Chapter 16

1 × 9 = 9 2 × 9 = 18 3 × 9 = 27 4 × 9 = 36 5 × 9 = 45 6 × 9 = 54 7 × 9 = 63 8 × 9 = 72 9 × 9 = 81 10 × 9 = 90

Now, you will see that the tens column reads down 1, 2, 3, 4, 5, 6, 7, 8, 9, and the units column up 1, 2, 3, 4, 5, 6, 7, 8, 9.

Here is a different property of the same number. If you arrange in a row the cardinal numbers from 1 to 9, with the single omission of 8, and multiply the sum so represented by any one of the figures multiplied by 9, the result will present a succession of figures identical with that which was multiplied by 9. Thus, if you wish a series of fives, you take 5 × 9 = 45 for a multiplier, with this result:

12345679 45 --------

61728395 49382716 --------

555555555

A very curious number is 142,857, which, multiplied by 1, 2, 3, 4, 5, or 6, gives the same figures in the same order, beginning at a different point, but if multiplied by 7 gives all nines. Multiplied by 1, it equals 142,857; multiplied by 2, equals 285,714; multiplied by 3, equals 428,571; multiplied by 4, equals 571,428; multiplied by 5, equals 714,285; multiplied by 6, equals 857,142; multiplied by 7, equals 999,999.

Multiply 142,857 by 8, and you have 1,142,856. Then add the first figure to the last, and you have 142,857, the original number, the figures exactly the same as at the start.

The number 37 has this strange peculiarity: multiplied by 3, or by any multiple of 3 up to 27, it gives three figures all alike. Thus, three times 37 will be 111. Twice three times (6 times) 37 will be 222; three times three times (9 times) 37 gives three threes; four times three times (12 times) 37, three fours, and so on.

The wonderfully procreative power of figures, or, rather, their accumulative growth, has been exemplified in that familiar story of the farmer, who, undertaking to pay his farrier one grain of wheat for the first nail, two for the second, four for the third, and so on, found that he had bargained to give the farrier more wheat than was grown in all England.

My beloved young friends who love to frequent the roulette-table, do you know that if you begin with a dime, and were allowed to leave all your winnings on the table, five consecutive lucky guesses would give you almost a million and a half of dollars, or, to be exact, $1,450,625.52?

Yet that would be the result of winning thirty-five for one five times hand-running.

Here is another example. Take the number 15, let us say. Multiply that by itself, and you get 225. Now multiply 225 by itself, and so on until fifteen products have been multiplied by themselves in turn.

You don't think that is a difficult problem? Well, you may be a clever mathematician, but it would take you about a quarter of a century to work out this simple little sum.

The final product called for contains 38,589 figures, the first of which are 1,442. Allowing three figures to an inch, the answer would be more than a thousand feet long. To perform the operation would require about 500,000,000 figures. If they can be made at the rate of one a minute, a person working ten hours a day for three hundred days in each year would be twenty-eight years about it.

NUMBERS THAT EQUIVOCATED.

The _Woman's Home Companion_ repeats a good story that is told of a quick-witted Irishman with a natural aptitude for mental arithmetic who was working in a field with a Dutchman, when they unearthed a box of silver coins. The covetous Dutchman at once laid claim to the whole booty, because he was the first to break it open and discover its valuable contents.

"Go softly," said the Irishman, "for the whole business is mine. It's a bit of money that was left me by an uncle, and I buried it here for safe-keeping. There was a thousand dollars."

"All right with that," replied the Dutchman, as he caught on to the bait. "If you tell me how much money there is, it's with you; if you miss, she's mine."

"That's fair, and you have the sentiments of a gentleman," replied Pat, as he made a quick mental calculation from the weight of the box that there must be somewhere between fifty and three hundred and fifty dollars. "I sent six hundred and forty-two dollars and fifty-three cents to my mother in the old country, so add that amount to what there is in the box."

"That is done so quick," said the Dutchman.

"Then deduct that amount from the sum of one thousand dollars, which was left me," said Pat.

"Done again," said the Dutchman.

"Now deduct those figures from three hundred and fifty-seven dollars and forty-seven cents, which I had to pay the lawyers, and it leaves the exact amount to one cent that you will find in the box."

"That's the right money to a penny," said the Dutchman, after he had counted it carefully, "and it proves that you are an honest man."

It is not every one who can see through the mathematics of this puzzle so as to know that Pat's problem would work out all right if the box contained any sum up to three hundred and fifty dollars.

FREAK COMBINATIONS.

A well-known professor has drawn attention to the following series of numbers, which are here given without remark:

1 × 9 + 2= 11 12 × 9 + 3 = 111 123 × 9 + 4 = 1111 1234 × 9 + 5 = 11111 12345 × 9 + 6 = 111111 123456 × 9 + 7 = 1111111 1234567 × 9 + 8 = 11111111 123456789 × 9 + 9 = 111111111 1 × 8 + 1 = 9 12 × 8 + 2 = 98 123 × 8 + 3 = 987 1234 × 8 + 4 = 9876 12345 × 8 + 5 = 98765 123456 × 8 + 6 = 987654 1234567 × 8 + 7 = 9876543 12345678 × 8 + 8 = 98765432 123456789 × 8 + 9 = 987654321

Eulogy on the Dog.

BY GEORGE G. VEST.

Gentlemen of the Jury:--The best friend a man has in this world may turn against him and become his enemy. His son or daughter that he has reared with loving care may prove ungrateful. Those who are nearest and dearest to us, those whom we trust with our happiness and our good name, may become traitors to their faith. The money that a man has he may lose. It flies away from him, perhaps when he needs it most. A man's reputation may be sacrificed in a moment of ill-considered action. The people who are prone to fall on their knees to do us honor when success is with us may be the first to throw the stone of malice when failure settles its cloud upon our heads. The one absolutely unselfish friend that man can have in this selfish world, the one that never deserts him, the one that never proves ungrateful or treacherous, is his dog.

Gentlemen of the jury, a man's dog stands by him in prosperity and in poverty, in health and in sickness. He will sleep on the cold ground, where the wintry winds blow and the snow drives fiercely, if only he may be near his master's side. He will kiss the hand that has no food to offer, he will lick the wounds and sores that come in encounter with the roughness of the world. He guards the sleep of his pauper master as if he were a prince. When all other friends desert he remains. When riches take wings and reputation falls to pieces he is as constant in his love as the sun in its journey through the heavens. If fortune drives the master forth an outcast in the world, friendless and homeless, the faithful dog asks no higher privilege than that of accompanying him to guard against danger, to fight against his enemies, and when the last scene of all comes, and death takes the master in its embrace and his body is laid away in the cold ground, no matter if all other friends pursue their way, there by his graveside will the noble dog be found, his head between his paws, his eyes sad but open in alert watchfulness, faithful and true even to death.

One of the most famous speeches ever made by the late Senator Vest, of Missouri, was made in the course of the trial of a man who had wantonly shot a dog belonging to a neighbor. Vest represented the plaintiff, who demanded two hundred dollars' damages. When Vest finished speaking, the jury, after two minutes' deliberation, awarded the plaintiff five hundred dollars. The full text of the speech is printed above.

Abou Ben Adhem.

BY LEIGH HUNT.

Abou Ben Adhem (may his tribe increase!) Awoke one night from a deep dream of peace, And saw within the moonlight in his room, Making it rich and like a lily in bloom, An angel writing in a book of gold. Exceeding peace had made Ben Adhem bold, And to the presence in the room he said, "What writest thou?" The vision raised its head, And with a look made of all sweet accord, Answered, "The names of those who love the Lord." "And is mine one?" said Abou. "Nay, not so," Replied the angel. Abou spoke more low, But cheerly still, and said, "I pray thee, then, Write me as one that loves his fellow-men."

The angel wrote and vanished. The next night It came again, with a great wakening light, And showed the names whom love of God had blessed-- And lo, Ben Adhem's name led all the rest!

* * * * *

Leigh Hunt was born at Southgate, Middlesex, England, October 19, 1784; and died at Putney, near London, August 28, 1859. The son of a clergyman, he was educated at Christ's Hospital, under the same master as Coleridge and Lamb.

He was an ardent political reformer, and it was while in prison for libel against the Prince Regent that he first met Lord Byron, whose biography he afterward wrote.

Besides this, a long poem, "Rimini," and an "Autobiography," his works are principally essays and shorter poems, of which "Abou Ben Adhem" is perhaps the most famous.

There are few school children who have not recited "Abou Ben Adhem," and in the more serious business of life it has served to point a moral, under most varied circumstances; in the marts of trade and the senate chamber it is equally familiar, for, short though it be, it is an epitome of true Christianity.

End of Project Gutenberg's The Scrap Book, Volume 1, No. 1, by Various