Part 3
IX. As we are always glad to see old friends, it will be particularly refreshing to receive visits and renewal of orders from any former Customer who has passed through the Bankruptcy Court, and paid us not more than Sixpence in the Pound. A WARM welcome may be relied on.
X. Having no occupation for our Office Boy, he is entirely at the service of callers.
XI. Our Telephone is always at the disposal of anyone desirous of using it.
XII. The following are kept at this Office for Public Convenience:-- A Stock of Umbrellas (silk), all the Local Newspapers, Railway Time Tables, and other Guides and Directories; also a supply of Note Paper, Envelopes, and Stamps.
XIII. Should you find our principals engaged, do not hesitate to interrupt them. No business can possibly be of greater importance than yours.
XIV. If you have the opportunity of overhearing any conversation, do not hesitate to listen. You may gain information which may be useful in the event of disputes arising.
XV. In case you wish to inspect our premises, kindly do so during wet weather, and carry your umbrella with you. We admire the effect on the floor; it gives an air of comfort to the establishment. (The Umbrella Stand is only for ornament, and on no account to be used).
_P.S.--Our hours for listening to Commercial Travellers, Beggars, Hawkers, and Advertising Men are all day. We attend to our Business at Night only._
A NEW WAY OF PUTTING IT.
“Dirty days hath September, April, June and November; From January up to May, The rain it raineth every day. All the rest have thirty-one, Without a blessed gleam of sun; And if any of them had two and thirty, They’d be just as wet and twice as dirty.”
Does the top of a carriage wheel move faster than the bottom? This question seems absurd. That the top moves faster, however, is perfectly correct; for if not it would simply move round in the same place: in a wheel on a fixed axle the bottom moves backward as fast as the top moves forward; but in a wheel that is going forward, drawn by a progressive axle, the bottom does not go back at all, but remains almost stationary until it is its turn to rise and go forward.
37. A General, arranging his army in a solid square, finds he has 284 men to spare, but on increasing the sides of the square by one man, he wants 25 men to complete the square. How many men has he?
“STEWING.”
38. A student reads two lines more of “Virgil” each day than he did the day before, and finds that, having read a certain quantity in 18 days, he will read at this rate the same quantity in the next 14 days. How much will he read in the whole time?
39. Two bootmakers who lived in the town of B., thrown out of employment, resolved to go to G., a town 24 miles north from B., where there is a large factory; one of them went straight on to G., but the other went first to C., a small township west of B., and then went direct to G., his whole journey being 45 miles. What is the distance from C. to G.?
40. A tree which grows each year 1 inch less than the previous year, grew a yard in the first year; the value of the tree at any time is equal to the number of pence in the cube of the number of yards of its height. What is the value of the tree when done growing?
THIS OFTEN “STICKS” PEOPLE UP.
41. What two odd numbers multiplied together make 7?
MAGIC SQUARES.
A Magic Square is a series of figures arranged in the equal divisions of a square in such a manner that the figures in each row when added up, whether horizontally, vertically, or diagonally, form exactly the same sum.
They have been called “Magic” because the ancients ascribed to them great virtues, and because this arrangement of numbers formed the basis and principle of their talismans. Archimedes devoted a great amount of attention to them, which has caused a great many to speak of them as “the squares of Archimedes.” They may be either odd or even. When the former, the following method will be found valuable:--
With the digits from 1 to 25 form a square so that the numbers when added up horizontally, vertically, or diagonally will amount to 65.
_Method._--Imagine an exterior line of squares above the magic square you wish to form, and another on the right hand of it. These two imaginary lines are shown in the diagram.
18 25 2 9 +----+----+----+----+----+ | 17 | 24 | 1 | 8 | 15 | 17 +----+----+----+----+----+ | 23 | 5 | 7 | 14 | 16 | 23 +----+----+----+----+----+ | 4 | 6 | 13 | 20 | 22 | 4 +----+----+----+----+----+ | 10 | 12 | 19 | 21 | 3 | 10 +----+----+----+----+----+ | 11 | 18 | 25 | 2 | 9 | +----+----+----+----+----+
1st. In placing the numbers in the square, we must go in the ascending diagonal direction from left to right, any number which, by pursuing this direction, would fall into the exterior line must be carried along that line of squares, whether vertical or horizontal, to the last square. Thus, 1 having been placed in the centre of the top row, 2 would fall into the exterior square above the fourth vertical line; then ascending diagonally 3 falls into the square diagonally from 2, but 4 falls out of it to the end of a horizontal line, and it must be carried along that line to the extreme left and there placed. Resuming our diagonal ascension to the right we place 5 where the reader sees it, and would place 6 in the middle of the top row, but as we find 1 is already there we look for the direction to
2nd. That when in ascending diagonally we come to a square already occupied, we must place the number which, according to the 1st rule should go into that occupied square directly under the last number placed: thus, in ascending with 4, 5, 6, the 6 must be placed under the 5, because the square next to 5 in diagonal direction is occupied.
A Promising Sign--I O U.
HOW TO FIND THE TOTAL OF A ROW OF FIGURES IN A MAGIC SQUARE.
_Rule._--Multiply half the sum of the extremes by the square root of the greatest extreme.
Referring to the example given above, we see that the extremes 1 and 25 added equal 26--half of which is 13; this multiplied by 5 (the square root of 25) gives 65 as the total for each row.
Again, in the next question, the two extremes 1 and 81 equal 82, half of this sum is 41, which multiplied by 9 (the square root of 81) gives 369 as the total for each row.
42. Arrange the figures from 1 to 81 in a square that when added up horizontally, vertically, or diagonally the sum will be 369.
HOW THEY WORKED IT.
Mick and Pat, working in the country some distance from a hotel, arranged with the landlord to take to their hut a small keg of rum. They were unable to pay for the liquor at the time, having only one threepenny piece between them; but Mick proposed that every time he had a drink he would give Pat threepence, and Pat also agreed to pay Mick for his drinks, the cash thus gathered to be brought to the publican when the keg was empty. This proposal was accepted by the publican, the keg of rum handed over to the two Irishmen, who immediately started on their journey. They had not proceeded very far before their burden made them thirsty. Mick is the first to pull up with: “Hold on, Pat, I think I’ll have a drink.” “Begorra,” replied Pat, “you’ll have to pay me for it then.” Mick hands the 3d. to Pat before having a good “pull.” Pat now being the possessor of the price of a drink, slakes his thirst by paying Mick 3d. for it. This form of payment is kept up till the rum has disappeared. On their next visit to the hotel, the 3d piece is handed to the landlord as being payment, according to terms of agreement adopted by him.
43. Arrange the figure’s from 1 to 9 in a square, so that they will add up to 15, horizontally, vertically, or diagonally.
44.
[Illustration: N.B.--Note this:]
[Illustration]
45. A man sold a horse for £35 and half as much as he gave for it, and gained thereby 10 guineas. What did he pay for the horse?
THE DISHONEST SERVANT.
46. A gentleman having bought 28 bottles of wine, and suspecting his servant of tampering with the contents of the wine cellar, caused these bottles to be arranged in a bin in such a way as to count 9 bottles on each side. Nothwithstanding this precaution, the servant in two successive visits stole 8 bottles--4 each time--re-arranging the bottles each time so that they still counted 9 on a side. How did he do it?
+-------------+ | 2 5 2 | | | | | | 5 5 | | | | | | 2 5 2 | +-------------+
FATHER--“You are very backward in your arithmetic. When I was your age I was doing cube roots.”
BOY--“What’s them?”
FATHER--“What! You don’t know what they are? My! my! that’s terrible! There, give me your pencil. Now, we take, say, 28764289, and find the cube root. First, you divide--no, you point off--no--let me see?--um--yes--no--don’t stand there grinning like a Cheshire cat; go upstairs and stay in your bedroom for an hour.”
A “TAKE-DOWN” WITH CARDS.
This is a card trick which depends upon a certain “key,” the possessor of which will always have the advantage over his uninstructed adversary. It is played with the first six of each suit--the four aces in one row, next row the deuces, threes, fours, fives and sixes. The object now will be to turn down cards alternately, and endeavour to make thirty-one points by so turning without over-running that number. The chief point is to count so as to end with the following numbers: 3, 10, 17 or 24.
For instance, we will suppose it your privilege to commence the count; you would commence with 3, and your adversary would add 6, which would make 9; it would be then your policy to add 1 and make 10; then, no matter what number he adds he cannot prevent you making 17, which gives you the command of the trick. We will suppose he adds 6 and make 16; then you add 1 and make 17; then he to add 6 and make 23, you add 1 and make 24; then he cannot add any number to make 31, as the highest number he can add is 6, which would only count 30, so that you can easily add the remaining 1 and make 31.
If your adversary is not wary, you may safely turn indifferent numbers at the beginning, trusting to his ignorance to let you count 17 or 24; but, as his knowledge increases, he will soon learn that 24 is a critical number, and to play for it accordingly.
If both players know the trick, the first to play must be the winner, as he is sure to begin with a 3, which commands the game.
ON AN OFFICE DOOR IN GOULBURN.
A baptism in Hades’ depths, As hot as boiling tar, Awaits the man who quits this room And leaves the door ajar. But he who softly shuts the door Shall dwell among the blest-- Where the wicked cease from troubling And the weary are at rest.
47. There are 5 eggs on a dish; divide them amongst 5 persons so that each will get 1 egg and yet 1 still remain on the dish.
48. If a goose weighs 10 lbs. and a half of its own weight, what is the weight of the goose?
THE GEOMETRICAL WONDER AND ARITHMETICAL ABSURDITY.
Take a piece of cardboard 13 inches long and 5 wide, thus giving a surface of 65 inches. Cut this strip diagonally, giving two pieces in the shape of a triangle, and measure exactly 5 inches from the larger end of each strip and cut in two pieces. Take these strips and put them into the shape of an exact square, and it will appear to be just 8 inches each way, or 64 inches--a loss of one square inch of superficial measurement with no diminution of surface.
[Illustration: 5 × 13 = 65 square inches.]
49. If we buy 20 sheep for 20 shillings, and give 2s. for wethers, 1s. 6d. for ewes, and 4d. for lambs, how many of each must we buy?
50. A sets out from a place and travels 5 miles an hour. B sets out 4½ hours after A and travels in the same direction 3 miles in the first hour, 3½ miles the second hour, 4 miles the third hour, and so on. In how many hours will B overtake A?
OFTEN ASKED.
51. What is the difference between 4 square miles and 4 miles square?
TO TELL THE NUMBER THOUGHT OF ON A CLOCK.
Ask a person to think of any number on the dial of a clock; you then point, promiscuously at the various numbers, telling the person to add the number of times you point to the number he thought of, and when the total reaches 20, you will be pointing at the number he selected.
For instance, suppose he selected the number 5. You point indifferently 7 times at the various numbers, but the 8th time your pointer must be at XII., his addition will then be 13 (for 5 and 8 added equal 13), the next at XI., his addition then 14, next at X., and so on. When he calls 20, you will be pointing at the number he thought of--5.
[Illustration]
A very amusing experiment is to ask a person to write down the figures around the dial of a clock. Nearly all know that the figures are generally the Roman numerals; but, in writing them down, when they come to the four, it is very often written IV. instead of IIII.
It is said that a certain king, being unable to find any other fault in a clock that had been constructed for him, declared that the figure four should be represented by four strokes (IIII) instead of IV. In vain did the clock-maker point out the mistake, for his majesty adhered obstinately to his own opinion, and angrily ordered the alteration to be made. This was done, and the precedent thus formed has been followed by clockmakers ever since.
52. At dinner table: one great grandfather, 2 grandfathers, 1 grandmother, 3 fathers, 2 mothers, 4 children, 3 grandchildren, 1 great grandchild, 3 sisters, 1 brother, 2 husbands, 2 wives, 1 mother-in-law, 1 father-in-law, 2 brothers-in-law, 3 sisters-in-law, 2 uncles, 3 aunts, 1 nephew, 2 nieces, and 2 cousins. How many persons?
“Can February March?” he asked. “No, but April May,” was the reply. “Look here, old man, you are out of June.” “Don’t July about it.” “It is not often one gets the better of your August personage.” “Ha! now you have me Noctober.” And then there was work for the coroner.
PANCAKE DAY.
53. On Shrove Tuesday last, I’ll tell you what pass’d In a neighbouring gentleman’s kitchen, Where pancakes were making, with eggs, and with bacon As good as e’er cut off a flitchen. The cook-maid she makes four lusty pancakes For William her favourite gardener, “Pray be quick with that four,” cries Jack, “and make more, For William won’t let me go partner.” Being sparing of lard, the pan’s bottom she marr’d In making the last of Will’s four; So she said, “Pr’ythee, John, run and borrow a pan, Or else I can’t make any more.” Jack soon got a pan, but found by his span That the first was more wide than the latter, This being a foot o’er, whereas that before Was three inches more and a quarter. Jack cries, “Don’t me cozen, but make half a dozen. For the pan is much less than before;” Says Will, “For a crown (and I’ll put the cash down) Your six will be more than my four.” “Tis done,” says brisk Jack, and his crown he did stake, So both of them sent for a gauger; The dimensions he takes, of all their pancakes, To determine this important wager. He found, by his stick, they were equally thick, So one of Will’s cakes he did take, Which he straight cut in twain, twelve one-fifth[1] the chord line; And gave the less piece unto Jack. “To the best of my skill,” says the gauger, “this will Make both of your shares equal and true;” Will swore that he lied, so, the point to decide, They refer themselves, sirs, unto you; Then pray give your answers, as soon as you can, sirs, For what with their quarrels and jars, We’re afraid of some murder, for no day goes over But they fight, and are cover’d with scars!
[Illustration]
[Illustration]
[Illustration]
[Illustration]
[1] Inches.
A Great Prophet--100 per cent.
Interesting Items About the Almanac.
The reason why February has only 28 days, while the other months have 30 and 31 is attributable to the vanity of the Emperor Augustus. His uncle and predecessor corrected the calendar, arranging the year almost as we have it now; he gave to the year 12 months, or 365¼ days. The months were--March (the first month), April, May, June, Quintilis, Sextiles, September, October, November, December, January, and February (the latter being the last month of the year, which among the Romans had consisted originally of 10 months). Cæsar ordered that the year should begin with January, and divided the days among them thus: January, March, May, Quintilis, September, and November each had 31 days; April, June, Sextiles, October and December had 30 days each; and February (the last month added to the year) had 29 days regularly and a 30th day every fourth year. After Julius Cæsar’s death, Mark Antony changed the name of Quintilis to July as we have it now. Augustus wanted a month for himself, and wanted it as long as his uncle’s month, so he took Sextiles for his and changed the name to August. Then he took February’s 29th day and added it to August, so that it might have 31 days; and, to avoid having 3 months of 31 days each in succession, September and November were reduced to 30 days, and October and December increased to 31 days each.
Previous to the year 1752, the legal year in England commenced on the 25th March. In that year it was enacted that the legal year should begin on 1st January. The change brought the calendar into unison with the actual state of the solar year. It is curious that in Scotland the change which made the legal year begin on January 1st was effected in 1600. For some time after the change in England, legal documents contained two dates for the period intervening between 1st January and 25th March--that of the old year and that of the new.
During the time of Oliver Cromwell, Christmas Day was described as a superstitious festival, and put down in England by the strong hand of the law.
There has been a superstitious notion that Fools’ Day dated back to the time of Noah’s Ark. The dove that was sent forth from the Ark is supposed to have returned on April 1st.
THE MOST REMARKABLE MONTH was February, 1866. It had no full moon. January had two full moons, and so had March, but February had none. This had not occurred since the creation of the world, and it will not occur again, so scientists tell us.
_All Fools’ Day_ had it’s origin in France, before the time of the Reformed Calendar. When the year commenced on March 25th, the French frequently paid their New Year’s visits and bestowed their gifts on April 1st, as March 25th occurred in Passion Week. After the adoption of the new calendar, however, these New Year’s observances took place on January 1st, and it was a common thing for people to forget the change of date. Pretended presents and mock ceremonial visits became common, and the persons thus imposed on were known as April fish, _i.e._, a mackerel, which, like a fool, is easily caught. Hence, All Fools’ Day.
54. Being at the summit of a tower 400 ft. high, I dropped a cricket ball from my hand, causing it to alight on a ledge 260 ft. from the base, over which it rolled and fell to the earth: supposing that 1½ seconds were occupied by the rolling of the ball over the ledge, how many seconds elapsed from the ball leaving my hand till it touched the earth, and what was the acquired velocity at the moment of contact?
PRACTICAL ILLUSTRATION.
In one of our great public schools a master known to successive generations of his pupils for fifty years as “old Buggus” delighted in surprising his boys with strange sayings and doings. On one occasion, desirous of illustrating a question in the arithmetic lesson, he said to a boy, “I am a tripe merchant, and this platform is my shop. You will come here and buy a pound of tripe. Now, begin.”
[Illustration]
“Please, I want a pound of tripe,” said a boy, sauntering up. “Where’s your money?” demanded old Buggus, hoping to put the boy out of countenance.
“Where’s your tripe?” was the ready retort; but it gained for its unfortunate author four hours’ detention on the next holiday.
55. A syphon would empty a cistern in 48 minutes, a tap would fill it in 36. How long will it take to fill the cistern when both taps are in action?
Born to rule--a book-keeper.
“MORE HASTE LESS SPEED.”
56. A compositor, hurrying whilst setting up type for an arithmetic book--“How to Become Quick at Figures”--accidentally dropped the work of a problem; unfortunately he mislaid the copy, and all that he remembered was that both multiplicand and multiplier consisted of two figures. The scattered type represented the following figures:--1, 2, 3, 3, 4, 6, 7, 8, 8, 9, 9. With the aid of a pencil and a piece of paper the compositor managed after a while to rearrange the figures in their proper place. What was the problem?
[Illustration]
PROFITABLE CARELESSNESS.
A very amusing story is told of a harness-maker who lived some years ago in London. He had a handsome saddle in his shop, occupying a conspicuous position therein. On his return from luncheon one day he observed that the saddle was gone. Calling to his foreman, he said:
“John, who has bought the saddle?”
“I’m sure I don’t know, sir,” said the foreman, scratching his head as if he were trying to think. “I cannot tell, and the worst part of it is, it hasn’t been paid for. While I was at work in the back of the shop a gentleman came in, priced it, decided to take it, told me to charge it, and throwing it into his trap, drove off, before I could think to ask his name.”
“That was very stupid of you,” said the harness-maker, disposed to be angry at the man’s carelessness. “Very likely we have been robbed.”
“I don’t think that sir,” said the foreman, “for I’m very sure that the gentleman has traded here before.”