Wonderful Calculations.

Although we are accustomed to speak in the most airy fashion of millions, billions, &c., and “rattle” off at a breath strings of figures, the fact still remains that we are unable to grasp their vastness. Man is finite—numbers are infinite!

ONE MILLION

Is beyond our conception. We can no more realise its immensity, than we can the tenth part of a second. It should be a pleasing fact to note that commercial calculations do not often extend beyond millions; generally speaking, it is in the realm of speculative calculation only, such as probability, astronomy, &c., that we are brought face to face with these unthinkable magnitudes.

Who, for instance, could form the slightest idea that the odds against a person tossing a coin in the air so as to bring a head 200 times in succession are

160693804425899027554196209234116260522202993782792835301375

(over I decillion, &c.) to 1 against him? Suppose that all the men, women and children on the face of the earth were to keep on tossing coins at the rate of a million a second for a million years, the odds would still be too great for us to realise against any one person succeeding in performing the above feat, and yet the number representing the odds would be only half as long as the one already given.

Or, who could understand the other equally astounding fact that Sirius, the Dog-star, is 130435000000000 miles from the earth, or even that the earth itself is 5426000000000000000000 tons in weight.

WHAT IS A BILLION

In Europe and America, the billion is 1,000,000,000—a thousand millions—but in Great Britain and her Colonies, a billion is reckoned 1,000,000,000,000—a million millions: a difference which should perhaps be worth remembering in the case of francs and dollars.

One billion sovereigns placed side by side would extend to a distance of over 18,000,000 miles, and make a band which would pass 736 times round the globe, or, if lying side by side, would form a golden belt around it over 26 ft. wide; if the sovereigns were placed on top of each other flatways, the golden column would be more than a million miles in height.

Supposing you could count at the rate of 200 a minute; then, in one hour, you could count 12,000—if you were not interrupted. Well, 12,000 an hour would be 288,000 a day; and a year, or 365 days, would produce 105,120,000. But this would not allow you a single moment for sleep, or for any other business whatever. If Adam at the beginning of his existence, had begun to count, had continued to count, and were counting still, he would not even now, according to the usually supposed age of man, have counted nearly enough. To count a billion, he would require 9,512 years, 342 days, 5 hours and 20 minutes, according to the above reckoning. But suppose we were to allow the poor counter twelve hours daily for rest, eating and sleeping, he would need 19,025 years, 319 days, 10 hours and 40 minutes to count one billion.

A comparison—

One million seconds = less than 12 days

" billion " = over 31,000 years

A GOOD CATCH.

1.—Ask a person to write, in figures, eleven thousand, eleven hundred and eleven. This often proves very amusing, few being able to write it correctly at first.

2.—If the eighth of £1 be 3s, what will the fifth of a £5 note be?

BOTHERSOME BILLS.

Defter at the anvil than at the desk was a village blacksmith who held a customer responsible for a little account running:

That the honest man’s services had been requisitioned for the mending of two saucepans, putting a new handle to an old cleaver, sharpening three blunted iron skewers, repairing a lantern, and providing a bell with a clapper is clear enough; and by resolving “a fillup” into “A. Phillip,” all obscurity is removed from the last two items, but “the numoraman a bad i” is a nut the reader must crack for himself.

ONE FROM A PUBLICAN.

He stabled a horse for a night, and sent it home next day with a bill debiting the owner:

A LAUNDRY BILL.

A tourist in Tasmania, being called upon to pay a native dame of the wash-tub “OOoIII,” opened his eyes and ejaculated, “O!” but the good woman explained that he owed her just two and ninepence, a big O standing for a shilling, a little one for sixpence, and each I for a penny.

THE DUTCHMAN’S ACCOUNT.

The two dolls were 7s 6d each, but one “wouldn’t do;” so, being returned, it was taken off the account in the above manner.

A carpenter in Melbourne who did a small job in an office, made out his bill:

To hanging one door and myself 14s.

A BILL MADE OUT BY A MAN WHO COULD NOT WRITE.

The bill reads thus: Two men and a boy, ¾ of a day, 2 hods of mortar, 10s 10d. Settled.

A BILL FROM AN IRISH TAILOR.

To receipting a pair of trousers 5s.

QUITE RIGHT.

At a large manufactory a patent pump refused to work. Several engineers failed to discover the cause. The local plumber, however, succeeded, after a few minutes, in putting it in working order, and sent to the company—

A VETERINARY SURGEON’S ACCOUNT.

To curing your pony, that died yesterday, £1 1s.

3. What is the number that the square of its half is equal to the number reversed?

HOW TO GET A HEAD-ACHE.

Naturalists state that snakes, when in danger, have been known to swallow each other; the above three snakes have just commenced to perform this operation. The snakes are from the same “hatch,” and are therefore equal in age, length, weight, &c. They all start at scratch—that is, commence swallowing simultaneously. They are twirling round at the express rate of 300 revolutions per minute, during which time the circumference is decreased by 1 inch.

We would like our readers to tell us what will be the final result? Heads or tails, and how many of each?

4. A man sold two horses for £100 each; he lost 25 per cent. on one, and gained 25 per cent. on the other. Was he “quits”; or did he lose or gain by the transaction; and, if so, how much?

A GOOD CARD TRICK.

The performer lays upon the table ten cards, side by side, face downwards. Anyone is then at liberty (the performer meanwhile retiring from the room) to shift any number of the cards (from one to nine inclusive) from the right hand end of the row to the left, but retaining the order of the cards so shifted. The performer, on his return, makes a little speech: “Ladies and gentlemen, you have shifted a certain number of these cards. Now, I don’t intend to ask you a single question. By a simple mental calculation I can ascertain the number you have moved, and by my clairvoyant faculty, though the cards are face downwards, I shall pick out one corresponding with that number. Let me see” (pretends to calculate, and presently turns up a card representing “five”). “You shifted five cards and I have turned up a five, the exact number.”

The cards moved are not replaced, but the performer again retires, and a second person is invited to move a few more from right to left. Again the performer on his return takes up the correct card indicating the number shifted. The trick, unlike most others, may be repeated without fear of detection.

The principle is arithmetical. To begin with, the cards are arranged, unknown to the spectators, in the following order:

Ten, nine, eight, seven, six, five, four, three, two, one.

Such being the case, it will be found that, however many are shifted from right to left, the first card of the new row will indicate their number. Thus, suppose three are shifted. The new order of the cards will then be:

Three, two, one, ten, nine, eight, seven, six, five, four.

So far, the trick is easy enough, but the method of its continuance is a trifle more complicated. To tell the position of the indicating card after the second removal, the performer privately adds the number of that last turned up (in this case three) to its place in the row—one. That gives us four, the card to be turned up after the next shift will be the fourth. Thus, suppose six cards are now shifted, their new order will be:

Nine, eight, seven, six, five, four, three, two, one, ten.

Had five cards only been shifted, the five would have been fourth in the row, and so on.

The performer now adds six, the number of the card, to its place in the row, four: the total, ten, gives him the position of the indicator for the next attempt. Thus, suppose four cards are next shifted, the new order will be:

Three, two, one, ten, nine, eight, seven, six, five, four.

The next calculation, 4 and 10, gives us a total 14. The ten is, in this case, cancelled, and the fourteen regarded as four, which will be found to be the correct indicator for the next shifting.

It looks more mystifying if the performer be blindfolded, for he can tell the position of the cards with his fingers. Keeping his hand on the card, he asks, “Will you please tell me how many cards were shifted?” As soon as the answer is given, he exhibits the card, and can continue the trick as long as he pleases.

5. Find 16 numbers in arithmetical progression (common difference 2) whose sum shall be equal to 7552, and arrange them in 4 columns, 4 numbers in each column—or, in other words, arrange in a square of 16 numbers that when added vertically, horizontally, or diagonally, the sum of each 4 numbers will amount to 1888.