everything, recorded in books, must have once been in some mind,
“Isn’t that rather like one of the Rules in Algebra?” my Lady enquired.
(“Algebra too!” I thought with increasing wonder.) “I mean, if we
consider thoughts as factors, may we not say that the Least Common
Multiple of all the minds contains that of all the books; but not the
“Certainly we may!” I replied, delighted with the illustration.
“And what a grand thing it would be,” I went on dreamily, thinking aloud
rather than talking, “if we could only apply that Rule to books!
You know, in finding the Least Common Multiple, we strike out a quantity
wherever it occurs, except in the term where it is raised to its
highest power. So we should have to erase every recorded thought,
except in the sentence where it is expressed with the greatest
My Lady laughed merrily. “Some books would be reduced to blank paper,
I’m afraid!” she said.
“They would. Most libraries would be terribly diminished in bulk.
But just think what they would gain in quality!”
“When will it be done?” she eagerly asked. “If there’s any chance of it
in my time, I think I’ll leave off reading, and wait for it!”
“Well, perhaps in another thousand years or so–”
“Then there’s no use waiting!”, said my Lady. “Let’s sit down.
Uggug, my pet, come and sit by me!”
“Anywhere but by me!” growled the Sub-warden. “The little wretch always
manages to upset his coffee!”
I guessed at once (as perhaps the reader will also have guessed, if,
like myself, he is very clever at drawing conclusions) that my Lady was
the Sub-Warden’s wife, and that Uggug (a hideous fat boy, about the
same age as Sylvie, with the expression of a prize-pig) was their son.
Sylvie and Bruno, with the Lord Chancellor, made up a party of seven.
[Image…A portable plunge-bath]
“And you actually got a plunge-bath every morning?” said the Sub-Warden,
seemingly in continuation of a conversation with the Professor.
“Even at the little roadside-inns?”
“Oh, certainly, certainly!” the Professor replied with a smile on his
jolly face. “Allow me to explain. It is, in fact, a very simple problem
in Hydrodynamics. (That means a combination of Water and Strength.)
If we take a plunge-bath, and a man of great strength (such as myself)
about to plunge into it, we have a perfect example of this science.
I am bound to admit,” the Professor continued, in a lower tone and with
downcast eyes, “that we need a man of remarkable strength. He must be
able to spring from the floor to about twice his own height, gradually
turning over as he rises, so as to come down again head first.”
“Why, you need a flea, not a man!” exclaimed the Sub-Warden.
“Pardon me,” said the Professor. “This particular kind of bath is
not adapted for a flea. Let us suppose,” he continued, folding his
table-napkin into a graceful festoon, “that this represents what is
perhaps the necessity of this Age–the Active Tourist’s Portable
Bath. You may describe it briefly, if you like,” looking at the
Chancellor, “by the letters A.T.P.B.”
The Chancellor, much disconcerted at finding everybody looking at him,
could only murmur, in a shy whisper, “Precisely so!”
“One great advantage of this plunge-bath,” continued the Professor,
“is that it requires only half-a-gallon of water–”
“I don’t call it a plunge-bath,” His Sub-Excellency remarked,
“unless your Active Tourist goes right under!”
“But he does go right under,” the old man gently replied. “The A.T.
hangs up the P. B. on a nail–thus. He then empties the water-jug
into it–places the empty jug below the bag–leaps into the
air–descends head-first into the bag–the water rises round him to
the top of the bag–and there you are!” he triumphantly concluded.
“The A.T. is as much under water as if he’d gone a mile or two down
into the Atlantic!”
“And he’s drowned, let us say, in about four minutes–”
“By no means!” the Professor answered with a proud smile. “After about
a minute, he quietly turns a tap at the lower end of the P. B.–all
the water runs back into the jug and there you are again!”