«Жизнь и письма Льюиса Кэрролла (преподобного Ч. Л. Доджсона)»

Двое мужчин некоторое время советуются вместе, а затем Радамант удаляется, и Минос засыпает. Вслед за этим появляется Призрак Евклида и обсуждает с Миносом причины сохранения его Руководства в целом, в его нынешнем порядке и расположении. Поскольку они в основном озабочены потребностями начинающих, их внимание ограничено Книгами I и II.

Мы должны довольствоваться одним коротким отрывком из диалога:

Euclid.—It is, I think, a friend of yours who has amused himself by tabulating the various Theorems which might be enunciated on the single subject of Pairs of Lines. How many did he make them out to be?

Minos.—About two hundred and fifty, I believe.

Euclid.—At that rate there would probably be within the limit of my First Book—how many?

Minos.—A thousand at least.

Euclid.—What a popular school-book it will be! How boys will bless the name of the writer who first brings out the complete thousand!

С целью обсуждения и критики своих различных современных соперников Евклид обещает прислать Миносу призрак немецкого профессора (герра Ниманда), который «прочитал все книги и готов защищать любой тезис, истинный или ложный».

«Очаровательный компаньон!» — как сухо замечает Минос.

Это приводит нас к Акту II, в котором Руководства, отвергающие трактовку параллельных линий Евклидом, рассматриваются одно за другим. Те Руководства, которые принимают ее, зарезервированы для Акта III, Сцены i.; в то время как в Сцене ii. рассматриваются «Программа Ассоциации по улучшению геометрического преподавания» и «Программа» Уилсона.

Нужно привести только один или два отрывка, которые, как ожидается, будут достаточны для иллюстрации характера и стиля книги:

Акт II, Сцена v. — Ниманд и Минос спорят за и против «Элементарной геометрии» Хенричи.

Minos.—I haven't quite done with points yet. I find an assertion that they never jump. Do you think that arises from their having "position," which they feel might be compromised by such conduct?

Niemand.—I cannot tell without hearing the passage read.

Minos.—It is this: "A point, in changing its position on a curve, passes in moving from one position to another through all intermediate positions. It does not move by jumps."

Niemand.—That is quite true.

Minos.—Tell me then—is every centre of gravity a point?

Niemand.—Certainly.

Minos.—Let us now consider the centre of gravity of a flea. Does it—

Niemand (indignantly).—Another word, and I shall vanish! I cannot waste a night on such trivialities.

Minos.—I can't resist giving you just one more tit-bit—the definition of a square at page 123: "A quadrilateral which is a kite, a symmetrical trapezium, and a parallelogram is a square!" And now, farewell, Henrici: "Euclid, with all thy faults, I love thee still!"

Снова, из Акта II, Сцены vi.:

Niemand.—He (Pierce, another "Modern Rival,") has a definition of direction which will, I think, be new to you. (Reads.)

"The direction of a line in any part is the direction of a point at that part from the next preceding point of the line!"

Minos.—That sounds mysterious. Which way along a line are "preceding" points to be found?

Niemand.—Both ways. He adds, directly afterwards, "A line has two different directions," &c.

Minos.—So your definition needs a postscript.... But there is yet another difficulty. How far from a point is the "next" point?

Niemand.—At an infinitely small distance, of course. You will find the matter fully discussed in my work on the Infinitesimal Calculus.

Minos.—A most satisfactory answer for a teacher to make to a pupil just beginning Geometry!

В Акте IV Евклид снова появляется перед Миносом, «в сопровождении призраков Архимеда, Пифагора и т. д., которые пришли посмотреть на честную игру». Евклид так подводит итог своему делу:

"'The cock doth craw, the day doth daw,' and all respectable ghosts ought to be going home. Let me carry with me the hope that I have convinced you of the necessity of retaining my order and numbering, and my method of treating Straight Lines, Angles, Right Angles, and (most especially) Parallels. Leave me these untouched, and I shall look on with great contentment while other changes are made—while my proofs are abridged and improved—while alternative proofs are appended to mine—and while new Problems and Theorems are interpolated. In all these matters my Manual is capable of almost unlimited improvement."

В Приложениях I и II мистер Доджсон цитирует мнения двух выдающихся учителей математики, мистера Тодхантера и профессора Де Моргана, в поддержку своего аргумента.

Прежде чем оставить эту тему, я хотел бы упомянуть об очень новом использовании книги мистера Доджсона — ее применении в школе. Мистер Г. Хопкинс, преподаватель математики в Высшей школе в Манчестере, США, и сам автор «Руководства по планиметрии», использовал ее таким образом в классе мальчиков в возрасте от четырнадцати или пятнадцати лет и старше. Сначала он обратил их внимание на некоторые из наиболее заметных трудностей, связанных с вопросом о параллельных линиях, вложил в их руки экземпляр Евклида и позволил им увидеть его трактовку, а после некоторого обсуждения представил им «Евклида и его современных соперников» и «Новую теорию параллельных линий» мистера Доджсона.

Возможно, дело в том, что американские мальчики сообразительнее английских, но, во всяком случае, сообщается, что юноши прочитали обе книги с таким усердием и настойчивостью, которые были столь же приятны их инструктору, сколь и лестны для мистера Доджсона.

В июне того же года запись в дневнике относится к предложению в Конвокации разрешить Университетскому клубу иметь площадку для крикета в Парках. Это было предложено в 1867 году, а затем отклонено. Мистер Доджсон разослал в общие комнаты копии поэмы «Покинутые парки», которая была опубликована братьями Паркер в 1867 году и которая впоследствии была включена в «Заметки оксфордского чила». Я цитирую первые несколько строк:

Museum! loveliest building of the plain

Where Cherwell winds towards the distant main;

How often have I loitered o'er thy green,

Where humble happiness endeared the scene!

How often have I paused on every charm,—

The rustic couple walking arm in arm,

The groups of trees, with seats beneath the shade

For prattling babes and whisp'ring lovers made,

The never-failing brawl, the busy mill,

Where tiny urchins vied in fistic skill.

(Two phrases only have that dusky race

Caught from the learned influence of the place;

Phrases in their simplicity sublime,

"Scramble a copper!" "Please, sir, what's the time?")

These round thy walks their cheerful influence shed;

These were thy charms—but all these charms are fled,

Amidst thy bowers the tyrant's hand is seen,

And rude pavilions sadden all thy green;

One selfish pastime grasps the whole domain,

And half a faction swallows up the plain;

Adown thy glades, all sacrificed to cricket,

The hollow-sounding bat now guards the wicket;

Sunk are thy mounds in shapeless level all,

Lest aught impede the swiftly rolling ball;

And trembling, shrinking from the fatal blow,

Far, far away thy hapless children go.

Ill fares the place, to luxury a prey,

Where wealth accumulates, and minds decay:

Athletic sports may flourish or may fade,

Fashion may make them, even as it has made;

But the broad Parks, the city's joy and pride,

When once destroyed can never be supplied!

Читатели «Сильви и Бруно» вспомнят, как невидимые дети-феи спасают пьяницу от его злой жизни, и я всегда чувствовал, что мистер Доджсон хотел, чтобы Сильви была чем-то большим, чем фея — своего рода ангелом-хранителем. Что такая идея не была бы несовместимой с его взглядом на вещи, показывает следующее письмо:

Ch. Ch., July, 1879.

My dear Ethel,—I have been long intending to answer your letter of April 11th, chiefly as to your question in reference to Mrs. N—'s letter about the little S—s [whose mother had recently died]. You say you don't see "how they can be guided aright by their dead mother, or how light can come from her." Many people believe that our friends in the other world can and do influence us in some way, and perhaps even "guide" us and give us light to show us our duty. My own feeling is, it may be so: but nothing has been revealed about it. That the angels do so is revealed, and we may feel sure of that; and there is a beautiful fancy (for I don't think one can call it more) that "a mother who has died leaving a child behind her in this world, is allowed to be a sort of guardian angel to that child." Perhaps Mrs. N— believes that.

Вот две другие записи в дневнике:

Aug. 26th.—Worked from about 9.45 to 6.45, and again from 10.15 to 11.45 (making 101/2 hours altogether) at an idea which occurred to me of finding limits for pi by elementary trigonometry, for the benefit of the circle-squarers.

Dec. 12th.—Invented a new way of working one word into another. I think of calling the puzzle "syzygies."

I give the first three specimens:— ЧЕЛОВЕК } постоянный } соблазнять } Пошли ЧЕЛОВЕКА на ЛЕД. ЛЕД. } АКР } священный } учетные данные } ПОЛАГАЙСЯ на АКР. полностью } ПОЛАГАЙСЯ } ПРИЗМА } призматический } драматический } Докажи, что ПРИЗМА ОТВРАТИТЕЛЬНА. мелодрама } мелодичный } ОТВРАТИТЕЛЬНА. }

В феврале 1880 года мистер Доджсон предложил «Совету по зарплатам персонала» Крайст-Черч, что, поскольку его преподавательская работа легче, он должен получать 200 фунтов стерлингов вместо 300 фунтов стерлингов в год. Не часто человек предлагает сократить свою собственную зарплату, но предложение в этом случае было направлено на то, чтобы помочь руководству колледжа в политике сокращения расходов, которую они пытались проводить.

May 24th.—Percival, President of Trin. Coll., who has Cardinal Newman as his guest, wrote to say that the Cardinal would sit for a photo, to me, at Trinity. But I could not take my photography there and he couldn't come to me: so nothing came of it.

Aug. 19th. [At Eastbourne].—Took Ruth and Maud to the Circus (Hutchinson and Tayleure's—from America). I made friends with Mr. Tayleure, who took me to the tents of horses, and the caravan he lived in. And I added to my theatrical experiences by a chat with a couple of circus children—Ada Costello, aged 9, and Polly (Evans, I think), aged 13. I found Ada in the outer tent, with the pony on which she was to perform—practising vaulting on to it, varied with somersaults on the ground. I showed her my wire puzzle, and ultimately gave it her, promising a duplicate to Polly. Both children seemed bright and happy, and they had pleasant manners.

Sept. 2nd.—Mrs. H— took me to Dr. Bell's (the old homoeopathic doctor) to hear Lord Radstock speak about "training children." It was a curious affair. First a very long hymn; then two very long extempore prayers (not by Lord R—), which were strangely self-sufficient and wanting in reverence. Lord R—'s remarks were commonplace enough, though some of his theories were new, but, I think, not true—e.g., that encouraging emulation in schoolboys, or desiring that they should make a good position in life, was un-Christian. I escaped at the first opportunity after his speech, and went down on the beach, where I made acquaintance with a family who were banking up with sand the feet and legs of a pretty little girl perched on a sand-castle. I got her father to make her stand to be drawn. Further along the beach a merry little mite began pelting me with sand; so I drew her too.

Nov. 16th.—Thought of a plan for simplifying money-orders, by making the sender fill up two duplicate papers, one of which he hands in to be transmitted by the postmaster—it containing a key—number which the receiver has to supply in his copy to get the money. I think of suggesting this, and my plan for double postage on Sunday, to the Government.

Dec. 19th.—The idea occurred to me that a game might be made of letters, to be moved about on a chess-board till they form words.

Небольшая книга, опубликованная в этом году, «Алиса (драматическая версия "Алисы" Льюиса Кэрролла) и другие сказки для детей» миссис Фрейлиграт-Крокер, была очень успешной и, я понимаю, до сих пор имеет регулярные продажи. Мистер Доджсон с радостью дал свое согласие на драматизацию своей истории столь талантливой писательницей, и вскоре после этого миссис Крокер выпустила «Алису в Зазеркалье» в аналогичной форме.

Jan. 17, 1881.—To the Lyceum to see "The Cup" and "The Corsican Brothers." The first is exquisitely put on, and Ellen Terry as Camma is the perfection of grace, and Irving as the villain, and Mr. Terriss as the husband, were very good. But the piece wants substance.

Jan. 19th.—Tried to go to Oxford, but the line is blocked near Didcot, so stayed another night in town. The next afternoon the line was reported clear, but the journey took 5 hours! On the day before the Dean of Ch. Ch. and his family were snowed up for 21 hours near Radley.

March 27th.—Went to S. Mary's and stayed for Holy Communion, and, as Ffoulkes was alone, I mustered up courage to help him. I read the exhortation, and was pleased to find I did not once hesitate. I think I must try preaching again soon, as he has often begged me to do.

April 16th.—Mr. Greenwood approves my theory about general elections, and wants me to write on it in the St. James's Gazette. (The letter appeared on May 5, 1881.)

May 14th.—Took the longest walk (I believe) I have ever done—round by Dorchester, Didcot and Abingdon—27 miles—took 8 hours—no blisters, I rejoice to find, and I feel very little tired.

May 26th.—The row-loving men in College are beginning to be troublesome again, and last night some 30 or 40 of them, aided by out-College men, made a great disturbance, and regularly defied the Censors. I have just been with the other Tutors into Hall, and heard the Dean make an excellent speech to the House. Some two or three will have to go down, and twelve or fifteen others will be punished in various ways. (A later note says): The punishments had to be modified—it turned out that the disturbers were nearly all out-College men.

Мистер Доджсон отправил письмо в «Обсервер» по этому поводу:

Sir,—Your paper of May 29th contains a leading article on Christ Church, resting on so many mis-statements of fact that I venture to appeal to your sense of justice to allow me, if no abler writer has addressed you on the subject, an opportunity of correcting them. It will, I think, be found that in so doing I shall have removed the whole foundation on which the writer has based his attack on the House, after which I may contentedly leave the superstructure to take care of itself. "Christ Church is always provoking the adverse criticism of the outer world." The writer justifies this rather broad generalisation by quoting three instances of such provocation, which I will take one by one.

At one time we are told that "The Dean ... neglects his functions, and spends the bulk of his time in Madeira." The fact is that the Dean's absence from England more than twenty years ago during two successive winters was a sad necessity, caused by the appearance of symptoms of grave disease, from which he has now, under God's blessing, perfectly recovered.

The second instance occurred eleven years ago, when some of the undergraduates destroyed some valuable statuary in the Library. Here the writer states that the Dean first announced that criminal proceedings would be taken, and then, on discovering that the offenders were "highly connected," found himself "converted to the opinion that mercy is preferable to stern justice, and charity to the strict letter of the law." The facts are that the punishment awarded to the offenders was deliberated on and determined on by the Governing Body, consisting of the Dean, the Canons, and some twenty Senior Students; that their deliberations were most assuredly in no way affected by any thoughts of the offenders being "highly connected"; and that, when all was over, we had the satisfaction of seeing ourselves roundly abused in the papers on both sides, and charged with having been too lenient, and also with having been too severe.

The third instance occurred the other night. Some undergraduates were making a disturbance, and the Junior Censor "made his appearance in person upon the scene of riot," and "was contumeliously handled." Here the only statement of any real importance, the alleged assault by Christ Church men on the Junior Censor, is untrue. The fact is that nearly all the disturbers were out-College men, and, though it is true that the Censor was struck by a stone thrown from a window, the unenviable distinction of having thrown it belongs to no member of the House. I doubt if we have one single man here who would be capable of so base and cowardly an act.

The writer then gives us a curious account of the present constitution of the House. The Dean, whom he calls "the right reverend gentleman," is, "in a kind of way, master of the College. The Canons, in a vague kind of way, are supposed to control the College." The Senior Students "dare not call their souls their own," and yet somehow dare "to vent their wrath" on the Junior Students. His hazy, mental picture of the position of the Canons may be cleared up by explaining to him that the "control" they exercise is neither more nor less than that of any other six members of the Governing Body. The description of the Students I pass over as not admitting any appeal to actual facts.

The truth is that Christ Church stands convicted of two unpardonable crimes—being great, and having a name. Such a place must always expect to find itself "a wide mark for scorn and jeers"—a target where the little and the nameless may display their skill. Only the other day an M.P., rising to ask a question about Westminster School, went on to speak of Christ Church, and wound up with a fierce attack on the ancient House. Shall we blame him? Do we blame the wanton schoolboy, with a pebble in his hand, all powerless to resist the alluring vastness of a barndoor?

The essence of the article seems to be summed up in the following sentence: "At Christ Church all attempts to preserve order by the usual means have hitherto proved uniformly unsuccessful, and apparently remain equally fruitless." It is hard for one who, like myself, has lived here most of his life, to believe that this is seriously intended as a description of the place. However, as general statements can only be met by general statements, permit me, as one who has lived here for thirty years and has taught for five-and-twenty, to say that in my experience order has been the rule, disorder the rare exception, and that, if the writer of your leading article has had an equal amount of experience in any similar place of education, and has found a set of young men more gentlemanly, more orderly, and more pleasant in every way to deal with, than I have found here, I cannot but think him an exceptionally favoured mortal.—Yours, &c.

Charles l. Dodgson,

Student and Mathematical Lecturer of Christ Church.

В июле началась забавная переписка между мистером Доджсоном и «квадратором круга», которая длилась несколько месяцев. Мистер Доджсон отправил увлеченному человеку, которого мы назовем мистером Б—, доказательство того, что площадь круга меньше 3,15 квадрата радиуса. Мистер Б— ответил: «Ваше доказательство не соответствует Евклиду, оно предполагает, что круг можно рассматривать как прямоугольник и что две прямые линии могут ограничивать пространство». Он вернул доказательство, сказав, что не может принять ничего из него как разъяснение точной площади круга или как евклидово. Поскольку метод мистера Доджсона предполагал небольшое знание тригонометрии, а у него были основания подозревать, что мистер Б— совершенно невежественен в этом предмете, он счел нужным подвергнуть его испытанию, задав ему несколько вопросов по нему, но квадратор круга, с похвальной осторожностью, отказался обсуждать что-либо неевклидово. Затем мистер Доджсон написал ему, «прощаясь с этой темой, пока он не пожелает расширить свою область знаний до элементов алгебраической геометрии». Мистер Б— ответил с нескрываемым презрением: «Алгебраическая геометрия — это все лунный свет». Он предпочитал «взвешивание картона» как средство установления точной истины в математических исследованиях. Наконец, он предположил, что мистер Доджсон, возможно, захочет принять участие в призовом конкурсе, который будет организован среди последователей Евклида, и, поскольку он, по-видимому, хотел, чтобы тот понял, что он (мистер Б—) невысокого мнения о его шансах на получение приза, мистер Доджсон счел, что психологический момент для прекращения переписки настал.

Тем временем он начал чувствовать, что его регулярные обязанности в колледже — ужасная помеха для его литературной работы. Стипендия, которую он получал, не предназначалась для того, чтобы привязывать его к лекциям и экзаменам. Такая работа была очень хороша для более молодого человека; он мог лучше всего служить «Дому» своей литературной славой.

July 14th.—Came to a more definite decision than I have ever yet done—that it is about time to resign the Mathematical Lectureship. My chief motive for holding on has been to provide money for others (for myself, I have been many years able to retire), but even the £300 a year I shall thus lose I may fairly hope to make by the additional time I shall have for book-writing. I think of asking the G.B. (Governing Body) next term to appoint my successor, so that I may retire at the end of the year, when I shall be close on fifty years old, and shall have held the Lectureship for exactly 26 years. (I had the Honourmen for the last two terms of 1855, but was not full Lecturer till Hilary, 1856.)

Oct. 18th.—I have just taken an important step in life, by sending to the Dean a proposal to resign the Mathematical Lectureship at the end of this year. I shall now have my whole time at my own disposal, and, if God gives me life and continued health and strength, may hope, before my powers fail, to do some worthy work in writing—partly in the cause of mathematical education, partly in the cause of innocent recreation for children, and partly, I hope (though so utterly unworthy of being allowed to take up such work) in the cause of religious thought. May God bless the new form of life that lies before me, that I may use it according to His holy will!

Oct. 21st.—I had a note in the evening from the Dean, to say that he had seen the Censors on the subject of my proposed resignation at the end of the year, and that arrangements should be made, as far as could be done, to carry out my wishes; and kindly adding an expression of regret at losing my services, but allowing that I had "earned a right to retirement." So my Lectureship seems to be near its end.

Nov. 30th.—I find by my Journal that I gave my first Euclid Lecture in the Lecture-room on Monday, January 28, 1856. It consisted of twelve men, of whom nine attended. This morning, I have given what is most probably my last: the lecture is now reduced to nine, of whom all attended on Monday: this morning being a Saint's Day, the attendance was voluntary, and only two appeared—E.H. Morris, and G. Lavie. I was Lecturer when the father of the latter took his degree, viz., in 1858.

There is a sadness in coming to the end of anything in life. Man's instincts cling to the Life that will never end.

May 30, 1882.—Called on Mrs. R—. During a good part of the evening I read The Times, while the party played a round game of spelling words—a thing I will never join in. Rational conversation and good music are the only things which, to me, seem worth the meeting for, for grown-up people.

June 1st.—Went out with Charsley, and did four miles on one of his velocimans, very pleasantly.

Велосиман был ранней и несколько громоздкой формой трехколесного велосипеда; мистер Доджсон сделал много предложений по его улучшению. Однако он никогда не пытался ездить на двухколесном велосипеде, но, в соответствии со своим собственным изречением: «В молодости попробуй велосипед, в старости купи трехколесный», ограничился трехколесной разновидностью.

Nov. 8th.—Whitehead, of Trinity, told us a charming story in Common Room of a father and son. They came up together: the son got into a College—the father had to go to New Inn Hall: the son passed Responsions, while his father had to put off: finally, the father failed in Mods and has gone down: the son will probably take his degree, and may then be able to prepare his father for another try.

Among the coloured cartoons in Shrimpton's window at Oxford there used to be, when I was up, a picture which I think referred to this story.

OXFORD TYPES.

From a photograph

by A.T. Shrimpton..

Nov. 23rd.—Spent two hours "invigilating" in the rooms of W.J. Grant (who has broken his collar-bone, and is allowed to do his Greats papers in this way) while he dictated his answers to another undergraduate, Pakenham, who acted as scribe.

Nov. 24th.—Dined with Fowler (now President of C.C.C.) in hall, to meet Ranken. Both men are now mostly bald, with quite grey hair: yet how short a time it seems since we were undergraduates together at Whitby! (in 1854).

Dec 8th.—A Common Room Meeting. Fresh powers were given to the Wine Committee, and then a new Curator elected. I was proposed by Holland, and seconded by Harcourt, and accepted office with no light heart: there will be much trouble and thought needed to work it satisfactorily, but it will take me out of myself a little, and so may be a real good—my life was tending to become too much that of a selfish recluse.

В течение этого года он сочинил слова песни «Страна грез». Мелодия была вымечтана его другом, покойным преподобным Ч. Э. Хатчинсоном из Чичестера. История сна приводится здесь словами мечтателя:

I found myself seated, with many others, in darkness, in a large amphitheatre. Deep stillness prevailed. A kind of hushed expectancy was upon us. We sat awaiting I know not what. Before us hung a vast and dark curtain, and between it and us was a kind of stage. Suddenly an intense wish seized me to look upon the forms of some of the heroes of past days. I cannot say whom in particular I longed to behold, but, even as I wished, a faint light flickered over the stage, and I was aware of a silent procession of figures moving from right to left across the platform in front of me. As each figure approached the left-hand corner it turned and gazed at me, and I knew (by what means I cannot say) its name. One only I recall—Saint George; the light shone with a peculiar blueish lustre on his shield and helmet as he turned and slowly faced me. The figures were shadowy, and floated like mist before me; as each one disappeared an invisible choir behind the curtain sang the "Dream music." I awoke with the melody ringing in my ears, and the words of the last line complete—"I see the shadows falling, and slowly pass away." The rest I could not recall.

DREAMLAND.

Words by LEWIS CARROLL.

Music by C.E. HUTCHINSON.

When midnight mists are creeping

And all the land is sleeping

Around me tread the mighty dead,

And slowly pass away.

Lo, warriors, saints, and sages,

From out the vanished ages,

With solemn pace and reverend face

Appear and pass away.

The blaze of noonday splendour,

The twilight soft and tender,

May charm the eye: yet they shall die,

Shall die and pass away

But here, in Dreamland's centre,

No spoiler's hand may enter,

These visions fair, this radiance rare,

Shall never pass away

I see the shadows falling,

The forms of eld recalling;

Around me tread the mighty dead,

And slowly pass away

Одной из лучших услуг образованию, которую оказал мистер Доджсон, было его издание «Евклида I и II», которое было опубликовано в 1882 году. В написании «Евклида и его современных соперников» он довольно сурово критиковал различные замены, предложенные для Евклида, насколько они касались начинающих; но в то же время он признавал, что в установленных пределах текст Евклида способен к поправкам и улучшениям, и это то, что он попытался сделать в этой книге. Что он был полностью оправдан, показывает тот факт, что в течение 1882—1889 годов книга выдержала восемь изданий. Во введении он перечисляет под тремя заголовками «Дополнения», «Пропуски» и «Изменения» основные пункты различия между своими собственными и обычными изданиями Евклида, с его причинами для их принятия. Они являются результатом долгого опыта, и самые консервативные учителя легко приняли бы их.

Доказательство I. 24, например, определенно лучше и удовлетворительнее, чем обычное доказательство, и введение определения «проекции» определенно упрощает громоздкие формулировки II. 12 и 13. Опять же, альтернативное доказательство II. 8, предложенное во введении, ценно и снимает всякое оправдание для пропуска этого предложения, как это обычно делается.

Использованные фигуры взяты из блоков, подготовленных для известного издания Евклида покойного мистера Тодхантера, к которому руководство мистера Доджсона является отличной ступенькой.

В начале 1883 года он отправился в город, чтобы увидеть коллекцию картин Д. Г. Россетти в галерее Берлингтон. Он был особенно поражен картиной «Найдена», которую он описывает так:

A picture of a man finding, in the streets of London, a girl he had loved years before in the days of her innocence. She is huddled up against the wall, dressed in gaudy colours, and trying to turn away her agonised face, while he, holding her wrists, is looking down with an expression of pain and pity, condemnation and love, which is one of the most marvellous things I have ever seen done in painting.

Jan. 27, 1883 [His birthday].—I cannot say I feel much older at 51 than at 21! Had my first "tasting-luncheon"; it seemed to give great satisfaction. [The object of the Curator's "tasting-luncheon" was, of course, to give members of Common Room an opportunity of deciding what wines should be bought.]

March 15th.—Went up to town to fulfil my promise to Lucy A.—: to take her for her first visit to the theatre. We got to the Lyceum in good time, and the play was capitally acted. I had hinted to Beatrice (Miss Ellen Terry) how much she could add to Lucy's pleasure by sending round a "carte" of herself; she sent a cabinet. She is certainly an adept in giving gifts that gratify.

April 23d.—Tried another long walk—22 miles, to Besilsleigh, Fyfield, Kingston, Bagpuize, Frilford, Marcham, and Abingdon. The last half of the way was in the face of wind, rain, snow, and hail. Was too lame to go into Hall.

ГЛАВА VI

(1883—1887)

"The Profits of Authorship"—"Rhyme? and Reason?"—The Common Room Cat—Visit to Jersey—Purity of elections—Parliamentary Representation—Various literary projects—Letters to Miss E. Rix—Being happy—"A Tangled Tale"—Religious arguments—The "Alice" Operetta—"Alice's Adventures Underground"—"The Game of Logic"—Mr. Harry Furniss.

В 1883 году Льюису Кэрроллу посоветовали выступить против большой скидки, предоставляемой издателями книготорговцам, а книготорговцами — публике. Соответственно, следующее уведомление начало появляться во всех его книгах: «При продаже книг мистера Льюиса Кэрролла Торговле, братья Макмиллан и Ко будут делать скидку 2 пенса с шиллинга (без нечетных экземпляров) и предоставлять 5 процентов скидки в течение шести месяцев и 10 процентов за наличные. При продаже их Публике (только за наличные) они будут предоставлять 10 процентов скидки».

Это был смелый шаг, который вызвал некоторые громкие выражения неодобрения. «Вместо того чтобы покупать на условиях, которые предлагает мистер Льюис Кэрролл, — писала "Фирма лондонских книготорговцев" в "Букселлере" от 4 августа, — торговле будет лучше отказаться брать экземпляры его книг, новых или старых, до тех пор, пока он придерживается условий, которые он только что объявил торговле для их удовольствия и восторга». С другой стороны, редакционная статья, появившаяся в том же номере «Букселлера», выразила теплое одобрение этого нововведения.

Чтобы избежать всех возможных недоразумений, автор полностью объяснил свои взгляды в небольшой брошюре «Прибыль от авторства». Он показал, что книготорговец получает столько же прибыли с каждого проданного тома (при условии, что покупатель платит полную опубликованную цену, что он делал в те дни более охотно, чем сегодня), сколько автор и издатель вместе взятые, тогда как его доля в работе очень мала. Он не говорит много об авторской части работы — то, что она очень тяжелая, само собой разумеется, — но, рассматривая долю издателя, он говорит:

The publisher contributes about as much as the bookseller in time and bodily labour, but in mental toil and trouble a great deal more. I speak with some personal knowledge of the matter, having myself, for some twenty years, inflicted on that most patient and painstaking firm, Messrs. Macmillan and Co., about as much wear and worry as ever publishers have lived through. The day when they undertake a book for me is a dies nefastus for them. From that day till the book is out—an interval of some two or three years on an average—there is no pause in "the pelting of the pitiless storm" of directions and questions on every conceivable detail. To say that every question gets a courteous and thoughtful reply—that they are still outside a lunatic asylum—and that they still regard me with some degree of charity—is to speak volumes in praise of their good temper and of their health, bodily and mental. I think the publisher's claim on the profits is on the whole stronger than the booksellers.

«Рифма? и Разум?» вышла к Рождеству; посвятительные стихи, озаглавленные «Дорогому ребенку: в память о золотых летних часах и шепоте летнего моря», были адресованы маленькой подруге автора, мисс Гертруде Чэтеуэй. Одно из самых популярных стихотворений в книге — «Фотографирование Гайаваты», восхитительная пародия на «Гайавату» Лонгфелло. «В век подражания, — пишет Льюис Кэрролл в примечании в начале, — я не могу претендовать на особые заслуги за эту слабую попытку сделать то, что, как известно, так легко». Не каждый, кто читал это примечание, заметил, что оно написано в том же метре, что и стихотворение под ним.

Другая превосходная пародия, «Аталанта в Камден-Тауне», точно передала стиль того поэта, который стоит особняком и остается недосягаемым среди поэтов наших дней и которого мистер Доджсон называл «величайшим из ныне живущих мастеров языка».

«Пенни-труба славы», с любовью посвященная всем «оригинальным исследователям», которые жаждут «финансирования», была направлена против вивисекторов,

Who preach of Justice—plead with tears

That Love and Mercy should abound—

While marking with complacent ears

The moaning of some tortured hound.

Льюис Кэрролл обращается к ним так:—

Fill all the air with hungry wails—

"Reward us, ere we think or write!

Without your gold mere knowledge fails

To sate the swinish appetite!"

And, where great Plato paced serene,

Or Newton paused with wistful eye,

Rush to the chase with hoofs unclean

And Babel-clamour of the stye!

Be yours the pay: be theirs the praise:

We will not rob them of their due,

Nor vex the ghosts of other days

By naming them along with you.

They sought and found undying fame:

They toiled not for reward nor thanks:

Their cheeks are hot with honest shame

For you, the modern mountebanks!

«В память о старых добрых временах» автор отправил экземпляр своей книги миссис Харгривс (мисс Алисе Лидделл), приложив короткую записку.

Christ Church, December 21, 1883.

Dear Mrs. Hargreaves,—Perhaps the shortest day in the year is not quite the most appropriate time for recalling the long dreamy summer afternoons of ancient times; but anyhow if this book gives you half as much pleasure to receive as it does me to send, it will be a success indeed.

Wishing you all happiness at this happy season, I am,

Sincerely yours,

C. L. Dodgson.

Начало 1884 года было посвящено главным образом делам общей комнаты. Должность куратора, по-видимому, была чем угодно, только не синекурой. Помимо более серьезных обязанностей, она включала заботу о кошке общей комнаты! В данном случае эта «забота» в конечном итоге погубила кошку — но лишь после того, как она прожила срок, обычно отпущенный этим животным, и за пределами которого их дальнейшее существование становится в равной степени обузой и для них самих, и для всех остальных. Относительно наилучшего способа «прекращения ее земного существования» мистер Доджсон проконсультировался с двумя хирургами, одним из которых был сэр Джеймс Пэджет. Я не знаю, какой метод был в итоге принят, но уверен, что он не причинил боли нервам кошечки и как можно меньше затронул ее чувства.

11 марта в Конгрегации состоялись дебаты по поводу предложенного допуска женщин к некоторым из почетных школ Оксфорда. Это была одна из многих тем, по которым мистер Доджсон написал брошюру. Во время дебатов он произнес одну из своих немногих речей и решительно выступил против этого предложения, аргументируя это вредом для здоровья, который оно нанесет студенткам.

Позднее в том же месяце он и преподобный Э. Ф. Сэмпсон, тьютор Крайст-Черч, посетили Джерси, где встретились с различными друзьями, в частности с преподобным Ф. Х. Аткинсоном, старым университетским другом мистера Доджсона, который помогал ему, когда он был редактором «College Rhymes». Я процитирую несколько строк из его письма к мистеру Аткинсону, поскольку они отражают его взгляды на брак:—

So you have been for twelve years a married man, while I am still a lonely old bachelor! And mean to keep so, for the matter of that. College life is by no means unmixed misery, though married life has no doubt many charms to which I am a stranger.

Запись в его дневнике от 5 мая показывает одно из изменений в образе жизни, к которому его вынудили преклонные годы:—

Wrote to—(who had invited me to dine) to beg off, on the ground that, in my old age, I find dinner parties more and more fatiguing. This is quite a new departure. I much grudge giving an evening (even if it were not tiring) to bandying small-talk with dull people.

Следующий отрывок, который я привожу, не очень-то похож на старость!

I called on Mrs. M—. She was out; and only one maid in, who, having come to the gate to answer the bell, found the door blown shut on her return. The poor thing seemed really alarmed and distressed. However, I got a man to come from a neighbouring yard with a ladder, and got in at the drawing-room window—a novel way of entering a friend's house!

Как ни странно, почти то же самое произошло с ним в 1888 году: «Дверь захлопнулась, горничная осталась снаружи, а в доме никого не было. Я попросил кухарку из соседнего дома позволить мне пройти через их владения и с помощью стремянки перебрался через стену между двумя задними дворами».

В июле в «Сент-Джеймс газет» появилась статья на тему «Парламентские выборы», написанная мистером Доджсоном. Это была тема, которая его очень интересовала, и несколькими годами ранее он опубликовал в той же газете длинное письмо о «чистоте выборов». Жаль, что у меня нет места, чтобы привести оба текста полностью; в нынешних обстоятельствах я осмелюсь предложить лишь краткое изложение и несколько выдержек. Автор утверждал, что существует огромное количество избирателей и, pari passu, огромное количество избирательных округов, которые любят быть на стороне победителя и чьи голоса зависят главным образом от этого соображения. Избирательная урна сделала практически невозможным для отдельного избирателя узнать, какая сторона окажется победителем, но после первых нескольких дней всеобщих выборов одна из сторон, как правило, получает более или менее решительное преимущество, и слабохарактерный избирательный округ испытывает сильное искушение примкнуть к волне победы.

But this is not all. The evil extends further than to the single constituency; nay, it extends further than to a single general election; it constitutes a feature in our national history; it is darkly ominous for the future of England. So long as general elections are conducted as at present we shall be liable to oscillations of political power, like those of 1874 and 1880, but of ever-increasing violence—one Parliament wholly at the mercy of one political party, the next wholly at the mercy of the other—while the Government of the hour, joyfully hastening to undo all that its predecessors have done, will wield a majority so immense that the fate of every question will be foredoomed, and debate will be a farce; in one word, we shall be a nation living from hand to mouth, and with no settled principle—an army, whose only marching orders will be "Right about face!"

Его решение заключалось в том, чтобы результаты каждых отдельных выборов держались в секрете до окончания всеобщих выборов:—

It surely would involve no practical difficulty to provide that the boxes of voting papers should be sealed up by a Government official and placed in such custody as would make it impossible to tamper with them; and that when the last election had been held they should be opened, the votes counted, and the results announced.

Статья о «Парламентских выборах» предлагала гораздо более радикальные изменения. Вступительный абзац покажет ее общую направленность:—

The question, how to arrange our constituencies and conduct our Parliamentary elections so as to make the House of Commons, as far as possible, a true index of the state of opinion in the nation it professes to represent, is surely equal in importance to any that the present generation has had to settle. And the leap in the dark, which we seem about to take in a sudden and vast extension of the franchise, would be robbed of half its terrors could we feel assured that each political party will be duly represented in the next Parliament, so that every side of a question will get a fair hearing.

Аксиомы, на которых основывалась его схема, были следующими:—

(1) That each Member of Parliament should represent approximately the same number of electors.

(2) That the minority of the two parties into which, broadly speaking, each district may be divided, should be adequately represented.

(3) That the waste of votes, caused by accidentally giving one candidate more than he needs and leaving another of the same party with less than he needs, should be, if possible, avoided.

(4) That the process of marking a ballot-paper should be reduced to the utmost possible simplicity, to meet the case of voters of the very narrowest mental calibre.

(5) That the process of counting votes should be as simple as possible.

Затем последовало конкретное предложение. Я не буду останавливаться, чтобы подробно сравнивать его с предложениями мистера Хэра, мистера Кортни и других:—

I proceed to give a summary of rules for the method I propose. Form districts which shall return three, four, or more Members, in proportion to their size. Let each elector vote for one candidate only. When the poll is closed, divide the total number of votes by the number of Members to be returned plus one, and take the next greater integer as "quota." Let the returning officer publish the list of candidates, with the votes given for each, and declare as "returned" each that has obtained the quota. If there are still Members to return, let him name a time when all the candidates shall appear before him; and each returned Member may then formally assign his surplus votes to whomsoever of the other candidates he will, while the other candidates may in like manner assign their votes to one another.

This method would enable each of the two parties in a district to return as many Members as it could muster "quotas," no matter how the votes were distributed. If, for example, 10,000 were the quota, and the "reds" mustered 30,000 votes, they could return three Members; for, suppose they had four candidates, and that A had 22,000 votes, B 4,000, C 3,000, D 1,000, A would simply have to assign 6,000 votes to B and 6,000 to C; while D, being hopeless of success, would naturally let C have his 1,000 also. There would be no risk of a seat being left vacant through two candidates of the same party sharing a quota between them—an unwritten law would soon come to be recognised—that the one with fewest votes should give place to the other. And, with candidates of two opposite parties, this difficulty could not arise at all; one or the other could always be returned by the surplus votes of his party.

Некоторые заметки из дневника за март 1885 года стоит воспроизвести здесь:—

March 1st.—Sent off two letters of literary importance, one to Mrs. Hargreaves, to ask her consent to my publishing the original MS. of "Alice" in facsimile (the idea occurred to me the other day); the other to Mr. H. Furniss, a very clever illustrator in Punch, asking if he is open to proposals to draw pictures for me.

Письмо к миссис Харгривс, которое, как можно заметить, было написано раньше, чем короткая записка, уже процитированная в этой главе, гласило:—

My Dear Mrs. Hargreaves,—I fancy this will come to you almost like a voice from the dead, after so many years of silence, and yet those years have made no difference that I can perceive in my clearness of memory of the days when we did correspond. I am getting to feel what an old man's failing memory is as to recent events and new friends, (for instance, I made friends, only a few weeks ago, with a very nice little maid of about twelve, and had a walk with her—and now I can't recall either of her names!), but my mental picture is as vivid as ever of one who was, through so many years, my ideal child-friend. I have had scores of child-friends since your time, but they have been quite a different thing.

However, I did not begin this letter to say all that. What I want to ask is, Would you have any objection to the original MS. book of "Alice's Adventures" (which I suppose you still possess) being published in facsimile? The idea of doing so occurred to me only the other day. If, on consideration, you come to the conclusion that you would rather not have it done, there is an end of the matter. If, however, you give a favourable reply, I would be much obliged if you would lend it me (registered post, I should think, would be safest) that I may consider the possibilities. I have not seen it for about twenty years, so am by no means sure that the illustrations may not prove to be so awfully bad that to reproduce them would be absurd.

There can be no doubt that I should incur the charge of gross egoism in publishing it. But I don't care for that in the least, knowing that I have no such motive; only I think, considering the extraordinary popularity the books have had (we have sold more than 120,000 of the two), there must be many who would like to see the original form.

Always your friend,

C.L. Dodgson.

H. FURNISS.

From a photograph.

Письмо Гарри Фёрниссу вызвало самый удовлетворительный ответ. Мистер Фёрнисс сказал, что давно хотел проиллюстрировать одну из книг Льюиса Кэрролла и что он вполне готов взяться за эту работу («Сильви и Бруно»).

Далее следуют еще две заметки из дневника, относящиеся к тому же месяцу:—

March 10th.—A great Convocation assembled in the theatre, about a proposed grant for Physiology, opposed by many (I was one) who wish restrictions to be enacted as to the practice of vivisection for research. Liddon made an excellent speech against the grant, but it was carried by 412 to 244.

March 29th.—Never before have I had so many literary projects on hand at once. For curiosity, I will here make a list of them.

(1) Supplement to "Euclid and Modern Rivals."

(2) 2nd Edition of "Euc. and Mod. Rivals."

(3) A book of Math. curiosities, which I think of calling "Pillow Problems, and other Math. Trifles." This will contain Problems worked out in the dark, Logarithms without Tables, Sines and angles do., a paper I am now writing on "Infinities and Infinitesimals," condensed Long Multiplication, and perhaps others.

(4) Euclid V.

(5) "Plain Facts for Circle-Squarers," which is nearly complete, and gives actual proof of limits 3.14158, 3.14160.

(6) A symbolical Logic, treated by my algebraic method.

(7) "A Tangled Tale."

(8) A collection of Games and Puzzles of my devising, with fairy pictures by Miss E.G. Thomson. This might also contain my "Mem. Tech." for dates; my "Cipher-writing" scheme for Letter-registration, &c., &c.

(9) Nursery Alice.

(10) Serious poems in "Phantasmagoria."

(11) "Alice's Adventures Underground."

(12) "Girl's Own Shakespeare." I have begun on "Tempest."

(13) New edition of "Parliamentary Representation."

(14) New edition of Euc. I., II.

(15) The new child's book, which Mr. Furniss is to illustrate. I have settled on no name as yet, but it will perhaps be "Sylvie and Bruno."

I have other shadowy ideas, e.g., a Geometry for Boys, a vol. of Essays on theological points freely and plainly treated, and a drama on "Alice" (for which Mr. Mackenzie would write music): but the above is a fair example of "too many irons in the fire!"

Письмо, написанное примерно в это время его подруге, мисс Эдит Рикс, содержит несколько очень хороших советов о том, как работать, — они тем более ценны, что он сам успешно их применял. Первый совет был следующим:—

When you have made a thorough and reasonably long effort, to understand a thing, and still feel puzzled by it, stop, you will only hurt yourself by going on. Put it aside till the next morning; and if then you can't make it out, and have no one to explain it to you, put it aside entirely, and go back to that part of the subject which you do understand. When I was reading Mathematics for University honours, I would sometimes, after working a week or two at some new book, and mastering ten or twenty pages, get into a hopeless muddle, and find it just as bad the next morning. My rule was to begin the book again. And perhaps in another fortnight I had come to the old difficulty with impetus enough to get over it. Or perhaps not. I have several books that I have begun over and over again.

My second hint shall be—Never leave an unsolved difficulty behind. I mean, don't go any further in that book till the difficulty is conquered. In this point, Mathematics differs entirely from most other subjects. Suppose you are reading an Italian book, and come to a hopelessly obscure sentence—don't waste too much time on it, skip it, and go on; you will do very well without it. But if you skip a mathematical difficulty, it is sure to crop up again: you will find some other proof depending on it, and you will only get deeper and deeper into the mud.

My third hint is, only go on working so long as the brain is quite clear. The moment you feel the ideas getting confused leave off and rest, or your penalty will be that you will never learn Mathematics at all!

Думаю, еще два письма к той же подруге заслуживают того, чтобы быть приведенными здесь:—

Eastbourne, Sept. 25, 1885.

My dear Edith,—One subject you touch on—"the Resurrection of the Body"—is very interesting to me, and I have given it much thought (I mean long ago). My conclusion was to give up the literal meaning of the material body altogether. Identity, in some mysterious way, there evidently is; but there is no resisting the scientific fact that the actual material usable for physical bodies has been used over and over again—so that each atom would have several owners. The mere solitary fact of the existence of cannibalism is to my mind a sufficient reductio ad absurdum of the theory that the particular set of atoms I shall happen to own at death (changed every seven years, they say) will be mine in the next life—and all the other insuperable difficulties (such as people born with bodily defects) are swept away at once if we accept S. Paul's "spiritual body," and his simile of the grain of corn. I have read very little of "Sartor Resartus," and don't know the passage you quote: but I accept the idea of the material body being the "dress" of the spiritual—a dress needed for material life.

Ch. Ch., Dec. 13, 1885.

Dear Edith,—I have been a severe sufferer from Logical puzzles of late. I got into a regular tangle about the "import of propositions," as the ordinary logical books declare that "all x is z" doesn't even hint that any x's exist, but merely that the qualities are so inseparable that, if ever x occurs, z must occur also. As to "some x is z" they are discreetly silent; and the living authorities I have appealed to, including our Professor of Logic, take opposite sides! Some say it means that the qualities are so connected that, if any x's did exist, some must be z—others that it only means compatibility, i.e., that some might be z, and they would go on asserting, with perfect belief in their truthfulness, "some boots are made of brass," even if they had all the boots in the world before them, and knew that none were so made, merely because there is no inherent impossibility in making boots of brass! Isn't it bewildering? I shall have to mention all this in my great work on Logic—but I shall take the line "any writer may mean exactly what he pleases by a phrase so long as he explains it beforehand." But I shall not venture to assert "some boots are made of brass" till I have found a pair! The Professor of Logic came over one day to talk about it, and we had a long and exciting argument, the result of which was "x —x"—a magnitude which you will be able to evaluate for yourself.

C. L. Dodgson.

В качестве примера добрых советов, которые мистер Доджсон давал своим юным друзьям, прекрасно подойдет следующее письмо мисс Изабель Стэнден:—

Eastbourne, Aug. 4, 1885.

I can quite understand, and much sympathise with, what you say of your feeling lonely, and not what you can honestly call "happy." Now I am going to give you a bit of philosophy about that—my own experience is, that every new form of life we try is, just at first, irksome rather than pleasant. My first day or two at the sea is a little depressing; I miss the Christ Church interests, and haven't taken up the threads of interest here; and, just in the same way, my first day or two, when I get back to Christ Church, I miss the seaside pleasures, and feel with unusual clearness the bothers of business-routine. In all such cases, the true philosophy, I believe, is "wait a bit." Our mental nerves seem to be so adjusted that we feel first and most keenly, the dis—comforts of any new form of life; but, after a bit, we get used to them, and cease to notice them; and then we have time to realise the enjoyable features, which at first we were too much worried to be conscious of.

Suppose you hurt your arm, and had to wear it in a sling for a month. For the first two or three days the discomfort of the bandage, the pressure of the sling on the neck and shoulder, the being unable to use the arm, would be a constant worry. You would feel as if all comfort in life were gone; after a couple of days you would be used to the new sensations, after a week you perhaps wouldn't notice them at all; and life would seem just as comfortable as ever.

So my advice is, don't think about loneliness, or happiness, or unhappiness, for a week or two. Then "take stock" again, and compare your feelings with what they were two weeks previously. If they have changed, even a little, for the better you are on the right track; if not, we may begin to suspect the life does not suit you. But what I want specially to urge is that there's no use in comparing one's feelings between one day and the next; you must allow a reasonable interval, for the direction of change to show itself.