the time be considered a part of it. If you hold a stick, six feet long, with its end in a tumbler of water, and wait long enough, you must eventually be immersed. The question as to the source from which the water is supplied—which belongs to a high branch of mathematics, and is therefore beyond our present scope—does not apply to the sea. Let us therefore take the familiar instance of a man standing at the edge of the sea, at ebb-tide, with a solid in his hand, which he partially immerses: he remains steadfast and unmoved, and we all know that he must be drowned. The multitudes who daily perish in this manner to attest a philosophical truth, and whose bodies the unreasoning wave casts sullenly upon our thankless shores, have a truer claim to be called the martyrs of science than a Galileo or a Kepler. To use Kossuth’s eloquent phrase, they are the unnamed demigods of the nineteenth century.” 2
“There’s a fallacy somewhere,” he murmured drowsily, as he stretched his long legs upon the sofa. “I must think it over again.” He closed his eyes, in order to concentrate his attention more perfectly, and for the next hour or so his slow and regular breathing bore witness to the careful deliberation with which he was investigating this new and perplexing view of the subject.
KnotX
Chelsea Buns
“Yea, buns, and buns, and buns!”
Old song.
“How very, very sad!” exclaimed Clara; and the eyes of the gentle girl filled with tears as she spoke.
“Sad—but very curious when you come to look at it arithmetically,” was her aunt’s less romantic reply. “Some of them have lost an arm in their country’s service, some a leg, some an ear, some an eye—”
“And some, perhaps, all!” Clara murmured dreamily, as they passed the long rows of weather-beaten heroes basking in the sun. “Did you notice that very old one, with a red face, who was drawing a map in the dust with his wooden leg, and all the others watching? I think it was a plan of a battle—”
“The battle of Trafalgar, no doubt,” her aunt interrupted, briskly.
“Hardly that, I think,” Clara ventured to say. “You see, in that case, he couldn’t well be alive—”
“Couldn’t well be alive!” the old lady contemptuously repeated. “He’s as lively as you and me put together! Why, if drawing a map in the dust—with one’s wooden leg—doesn’t prove one to be alive, perhaps you’ll kindly mention what does prove it!”
Clara did not see her way out of it. Logic had never been her forte.
“To return to the arithmetic,” Mad Mathesis resumed—the eccentric old lady never let slip an opportunity of driving her niece into a calculation—“what percentage do you suppose must have lost all four—a leg, an arm, an eye, and an ear?”
“How can I tell?” gasped the terrified girl. She knew well what was coming.
“You can’t, of course, without data,” her aunt replied: “but I’m just going to give you—”
“Give her a Chelsea bun, Miss! That’s what most young ladies likes best!” The voice was rich and musical, and the speaker dexterously whipped back the snowy cloth that covered his basket, and disclosed a tempting array of the familiar square buns, joined together in rows, richly egged and browned, and glistening in the sun.
“No, sir! I shall give her nothing so indigestible! Be off!” The old lady waved her parasol threateningly: but nothing seemed to disturb the good-humour of the jolly old man, who marched on, chanting his melodious refrain:—
“Far too indigestible, my love!” said the old lady. “Percentages will agree with you ever so much better!”
Clara sighed, and there was a hungry look in her eyes as she watched the basket lessening in the distance: but she meekly listened to the relentless old lady, who at once proceeded to count off the data on her fingers.
“Say that 70 percent have lost an eye—75 percent an ear—80 percent an arm—85 percent a leg—that’ll do it beautifully. Now, my dear, what percentage, at least, must have lost all four?”
No more conversation occurred—unless a smothered exclamation of “Piping hot!” which escaped from Clara’s lips as the basket vanished round a corner could be counted as such—until they reached the old Chelsea mansion, where Clara’s father was then staying, with his three sons and their old tutor.
Balbus, Lambert, and Hugh had entered the house only a few minutes before them. They had been out walking, and Hugh had been propounding a difficulty which had reduced Lambert to the depths of gloom, and had even puzzled Balbus.
“It changes from Wednesday to Thursday at midnight, doesn’t it?” Hugh had begun.
“Sometimes,” said Balbus, cautiously.
“Always,” said Lambert, decisively.
“Sometimes,” Balbus gently insisted. “Six midnights out of seven, it changes to some other name.”
“I meant, of course,” Hugh corrected himself, “when it does change from Wednesday to Thursday, it does it at midnight—and only at midnight.”
“Surely,” said Balbus. Lambert was silent.
“Well, now, suppose it’s midnight here in Chelsea. Then it’s Wednesday west of Chelsea (say in Ireland or America) where midnight hasn’t arrived yet: and it’s Thursday east of Chelsea (say in Germany or Russia) where midnight has just passed by?”
“Surely,” Balbus said again. Even Lambert nodded this time.
“But it isn’t midnight, anywhere else; so it can’t be changing from one day to another anywhere else. And yet, if Ireland and America and so on call it Wednesday, and Germany and Russia and so on call it Thursday, there must be some place—not Chelsea—that has different days on the two sides of it. And the worst of it is, the people there get their days in the wrong order: they’ve got Wednesday east of them, and Thursday west—just as if their day had changed from Thursday to Wednesday!”
“I’ve heard that puzzle before!” cried Lambert. “And I’ll tell you the explanation. When a ship goes round the world from east to west, we know that it loses a
