"P.S. Do you believe in Fate?"
This Postscript puzzled me sorely. "He is far too sensible a man,"

I thought, "to have become a Fatalist. And yet what else can he mean by
it?" And, as I folded up the letter and put it away, I inadvertently

repeated the words aloud. "Do you believe in Fate?"
The fair 'Incognita' turned her head quickly at the sudden question.

"No, I don't!" she said with a smile. "Do you?"
"I--I didn't mean to ask the question!" I stammered, a little taken

aback at having begun a conversation in so unconventional a fashion.
The lady's smile became a laugh--not a mocking laugh, but the laugh

of a happy child who is perfectly at her ease. "Didn't you?" she said.
"Then it was a case of what you Doctors call 'unconscious cerebration'?"

"I am no Doctor," I replied. "Do I look so like one? Or what makes you
think it?"

She pointed to the book I had been reading, which was so lying that its
title, "Diseases of the Heart," was plainly visible.

"One needn't be a Doctor," I said, "to take an interest in medical
books. There's another class of readers, who are yet more deeply

interested--"
"You mean the Patients?" she interrupted, while a look of tender pity

gave new sweetness to her face. "But," with an evident wish to avoid a
possibly painful topic, "one needn't be either, to take an interest in

books of Science. Which contain the greatest amount of Science,
do you think, the books, or the minds?"

"Rather a profound question for a lady!" I said to myself, holding,
with the conceit so natural to Man, that Woman's intellect is

essentially shallow. And I considered a minute before replying.
"If you mean living minds, I don't think it's possible to decide.

There is so much written Science that no living person has ever read:
and there is so much thought-out Science that hasn't yet been written.

But, if you mean the whole human race, then I think the minds have it:
everything, recorded in books, must have once been in some mind,

you know."
"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
other way?"

"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
intensity."

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 portableplunge-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!"
"But how in the world is he to get out of the bag again?"

"That, I take it," said the Professor, "is the most beautiful part of
the whole invention. All the way up the P.B., inside, are loops for the

thumbs; so it's something like going up-stairs, only perhaps less
comfortable; and, by the time the A. T. has risen out of the bag, all

but his head, he's sure to topple over, one way or the other--the Law
of Gravity secures that. And there he is on the floor again!"

"A little bruised, perhaps?"
"Well, yes, a little bruised; but having had his plunge-bath: that's

the great thing."
"Wonderful! It's almost beyond belief!" murmured the Sub-Warden.

The Professor took it as a compliment, and bowed with a gratified smile.
"Quite beyond belief!" my Lady added--meaning, no doubt, to be more

complimentary still. The Professor bowed, but he didn't smile this
time. "I can assure you," he said earnestly, "that, provided the bath

was made, I used it every morning. I certainly ordered it--that I am
clear about--my only doubt is, whether the man ever finished making

it. It's difficult to remember, after so many years--"
At this moment the door, very slowly and creakingly, began to open,

and Sylvie and Bruno jumped up, and ran to meet the well-known footstep.
CHAPTER 3.

BIRTHDAY-PRESENTS.
"It's my brother!" the Sub-warden exclaimed, in a warningwhisper.

"Speak out, and be quick about it!"
The appeal was evidently addressed to the Lord Chancellor, who

instantly replied, in a shrill monotone, like a little boy repeating
the alphabet, "As I was remarking, your Sub-Excellency, this portentous

movement--"
"You began too soon!" the other interrupted, scarcely able to restrain

himself to a whisper, so great was his excitement. "He couldn't have
heard you. Begin again!" "As I was remarking," chanted the obedient

Lord Chancellor, "this portentous movement has already assumed the
dimensions of a Revolution!"