not_ know the proverb, but they accepted it in perfect
good faith, as they did every piece of information, however startling,
that came from so infallible an authority as their tutor. They ate on
steadily in silence, and, when dinner was over, Hugh set out the usual
array of pens, ink, and paper, while Balbus repeated to them the problem
he had prepared for their afternoon's task.

"A friend of mine has a flower-garden--a very pretty one, though no
great size--"

"How big is it?" said Hugh.

"That's what _you_ have to find out!" Balbus gaily replied. "All _I_
tell you is that it is oblong in shape--just half a yard longer than its
width--and that a gravel-walk, one yard wide, begins at one corner and
runs all round it."

"Joining into itself?" said Hugh.

"_Not_ joining into itself, young man. Just before doing _that_, it
turns a corner, and runs round the garden again, alongside of the first
portion, and then inside that again, winding in and in, and each lap
touching the last one, till it has used up the whole of the area."

"Like a serpent with corners?" said Lambert.

"Exactly so. And if you walk the whole length of it, to the last inch,
keeping in the centre of the path, it's exactly two miles and half a
furlong. Now, while you find out the length and breadth of the garden,
I'll see if I can think out that sea-water puzzle."

"You said it was a flower-garden?" Hugh inquired, as Balbus was leaving
the room.

"I did," said Balbus.

"Where do the flowers grow?" said Hugh. But Balbus thought it best not
to hear the question. He left the boys to their problem, and, in the
silence of his own room, set himself to unravel Hugh's mechanical
paradox.

"To fix our thoughts," he murmured to himself, as, with hands
deep-buried in his pockets, he paced up and down the room, "we will take
a cylindrical glass jar, with a scale of inches marked up the side, and
fill it with water up to the 10-inch mark: and we will assume that every
inch depth of jar contains a pint of water. We will now take a solid
cylinder, such that every inch of it is equal in bulk to _half_ a pint
of water, and plunge 4 inches of it into the water, so that the end of
the cylinder comes down to the 6-inch mark. Well, that displaces 2
pints of water. What becomes of them? Why, if there were no more
cylinder, they would lie comfortably on the top, and fill the jar up to
the 12-inch mark. But unfortunately there _is_ more cylinder, occupying
half t