authorities in 1902. These Authorities have been able to survey over a wide range of Secondary Schools the working of the examination system and to estimate to some extent its effects on Secondary Education as a whole. Consequent on this, but not wholly the result of it, came some general reforms, e.g. the formation of the Secondary Schools Examination Council. But L.E.A.’s are also involved in the examination system as examiners, since they test candidates for scholarships and free places in Secondary Schools. Their examination view-point is therefore a wide one, embracing that of both teacher and examiner. The full effect of this dual point of view has not yet matured, but some innovations or improvements in junior scholarship examinations have already resulted from it; for instance, the development of the oral examination and the use of the teacher’s assessment of a pupil. In some areas, too, teachers participate in marking scripts. Examinations of School Certificate standard are so far little affected, but it would be in accord with the trend of events if the wide powers of University Examining Authorities were further modified and the school record of the candidate made to play a more important part in the examination than at present.
Approximate Evaluation of ∫ are sin F(t) dt
Authors: Naylor V.
Published: January 2007

There are not many integrals of the type ∫ arc sin F(t) dt whose values can be expressed in terms of functions already defined. Nor is the inverse sine function allowed to play its free part in suggesting what new functions are necessary for the evaluation of integrals. The moment an inverse sine appears in an integral, the integrand is transformed into one involving the direct function.
The Aim and Methods of School Algebra
Authors: Nunn T. P.
Published: January 2007

§ 1. The rhythm, of mathematical progress. To the question how the aim described in the preceding lecture is to be realised, the whole of the rest of the course is proffered as an answer. Here, it, will be sufficient to summarise the main features of the. methods which are later to be given in detail.

The professed aim is to make school mathematics a reproduction, as faithful as the difference of the situations permits, of the mathematical activities of the great world. The method must, then, be based upon an analysis of the general course of development which these activities display. Remembering, as before, that this kind of analysis always introduces an artificial simplicity into a naturally complicated matter, we may yet lay it down that mathematics advances by the constant repetition of a normal cycle of progress—a cycle in which three typical phases may be distinguished. In the first, the heuristic phase, the mathematician, face to face with a new type of problem, devises a new notation or mathematical method to deal with it. In the second, the formal phase, the new notation or method is studied apart from the immediate needs of practical application. The conditions and the range of its validity are investigated, its wider possibilities are explored, and its relation to other methods examined. In the third, the application phase, the extended notation or the perfected method becomes once more an instrument for the solution of problems, and is found to be applicable successfully over a field often many times wider than the area in which it originated. Any one of these problems may, in turn, become’ the starting point of a new cycle.
The Teaching of Mathematics to Textile Students
Authors: Whitwam J. H.
Published: January 2007

Before commencing his purely Textile Course, the student has had, at least, a two years’ course consisting of Practical Mathematics and Drawing, English, and Laboratory Work in Mechanics and Physics. The syllabus for Mathematics includes: Mensuration of the rectangle, parallelogram, triangle and oircle; surface areas and volumes of the cylinder, cone and sphere; measurements are made from everyday objects and models, and symbolical representation of the results leads to formulae and substitution of numbers in these formulae. From this we pass to simple equations. Squared paper is used to plot results of measurements made (either in the Mathematics lessons or the Laboratory), such as comparing:—circumferences and diameters of circles; areas of triangles of equal altitudes and different bases; extensions and loads for a spring; corresponding readings of temperatures in C.° and F.°, and from these we pass to proportionality, or variation. Powers and roots are dealt with, and the use of Logarithms taught. The Drawing, which is taught alongside the Mathematics, consists of: Hand-sketches, plans, elevations and sections of models and parts of machinery used by the students.
The Manchester University Summer School of Mathematics at Bangor
Authors: Chapman S.
Published: January 2007

The desirability of affording facilities, to mathematical teachers and others, for post-graduate studies in mathematics during the summer vacation, was commented on by the writer in an article in the March, issue of this Gazette. It was there proposed that a “Summer School” should be organized for this purpose by teachers themselves, acting through the Mathematical Association, and after the publication of the article the suggestion was more formally communicated to the Association through the Manchester branch. It proved to be unlikely, however, that the matter could be taken up by the representative body, whose members met rather infrequently, and who were already fully occupied in other business of the Association, in sufficient time to make arrangements for such a School during the present year. The proposal was therefore brought before the Extra-Mural Committee of the University of Manchester, who agreed to the experiment being made under their auspices, and voted a grant for organizing and advertising the project. The Board of Education were next approached, and they agreed to recognize the School and to make a limited grant to cover a possible deficit on the cost of working it. Provisional arrangements were proceeded with meanwhile, and in April and the early part of May circulars announcing the School and inviting students to register were distributed to the heads of the mathematical departments of nearly every secondary, grammar and high school, and many technical schools and colleges, throughout England and Wales. The School was also advertised in various educational journals. The response was satisfactory, thirty-two students being registered, whereas twenty was the number decided upon as the minimum required if the School was to be held.
A School Course in Surveying
Authors: Vernon H. R.
Published: January 2007

The Course described here has been evolved at Northallerton Grammar School during the past nine years. The field-work and plan-drawing are done during Geography lessons, while the calculation of area, height finding and resection are undertaken by the mathematics classes. Many mathematical ideas are involved throughout the Course, which acts as a connecting link between the two subjects. The ages given are only approximate.
The Differentiation of a Function of a Function
Authors: Carslaw H. S.
Published: January 2007

If z is a function of y having a differential coefficient at a certain point, and y is a function of x having a differential coefficient at the corresponding point, then z is a function of x having a differential coefficient at that point, and this differential coefficient is given by the formula

This theorem, thought not always stated so carefully, will be found in all texts on the calculus; but, so far as I am aware, no English writer, not even the most exact, offers a valid proof.
A Study of the Life and Writings of Colin Maclaurin
Authors: Tweedie Charles
Published: January 2007

Colin Maclaurin was one of the most distinguished of the brilliant coterie of Scottish mathematicians that marked the course of the eighteenth century. He was born at Kilmodan in Glendaruel, Argyleshire, in February, 1698, and was the youngest of a family of three sons. His father, John Maclaurin, who was minister of the parish and a man of mark in his day, died when Colin was but six weeks old. His mother, after residing for some time in Argyleshire, removed to Dumbarton, and died in 1707 when Colin was nine years of age. The orphans were taken in charge by their uncle, Daniel Maclaurin, minister of Kilfinnan, who faithfully discharged his duty to them.
The Simple Pendulum
Authors: Picken D. K.
Published: January 2007

The current elementary discussion of the Simple Pendulum is unsatisfactory, in that the problem is not reduced with sufficient directness to a case of S.H.M. It has to be artificially prefaced by consideration of a curvilinear motion in which the tangential resolute of the acceleration is proportional in magnitude to the arcual distance from a point of the path; and the discussion of this motion raises new points of difficulty altogether out of proportion to its significance in this connection. The net result is that the student’s appreciation of this first of the important applications of S.H.M. to “small oscillations” is lost, in dismay at finding that, even after he has mastered the essential difficulties of the S.H.M. itself, the first good application of it brings yet another awkward hurdle. And the physicist or engineer may well make this another case for railing impatiently at the devices for “dodging the Calculus” by which elementary theory is so apt to be obscured. Nevertheless, the teacher of Mathematics knows how important it is to postpone such Calculus difficulties as, e.g., to pave the way to the complete primitive of the S.H.M. differential equation and its uses (one of which gives the only clear-cut way of handling the ordinary discussion of the Simple Pendulum). But the postponement must not be obtained at the disproportionate cost of artificial complications which, for the sake of “elementary” treatment, cast a fog round the important features of the argument, without contributing anything of independent value to the student’s store of knowledge.
On Two fragments of Geometrical Treatises Found in Worcester Cathedral Library
Authors: Wilson J. M.
Published: January 2007

I believe I am the only surviving original-member of that A.I.G.T., to which the President bas referred (The Association for the Improvement of Geometrical Teaching). This Association arose out of a book which I wrote at Dr. Temple’s (the late Archbishop of Canterbury’s) suggestion, after the Commission of Inquiry into Secondary Education (the Endowed Schools Commission), that some new method, simpler than Euclid, should be brought into our geometrical teaching. It was very desirable that there should not be competition between private individual writers of text-books competing for public approval and public use, and so we formed the Association in order to unify the teaching on the new lines.
Notes on the Radix Method of Calculating Logarithms
Authors: Lupton Sydney
Published: January 2007

It occasionally happens that logarithms and anti-logarithms are required to many figures, and in default of tables must be calculated. If a series of such logarithms are required, they are probably most easily obtained by interpolation between nntnbers, the logarithms of which have been calculated to many figures by Briggs, Gardiner, Sharp and others.

If only a few values aro required, this method is practically inapplicable, since it is tedious and requires somewhat large tables. Many ingenious methods have been suggested to meet such cases, but in general they necessitate special artifices and tables, which require considerable practice to use with safety.
Extension of Huygens’ Approximation to a Circular arc
Authors: Milne E. M.
Published: January 2007

Huygens’ approximation to the length of a circular arc is , where l0 is the chord of the arc and l1 is the chord of half the arc. This result is most easily obtained from the series for sin and sin by neglecting powers of beyond the third, L being the true length of the arc and R the radius of the circle. For arcs less than 45° Huygens’ rule is very accurate, the error for an arc of 30° being less than 1 in 300,000.
Parametric Equations in Elementary Analytical Geometry
Authors: Robson A.
Published: January 2007

Mathematical students are usually familiar with the parametric coordinates (at2, 2at) of a point on a parabola, and with the eccentric-angle coordinates of a point on an ellipse, and with similar coordinates for a hyperbola. Such coordinates are probably welcomed by the student just because they reduce by one the number of letters and the number of equations with which he has to deal.

If at2 is substituted for x1, and 2at for y1, but everything else is done in just the same way as before, parametric methods are not really being used. Parametric equations are something more than convenient coordinates.
Logarithms by Interpolation
Authors: Gibbins N. M.
Published: January 2007

The method of introducing logarithms given in the Algebra Report consists in taking the powers of 1·1, which are easily calculated and are so closely packed that common logarithms can be deduced by proportional parts correct to three decimal places. It forms an interesting set of lessons for post-certificate pupils to discuss why this is so, and to extend the method with a view to obtaining greater accuracy Furthermore, one of the most important principles in pure mathematics is amply illustrated—that of sandwiching a function between two bounds. It is assumed that the expansion of loge(l + x) is known by the pupils and also its differential coefficient.