Complete Works of Lewis Carroll (236 page)

But while he fully recognised the limits of his powers, he had great faith in his own critical judgment; and with good reason, for his perception of the beautiful in contour and attitude and grouping was almost unerring.
All the drawings which Miss Thomson made for his "Three Sunsets" were submitted to his criticism, which descended to the smallest details.
He concludes a letter to her, which contained the most elaborate and minute suggestions for the improvement of one of these pictures, with the following words: "I make all these suggestions with diffidence, feeling that I have
really no
right at all, as an amateur, to criticise the work of a real artist."

The following extract from another letter to Miss Thomson shows that seeking after perfection, that discontent with everything short of the best, which was so marked a feature of his character.
She had sent him two drawings of the head of some child-friend of his:—

Your note is a puzzle—you say that "No.
2 would have been still more like if the paper had been exactly the same shade—but I'd no more at hand of the darker colour."
Had I given you the impression that I was in a
hurry
, and was willing to have No.
2
less
good than it
might
be made, so long as I could have it
quick?
If I did, I'm very sorry: I never
meant
to say a word like it: and, if you had written "I could make it still more like, on darker paper; but I've no more at hand.
How long can you wait for me to get some?"
I should have replied, "Six weeks, or six
months
, if you prefer it!"

I have already spoken of his love of nature, as opposed to the admiration for the morbid and abnormal.
"I want you," he writes to Miss Thomson, "to do my fairy drawings from
life
.
They would be very pretty, no doubt, done out of your own head, but they will be ten times as valuable if done from life.
Mr.
Furniss drew the pictures of 'Sylvie' from life.
Mr.
Tenniel is the only artist, who has drawn for me, who resolutely refused to use a model, and declared he no more needed one than I should need a multiplication-table to work a mathematical problem!"
On another occasion he urges the importance of using models, in order to avoid the similarity of features which would otherwise spoil the pictures: "Cruikshank's splendid illustrations were terribly spoiled by his having only
one
pretty female face in them all.
Leech settled down into
two
female faces.
Du Maurier, I think, has only
one
, now.
All the ladies, and all the little girls in his pictures look like twin sisters."

It is interesting to know that Sir Noel Paton and Mr.
Walter Crane were, in Lewis Carroll's opinion, the most successful drawers of children: "There are but few artists who seem to draw the forms of children
con amore
.
Walter Crane is perhaps the best (always excepting Sir Noel Paton): but the thick outlines, which he insists on using, seem to take off a good deal from the beauty of the result."

He held that no artist can hope to effect a higher type of beauty than that which life itself exhibits, as the following words show:—

I don't quite understand about fairies losing "grace," if too like human children.
Of course I grant that to be like some
actual
child is to lose grace, because no living child is perfect in form: many causes have lowered the race from what God made it.
But the
perfect
human form, free from these faults, is surely equally applicable to men, and fairies, and angels?
Perhaps that is what you mean—that the Artist can imagine, and design, more perfect forms than we ever find in life?

I have already referred several times to Miss Ellen Terry as having been one of Mr.
Dodgson's friends, but he was intimate with the whole family, and used often to pay them a visit when he was in town.
On May 15, 1879, he records a very curious dream which he had about Miss Marion ("Polly") Terry:—

Last night I had a dream which I record as a curiosity, so far as I know, in the literature of dreams.
I was staying, with my sisters, in some suburb of London, and had heard that the Terrys were staying near us, so went to call, and found Mrs.
Terry at home, who told us that Marion and Florence were at the theatre, "the Walter House," where they had a good engagement.
"In that case," I said, "I'll go on there at once, and see the performance—and may I take Polly with me?"
"Certainly," said Mrs.
Terry.
And there was Polly, the child, seated in the room, and looking about nine or ten years old: and I was distinctly conscious of the fact, yet without any feeling of surprise at its incongruity, that I was going to take the
child
Polly with me to the theatre, to see the
grown-up
Polly act!
Both pictures—Polly as a child, and Polly as a woman, are, I suppose, equally clear in my ordinary waking memory: and it seems that in sleep I had contrived to give the two pictures separate individualities.

Of all the mathematical books which Mr.
Dodgson wrote, by far the most elaborate, if not the most original, was "Euclid and His Modern Rivals."
The first edition was issued in 1879, and a supplement, afterwards incorporated into the second edition, appeared in 1885.

This book, as the author says, has for its object

to furnish evidence (1) that it is essential for the purposes of teaching or examining in Elementary Geometry to employ one text—book only; (2) that there are strong
a priori
reasons for retaining in all its main features, and especially in its sequence and numbering of Propositions, and in its treatment of Parallels, the Manual of Euclid; and (3) that no sufficient reasons have yet been shown for abandoning it in favour of any one of the modern Manuals which have been offered as substitutes.

The book is written in dramatic form, and relieved throughout by many touches in the author's happiest vein, which make it delightful not only to the scientific reader, but also to any one of average intelligence with the slightest sense of humour.

Whether the conclusions are accepted in their entirety or not, it is certain that the arguments are far more effective than if the writer had presented them in the form of an essay.
Mr.
Dodgson had a wide experience as a teacher and examiner, so that he knew well what he was writing about, and undoubtedly the appearance of this book has done very much to stay the hand of the innovator.

The scene opens in a College study-time, midnight.
Minos, an examiner, is discovered seated between two immense piles of manuscripts.
He is driven almost to distraction in his efforts to mark fairly the papers sent up, by reason of the confusion caused through the candidates offering various substitutes for Euclid.
Rhadamanthus, another equally distracted examiner, comes to his room.

The two men consult together for a time, and then Rhadamanthus retires, and Minos falls asleep.
Hereupon the Ghost of Euclid appears, and discusses with Minos the reasons for retaining his Manual as a whole, in its present order and arrangement.
As they are mainly concerned with the wants of beginners, their attention is confined to Books I.
and II.

We must be content with one short extract from the dialogue:—

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!

With a view to discussing and criticising his various modern rivals, Euclid promises to send to Minos the ghost of a German Professor (Herr Niemand) who "has read all books, and is ready to defend any thesis, true or untrue."

"A charming companion!"
as Minos drily remarks.

This brings us to Act II., in which the Manuals which reject Euclid's treatment of Parallels are dealt with one by one.
Those Manuals which adopt it are reserved for Act III., Scene i.; while in Scene ii., "The Syllabus of the Association for the Improvement of Geometrical Teaching," and Wilson's "Syllabus," come under review.

Only one or two extracts need be given, which, it is hoped, will suffice to illustrate the character and style of the book:

Act II., Scene v.—Niemand and Minos are arguing for and against Henrici's "Elementary Geometry."

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!"

Again, from Act II., Scene 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!

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 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."

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.