CHAPTER XI.IN-DOOR AMUSEMENTS.

THE fall term of the academy closed a few days after the district school, and Oscar, also, was released from his lessons, so that all the young folks were now having a short vacation. Kate and Otis, however, were greatly disappointed, on receiving a letter from their father, a few days before the term closed, stating that they were to remain in Highburg through the vacation, instead of visiting their home. The serious illness of their little sister was the reason given for this new arrangement, and as a partial offset to the disappointment, their parents promised to make them a brief visit at the earliest possible day.

The weather was now cold, and often dull or stormy, rendering out-door amusements unpleasant,and much of the time impracticable. Marcus, though busily engaged in finishing up his work for the winter, was untiring in his efforts to relieve the disappointment of Kate and Otis, by finding amusements for them and the other children. When the weather would not admit of a ride in the wagon, an excursion in the woods, or a frolic in the fields and on the hill-sides, he was always ready with some game or amusement that could be played in the house or barn. The long evenings, too, were beguiled with innocent and often instructive diversions, and when the wind raved loudest without, there were no gloomy hearts within.

“I’m going to propose a new play,” said Marcus, one evening, as the little party gathered around the table; “it is calledConglomeration.”

“Conglomeration! I hope the play is as funny as the name,” said Kate.

“We shall see,” observed Marcus, as he distributed some slips of paper among the children. “Now I want each of you to write five words on separate pieces of paper, and throw them all in a heap on the middle of the table. You can select any words you choose.”

When all had written, Marcus mixed together the bits of paper, and then directed each one to take five words from the heap, as they happened to come, and to write one or more sentences containing those words in the order in which they were drawn from the pile.

There was a good deal of merriment among the party, as they glanced at the slips, and perceived what a droll “conglomeration” they had got to weave together. Here are some specimens of them:—

No one thought of saying “I can’t,” however, and in a few minutes, after some rubbing of foreheads and scratching of heads, the last of the sentences was completed.

“Now each one may read his own sentence aloud, emphasizing the words that were given. Otis, we will begin with you.”

Otis read:—

“It would befunnyif thetoothachecould be cured with ajewsharp, but I am notgoingtoJerichoto find out about it.”

“No, I should not,” said Marcus; “now, Ronald, what have you written?”

Ronald then read:—

“Thespidermay not care anything about abook, but asoberboy like mecannothelp loving roastturkey.”

“Asoberboy, I should think!” said Kate.

“Don’t interrupt us,” said Marcus; “now, what’s yours, Oscar?”

“I couldn’t make much out of my list,” remarked Oscar, and after a moment’s hesitation, he read:—

“If I couldshoota rabbit, I would makegravyof him; and then thegirlshould serve him up withonions, in the mostsublimestyle.”

“Why, I bet I could do better than that,” exclaimed Ronald.

“Stop, stop, Ronald!” cried Marcus; “where are your manners?”

“Something came into my head, just then, and I spoke before I thought,” replied the impulsive boy, somewhat abashed.

“Let him try my list—I don’t care if he does beat me,” said Oscar, good naturedly.

“No,” replied Marcus, “I think he had better not—you have done well enough yourself. Now, Kate, we will hear yours.”

Kate then read:—

“I don’t care much aboutpoetry, and I hatephysic, but Ishouldlike to hitRonaldwith abroomstick.”

“You’d better try it!” cried Ronald, jumping into an attitude of self-defence, as the merry laugh rang over the house.

Sentences were also read by Marcus and Ellen Blake, who had now become an inmate of the house. Another round was then proposed with a larger list of words; and now that the character of the play was better understood, they found it even more amusing than at first.

The “Hay-Mow Debating Society,” so named from the place in which it usually held its meetings, was established at the commencement of the vacation, and met once or twice a week until the new term commenced. All the children belonged to it, and all were required to take part in the discussions.Subjects were assigned beforehand, and disputants appointed for each side, so that all were prepared to say something. The questions discussed were not perhaps so important as those which sometimes agitate senates and parliaments, but they were such as the young debaters could grasp, and feel an interest in. Marcus gave out for the first discussion the proposition, “Education is of more value to a man than wealth.” The manner in which this grave theme was handled, induced him to throw away his list of propositions for discussion, and to make a new set, of a very different order. Some of these were as follows: “Which is preferable, summer or winter?” “Which is pleasanter, a residence on a hill, or in a valley?” “Which is most desirable, a half holiday, Wednesday and Saturday afternoons, or a whole holiday, every Saturday?” “Who enjoy themselves most, boys or girls?” Though these may look like trivial questions, they served to wake up the ideas of the young people, and sometimes the debates became quite exciting, occasionally taking a very amusing turn.

One evening, as riddles, puzzles, etc., were in theascendant, Ellen read the following from a scrap of paper:—

“There was a man of Adam’s race,Who had a certain dwelling place;He had a house well covered o’er,Where no man dwelt since nor before.It was not built by human art,Nor brick nor lime in any part,Nor wood, nor rock, nor nails, nor kiln,But curiously was wrought within.’T was not in heaven, nor yet in hell,Nor on the earth where mortals dwell.Now if you know this man of fame,Tell where he lived and what’s his name.”

“There was a man of Adam’s race,

Who had a certain dwelling place;

He had a house well covered o’er,

Where no man dwelt since nor before.

It was not built by human art,

Nor brick nor lime in any part,

Nor wood, nor rock, nor nails, nor kiln,

But curiously was wrought within.

’T was not in heaven, nor yet in hell,

Nor on the earth where mortals dwell.

Now if you know this man of fame,

Tell where he lived and what’s his name.”

“Jonah in the whale’s belly!” promptly cried Ronald.

“Did you ever see this puzzle?” inquired Otis. “A man has a wolf, a goat and a cabbage to carry across a river. It wont do to leave the wolf and goat together, nor the goat and the cabbage, and he can carry only one at a time, the boat is so small. Now what shall he do?”

After a moment’s thought, Kate gave the solution, as follows:—

“First he carried over the goat; then returned and got the cabbage; then he took back the goat,and left it, and carried over the wolf; then last of all he went and got the goat.”

“Let’s see who can find this one out,” said Ronald. “A sea captain on a voyage had thirty passengers—fifteen Christians and fifteen Turks. A great tempest arose, and he had to throw half of them overboard. They agreed to let him place them in a circle, and throw every ninth man overboard, till only fifteen were left. He did so, and when he got through, every Christian was saved, and every Turk drowned. How did he do it?”

“That is easy enough,” said Kate; and writing down the figures from one to thirty, she counted off every ninth one, and found that the Christians and Turks were arranged as follows:—

CCCC, TTTTT, CC, T, CCC, T, C, TT, CC, TTT, C, TT, CC, T.

“Let me propose the next puzzle,” said Aunt Fanny. “What English word of seven letters can be so transposed as to make over fifty different words?”

No one could solve this question, and when the word “weather” was named, as the answer, the children could hardly credit the fact that it was soprolific, until they had each made out a list of words. Throwing out quite a number that were obtained by using a single letter more than once, the following long list remained, which perhaps does not exhaust the subject:—

“There, I have made forty angles with only five straight lines,” said Kate, holding up a slip of paper; “can any body beat that?”

“Let me try,” said Marcus; and in a few minutes he pushed towards Kate the accompanying figure, remarking, “There, I’ve made only six lines, and if I’ve counted right, there are sixty angles.”

While the others were amusing themselves with angles, Oscar made the annexed sketch, and now passed it to the others, giving out with it the following problem:

“A man had a piece of land exactly square, and having four trees scattered over it, as you see in the picture. The house took up one quarter of the land, and was occupied by four tenants. The owner promised them the use of the land, rent free, if they could divide it into four parts of the same size and shape, and each to have one tree. The question is, how did they do it?”

After some little puzzling of wits, the lot was divided as in the annexed illustration, and the tenants were congratulated on the good bargain they had made.

“Otis,” said Ronald, “I’ll bet you can’t tell what the half of nine is.”

“It’s four and a half—any fool might know that,” replied Otis.

“No it isn’t,” continued Ronald, “it’s eitherfour or six, just as you please, and I can prove it;” and writing IX, he folded the paper across the middle and made his promise good.

“Speaking of arithmetical puzzles,” said Aunt Fanny, “I remember one that I worked over for a long time, before I could see into it. It was something like this: Two Arabs sat down to dinner, one having five loaves, and the other three. A stranger came along and asked permission to eat with them, which they granted. After the stranger had dined, he laid down eight pieces of money and departed. The owner of the five loaves took five pieces, and left three for the other, who thought he had not received his share. So they went to a magistrate, and he ordered that the owner of the five loaves should havesevenpieces of the money, and the other only one. Was this just?”

“Why, no, it’s plain enough that it wasn’t,” said Otis. “Each man ought to have as many pieces of money as he had loaves.”

“Yes, it was just,” continued Aunt Fanny; “otherwise you would pay the man of three loaves for the bread he ate himself. To prove this, divide each loaf into three equal parts, making in alltwenty-four parts, and take it for granted that each person ate an equal or one-third part of the whole. You will find that the stranger had seven parts of the person who contributed five loaves or fifteen parts, and only one of him who contributed three loaves, or nine parts.”

“O yes, I see into it, now,” said Otis.

“That reminds me,” said Marcus, “of an anecdote that I read in a newspaper the other day. I treasured it up, intending to relate it in school some day, to illustrate the importance of understanding arithmetic. It seems two carpenters took a job for one hundred and fifty dollars. One of them, whom we will call A, worked one day more than the other, B. The wages of a carpenter were two dollars per day. When the work was finished, they divided the money, each taking seventy-five dollars. Then A wished B to give him two dollars more for the extra day, but B refused, as he saw that if he did so, A would have four dollars more than he, which was evidently unjust. A insisted, and B insisted, and finally they quarrelled. Some of the bystanders took the part of A, and some of B; and yet the paper adds that all the partieswere Americans, and had attended the common schools six or eight years, where I suppose they studied arithmetic, just as I suppose a good many other children do, without troubling themselves to understand it.”

“How should you have settled that dispute, Otis?” inquired Mrs. Page.

“I should have told them to give A two dollars for his extra day, and divide the rest equally,” replied Otis.

“Or if B had given A one dollar, it would have amounted to the same thing,” said Mrs. Page.

“Your story,” said Aunt Fanny, “reminds me of an anecdote of a very rich miser who lived in England, in the time of Cromwell. His name was Audley. He had a wonderful knack of getting and keeping money, and was not at all particular how he obtained it, if he did not make himself liable to the law. He once heard of a poor tradesman who had been sued by a merchant for two hundred pounds. The debtor could not meet the demand, and was declared insolvent. Audley then went to the merchant, and offered him forty pounds for the debt, which was gladly accepted. He next wentto the tradesman, and offered to release him from the debt for fifty pounds, on condition that he would enter into a bond to pay for the accommodation. The debtor was delighted with the offer, especially as the terms of the bond were so easy. He was only required to pay to Audley, sometime within twenty years of that time, one penny progressively doubled, on the first day of twenty consecutive months; and in case he failed to fulfil these easy terms, he was to forfeit five hundred pounds. Thus relieved of his debt, he again commenced business, and flourished more than ever. Two or three years after, Audley walked into his shop one morning, and demanded his first payment. The tradesman paid him his penny, and thanked him for the favor he had done him. On the first day of the next month, Audley again called, and received his two pence; a month later, he received four pence; and so on for several months, doubling the sum each time. But at last the tradesman’s suspicions were aroused, and he entered into a calculation of his subsequent payments. I do not remember the sum which it amounted to—”

“Wait a minute—let me figure it up,” interruptedKate, and she at once set her pencil in motion. The calculation employed her and the others several minutes. It was ascertained that the tradesman’s last payment would have amounted to two thousand one hundred and eighty-six pounds, and that the total sum of all the payments would have been four thousand three hundred and sixty-nine pounds, omitting odd shillings and pence!

“I suppose the man paid the forfeit, when he found that out,” said Ellen.

“Yes, he paid the miser five hundred pounds for his kindness,” replied Aunt Fanny.

“I don’t see how any one can dislike arithmetic—I think it is a very interesting study,” remarked Kate.

“How curious it is about the figure 9,” said Oscar; “you may multiply any number you please by 9, and the figures in the product, added together, will make 9, or a series of 9’s. As—

97—63—6 + 3 = 993—27—2 + 7 = 9912——108—1 + 8 = 9

97—63—6 + 3 = 9

—

63—6 + 3 = 9

93—27—2 + 7 = 9

—

27—2 + 7 = 9

912——108—1 + 8 = 9

——

108—1 + 8 = 9

and so on with any number, no matter how large.”

“You can do the same with any of the multiples of 9,” said Aunt Fanny, “as 18, 27, 36, 45, 54, etc. If you multiply these by any number whatever, you will have a series of 9’s in the product. Try it.”

Several experiments were made, with such results as the following:

4618——828—8 + 2 + 8 = 18—1 + 8 = 911727——3159—3 + 1 + 5 + 9 = 18—1 + 8 = 9

4618——828—8 + 2 + 8 = 18—1 + 8 = 9

——

828—8 + 2 + 8 = 18—1 + 8 = 9

11727——3159—3 + 1 + 5 + 9 = 18—1 + 8 = 9

117

——

3159—3 + 1 + 5 + 9 = 18—1 + 8 = 9

“There is another thing about the figure 9 very curious,” said Marcus. “If you take any number composed of two figures, reverse it, and subtract the smaller from the larger, the sum of the figures in the answer will always be 9.”

This was found to be true, as in the following examples:

9669—27—2 + 7 = 95445—98448—36—3 + 6 = 99889—9

9669—27—2 + 7 = 9

—

27—2 + 7 = 9

5445—9

—

8448—36—3 + 6 = 9

—

36—3 + 6 = 9

9889—9

—

Marcus then explained that numbers composedof three or more figures, transposed and subtracted in the same way, would always give a series of 9’s in the product. The children tried the experiment, and the following are some of their examples:

723237—-486—4 + 8 + 6 = 1889622698——6264—6 + 2 + 6 + 4 = 183218928913——-3276—3 + 2 + 7 + 6 = 18863577736578———126999 = four 9’s92163581982536———-7233822 = three 9’s

723237—-486—4 + 8 + 6 = 18

723

237

—-

486—4 + 8 + 6 = 18

89622698——6264—6 + 2 + 6 + 4 = 18

8962

2698

——

6264—6 + 2 + 6 + 4 = 18

3218928913——-3276—3 + 2 + 7 + 6 = 18

32189

28913

——-

3276—3 + 2 + 7 + 6 = 18

863577736578———126999 = four 9’s

863577

736578

———

126999 = four 9’s

92163581982536———-7233822 = three 9’s

9216358

1982536

———-

7233822 = three 9’s

“Thatiscurious; but why is it so—does anybody know?” inquired Ronald.

“It will take a wiser head than mine to tell why it is so,” replied Marcus.

“I found out something the other day about figures that I didn’t know before,” remarked Ronald; “and that is, that if you wish to multiply a number by five, you can get the same result by dividing by 2, and adding a 0 if there is no remainder, or 5 if there is a remainder. Thus, 5 times 12 are60. Divide 12 by 2, and add a 0, and you get 60. Or 5 times 83 are 415; divide 83 by 2, and add 5, because there is a remainder, and you have the same number, 415.”

“That is quite a convenient process, sometimes,” said Miss Lee, “but there is no mystery about it, like the properties of the figure 9. It is in fact the same thing as multiplying by 10 and dividing by 2.”

“So it is,” replied Ronald. “Well, it’s queer that I didn’t find that out myself—I thought that I had discovered something new.”

“Do you know how to make the magic square, Marcus?” inquired Otis.

“I used to know how to makeamagic square, for there are several hundreds of them,” replied Marcus. “Let me see if I can do it, now—I suppose I have forgotten all about it.”

“What is a magic square?” inquired Ellen.

“It is a table of figures that can be added together in a great many different ways with the same result,” replied Miss Lee.

Marcus in a few minutes produced the simplest form of the magic square; and turning to a book inthe library, he found another one, both of which are here given:

The several columns in these tables may be added up in the usual way, or crosswise, or diagonally (from one angle to its opposite) and the result will always be the same—15 in the first, and 34 in the second square.

Such were some of the methods by which the children were amused, at Mrs. Page’s, during the long evenings and stormy days of their vacation. They also had singing, reading aloud, story telling, and newspaper publishing, by way of change. Of this last I must tell you more.

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