_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!

In Act IV. Euclid reappears to Minos, "followed by the ghosts of Archimedes, Pythagoras, &c., who have come to see fair play." Euclid thus sums up his case:--

"'The c.o.c.k 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."

In Appendices I. and II. Mr. Dodgson quotes the opinions of two eminent mathematical teachers, Mr. Todhunter and Professor De Morgan, in support of his argument.

Before leaving this subject I should like to refer to a very novel use of Mr. Dodgson's book--its employment in a school. Mr. G. Hopkins, Mathematical Master in the High School at Manchester, U.S., and himself the author of a "Manual of Plane Geometry," has so employed it in a cla.s.s of boys aged from fourteen or fifteen upwards. He first called their attention to some of the more prominent difficulties relating to the question of Parallels, put a copy of Euclid in their hands, and let them see his treatment of them, and after some discussion placed before them Mr. Dodgson's "Euclid and His Modern Rivals" and "New Theory of Parallels."

Perhaps it is the fact that American boys are sharper than English, but at any rate the youngsters are reported to have read the two books with an earnestness and a persistency that were as gratifying to their instructor as they were complimentary to Mr. Dodgson.

In June of the same year an entry in the Diary refers to a proposal in Convocation to allow the University Club to have a cricket-ground in the Parks. This had been proposed in 1867, and then rejected. Mr.

Dodgson sent round to the Common Rooms copies of a poem on "The Deserted Parks," which had been published by Messrs. Parker in 1867, and which was afterwards included in "Notes by an Oxford Chiel." I quote the first few lines:--

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 acc.u.mulates, 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!

Readers of "Sylvie and Bruno" will remember the way in which the invisible fairy-children save the drunkard from his evil life, and I have always felt that Mr. Dodgson meant Sylvie to be something more than a fairy--a sort of guardian angel. That such an idea would not have been inconsistent with his way of looking at things is shown by the following letter:

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.

Here are two other entries in the Diary:--

_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:--

MAN } permanent } entice } Send MAN on ICE.

ICE. }

ACRE } sacred } credentials } RELY on ACRE.

entirely } RELY }

PRISM } prismatic } dramatic } Prove PRISM to be ODIOUS.

melodrama } melodious } ODIOUS. }

In February, 1880, Mr. Dodgson proposed to the Christ Church "Staff-salaries Board," that as his tutorial work was lighter he should have 200 instead of 300 a year. It is not often that a man proposes to cut down _his own_ salary, but the suggestion in this case was intended to help the College authorities in the policy of retrenchment which they were trying to carry out.

_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 h.o.m.oeopathic 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.

A little book, published during this year, "Alice (a dramatic version of Lewis Carroll's 'Alice'), and other Fairy Tales for Children," by Mrs. Freiligrath-Kroeker, was very successful, and, I understand, still has a regular sale. Mr. Dodgson most gladly gave his consent to the dramatisation of his story by so talented an auth.o.r.ess, and shortly afterwards Mrs. Kroeker brought out "Through the Looking-Gla.s.s" in a similar form.

_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._ 19_th_.--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_ 27_th_.--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_ 16_th_.--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_ 14_th_.--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_ 26_th_.--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.

[Ill.u.s.tration 229: DR. Liddell. _From a photograph by Hill & Saunders._]

Mr. Dodgson sent a letter to _The Observer_ on this subject:--

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 G.o.d'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 a.s.suredly 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 a.s.sault 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 const.i.tution 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 pa.s.s 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_.