Water, water, everywhere,

Nor any drop to drink.

“It’ll just take one more pebble.”

“Whatever are you doing with those buckets?”

The speakers were Hugh and Lambert. Place, the beach of Little Mendip. Time 1:30 p.m. Hugh was floating a bucket in another a size larger, and trying how many pebbles it would carry without sinking. Lambert was lying on his back, doing nothing.

For the next minute or two Hugh was silent, evidently deep in thought. Suddenly he started. “I say, look here, Lambert!” he cried.

“If it’s alive, and slimy, and with legs, I don’t care to,” said Lambert.

“Didn’t Balbus say this morning that, if a body is immersed in liquid it displaces as much liquid as is equal to its own bulk?” said Hugh.

“He said things of that sort,” Lambert vaguely replied.

“Well, just look here a minute. Here’s the little bucket almost quite immersed: so the water displaced ought to be just about the same bulk. And now just look at itl” He took out the little bucket as he spoke, and handed the big one to Lambert. “Why, there’s hardly a teacupful! Do you mean to say that water is the same bulk as the little bucket?”

“Course it is,” said Lambert.

“Well, look here again!” cried Hugh, triumphantly, as he poured the water from the big bucket into the little one. “Why, it doesn’t half fill it!”

“That’s its business,” said Lambert. “If Balbus says it’s the same bulk, why, it is the same bulk, you know.”

“Well, I don’t believe it,” said Hugh.

“You needn’t,” said Lambert. “Besides, it’s dinner-time. Come along.” They found Balbus waiting dinner for them, and to him Hugh at once propounded his difficulty.

“Let’s get you helped first,” said Balbus, briskly cutting away at the joint. “You know the old proverb, ‘Mutton first, mechanics afterwards’?”

The boys did 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 wind 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 ............