Then ensued a perfect Babel of noise, as the five natives explained, all screaming together, how the sailors had carried off the weights, and they had done what they could with whatever came handy.
Two iron belaying-pins, three blocks, six holystones, four winch-handles, and a large hammer, were now carefully weighed, the Captain superintending and noting the results. But the matter did not seem to be settled, even then: an angry discussion followed, in which the sailors and the five natives all joined: and at last the Captain approached our tourists with a disconcerted look, which he tried to conceal under a laugh.
“It’s an absurd difficulty,” he said. “Perhaps one of you gentlemen can suggest something. It seems they weighed the sacks two at a time!”
“If they didn’t have five separate weighings, of course you can’t value them separately,” the youth hastily decided.
“Let’s hear all about it,” was the old man’s more cautious remark.
“They did have five separate weighings,” the Captain said, “but—Well, it beats me entirely!” he added, in a sudden burst of candour. “Here’s the result. First and second sack weighed twelve pounds; second and third, thirteen and a half; third and fourth, eleven and a half; fourth and fifth, eight: and then they say they had only the large hammer left, and it took three sacks to weigh it down—that’s the first, third and fifth—and they weighed sixteen pounds. There, gentlemen! Did you ever hear anything like that?”
The old man muttered under his breath “If only my sister were here!” and looked helplessly at his son. His son looked at the five natives. The five natives looked at the Captain. The Captain looked at nobody: his eyes were cast down, and he seemed to be saying softly to himself “Contemplate one another, gentlemen, if such be your good pleasure. I contemplate Myself!”
Knot V
Oughts and Crosses
“Look here, upon this picture, and on this.”
“And what made you choose the first train, Goosey?” said Mad Mathesis, as they got into the cab. “Couldn’t you count better than that?”
“I took an extreme case,” was the tearful reply. “Our excellent preceptress always says ‘When in doubt, my dears, take an extreme case.’ And I was in doubt.”
“Does it always succeed?” her aunt enquired.
Clara sighed. “Not always,” she reluctantly admitted. “And I can’t make out why. One day she was telling the little girls—they make such a noise at tea, you know—‘The more noise you make, the less jam you will have, and vice versa.’ And I thought they wouldn’t know what ‘vice versa’ meant: so I explained it to them. I said ‘If you make an infinite noise, you’ll get no jam: and if you make no noise, you’ll get an infinite lot of jam.’ But our excellent preceptress said that wasn’t a good instance. Why wasn’t it?” she added plaintively.
Her aunt evaded the question. “One sees certain objections to it,” she said. “But how did you work it with the Metropolitan trains? None of them go infinitely fast, I believe.”
“I called them hares and tortoises,” Clara said—a little timidly, for she dreaded being laughed at. “And I thought there couldn’t be so many hares as tortoises on the Line: so I took an extreme case—one hare and an infinite number of tortoises.”
“An extreme case, indeed,” her aunt remarked with admirable gravity: “and a most dangerous state of things!”
“And I thought, if I went with a tortoise, there would be only one hare to meet: but if I went with the hare—you know there were crowds of tortoises!”
“It wasn’t a bad idea,” said the elder lady, as they left the cab, at the entrance of Burlington House. “You shall have another chance today. We’ll have a match in marking pictures.”
Clara brightened up. “I should like to try again, very much,” she said. “I’ll take more care this time. How are we to play?”
To this question Mad Mathesis made no reply: she was busy drawing lines down the margins of the catalogue. “See,” she said after a minute, “I’ve drawn three columns against the names of the pictures in the long room, and I want you to fill them with oughts and crosses—crosses for good marks and oughts for bad. The first column is for choice of subject, the second for arrangement, the third for colouring. And these are the conditions of the match. You must give three crosses to two or three pictures. You must give two crosses to four or five—”
“Do you mean only two crosses?” said Clara. “Or may I count the three-cross pictures among the two-cross pictures?”
“Of course you may,” said her aunt. “Anyone, that has three eyes, may be said to have two eyes, I suppose?”
Clara followed her aunt’s dreamy gaze across the crowded gallery, half-dreading to find that there was a three-eyed person in sight.
“And you must give one cross to nine or ten.”
“And which wins the match?” Clara asked, as she carefully entered these conditions on a blank leaf in her catalogue.
“Whichever marks fewest pictures.”
“But suppose we marked the same number?”
“Then whichever uses most marks.”
Clara considered. “I don’t think it’s much of a match,” she said. “I shall mark nine pictures, and give three crosses to three of them, two crosses to two more, and one cross each to all the rest.”
“Will you, indeed?” said her aunt. “Wait till you’ve heard all the conditions, my impetuous child. You must give three oughts to one or two pictures, two oughts to three or four, and one ought to eight or nine. I don’t want you to be too hard on the R.A.’s.”
Clara quite gasped as she wrote down all these fresh conditions. “It’s a great deal worse than Circulating Decimals!” she said. “But I’m determined to win, all the same!”
Her aunt smiled
