Multiply the dividend by the divisor inverted.

_Example_. Divide 7/8 by 5/6.

7/8 X 6/5 = 42/40. Reduced to simple form by dividing by 2 is 21/20 = [Transcriber's Note: The original text reads '1^{1}'] 1-1/20. Ans.

TO MULTIPLY MIXED NUMBERS.

When two numbers are to be multiplied, one of which contains a fraction, first multiply the whole numbers together, then multiply the fraction by the other whole number, add the two results together for the correct answer.

_Example_. What cost 5-1/3 yards at 18c a yard?

18c 5-1/3 --- 18 x 5 = 90 18 x 1/3 = 6 --- 96c

When both numbers contain a fraction,

First, multiply the whole numbers together,

Second, multiply the, lower whole number by the upper fraction;

Third, multiply the upper whole number by the lower fraction;

Fourth, multiply the fractions together;

Fifth, add all the results for the correct answer.

_Example_. What cost 12-2/3 pounds of b.u.t.ter at 18-3/4c per pound?

18-3/4 12-2/3 ------- 18 X 12 = 216 12 x 3/4 = 9 18 X 2/3 = 12 3/4 X 2/3 = 6/12 = 1/2 ------- $2.37-1/2

Common fractions may often be changed to decimals very readily, and the calculations thereby made much easier.

TO CHANGE COMMON FRACTIONS TO DECIMALS.

Annex one or more ciphers to the numerator and divide by the denominator.

_Example_. Change 3/4 to a decimal. Ans. .75.

We add two ciphers to the 3, making it 300, and divide by 4, which gives us.75. In the same way 1/2 =.5, or 3/4 =.75, and so on. When a quant.i.ty is in dollars and fractions of a dollar, the fractions should always be thus reduced to cents and mills.

TWENTY THOUSAND THINGS WORTH KNOWING.

RELATIVE HARDNESS OF WOODS.

Taking sh.e.l.l bark hickory as the highest standard of our forest trees, and calling that 100, other trees will compare with it for hardness as follows:

Sh.e.l.l Bark Hickory 100 Pignut Hickory 96 White Oak 84 White Ash 77 Dogwood 75 Scrub Oak 73 White Hazel 72 Apple Tree 70 Red Oak 69 White Beech 65 Black Walnut 65 Black Birch 62 Yellow Oak 60 Hard Maple 56 White Elm 58 Red Cedar 56 Wild Cherry 55 Yellow Pine 54 [Transcriber's Note: The original text reads 'Chesnut']

Chestnut 52 Yellow Poplar 51 [Transcriber's Note: The original text reads 'Buternut']

b.u.t.ternut 43 White Birch 43 White Pine 30

Timber intended for posts is rendered almost proof against rot by thorough seasoning, charring and immersion in hot coal tar.

The slide of Alpnach, extending from Mount Pilatus to Lake Lucerne, a distance of 8 miles, is composed of 25,000 trees, stripped of their bark, and laid at an inclination of 10 to 18 degrees. Trees placed in the slide rush from the mountain into the lake in 6 minutes.

The Alps comprise about 180 mountains, from 4,000 to 15,732 feet high, the latter being the height of Mount Blanc, the highest spot in Europe.

The summit is a sharp ridge, like the roof of a house, consisting of nearly vertical granite rocks. The ascent requires 2 days, 6 or 8 guides are required, and each guide is paid 100 francs ($20.00). It was ascended by two natives, Jacques Belmat and Dr. Packard, August 8, 1786, at 6 a.m. They staid up 30 minutes, with the thermometer at 14 degrees below the freezing point. The provisions froze in their pockets; their faces were frost-bitten, lips swollen, and their sight much weakened, but they soon recovered on their descent. De Saussure records in his ascent August 2, 1760, that the color of the sky was deep blue; the stars were visible in the shade; the barometer sunk to 16.08 inches (being 27.08 in Geneva) the thermometer was 26-1/2 degrees, in the sun 29 degrees (being 87 degrees at Geneva). The thin air works the blood into a high fever, you feel as if you hardly touched the ground, and you scarcely make yourself heard. A French woman, Mademoiselle d'Angeville, ascended in September, 1840, being dragged up the last 1,200 feet by guides, and crying out: "If I die, carry me to the top." When there, she made them lift her up, that she might boast she had been higher than any man in Europe. The ascent of these awful solitudes is most perilous, owing to the narrow paths, tremendous ravines, icy barriers, precipices, etc. In many places every step has to be cut in the ice, the party being tied to each other by ropes, so that if one slips he may be held up by the rest, and silence is enforced, lest the noise of talking should dislodge the avalanches of the Aiguille du Midi. The view from the mountain is inexpressibly grand. On the Alps the limit of the vine is an elevation of 1,600 feet; below 1,000 feet, figs, oranges and olives are produced. The limit of the oak is 3,800 feet, of the [Transcriber's Note: The original text reads 'chesnut'] chestnut 2,800 feet,of the pine 6,500 feet, of heaths and furze to 8,700 and 9,700 feet; and perpetual snow exists at an elevation of 8,200 feet.

On the Andes, in lat. 2 degrees, the limit of perpetual snow is 14,760 feet; in Mexico, lat. 19 degrees, the limit is 13,800 feet; on the peak of Teneriffe, 11,454 feet; on Mount Etna, 9,000 feet; on the Caucasus, 9,900 feet; in the Pyrenees, 8,400 feet; in Lapland, 3,100 feet; in Iceland, 2,890 feet. The walnut ceases to grow at an elevation of 3,600 feet; the yellow pine at 6,200 feet; the ash at 4,800 feet, and the fir at 6,700 feet. The loftiest inhabited spot on the globe is the Port House of Ancomarca, on the Andes, in Peru, 16,000 feet above the level of the sea. The 14th peak of the Himalayas, in Asia, 25,659 feet high, is the loftiest mountain in the world.

Lauterbrunnen is a deep part of an Alpine pa.s.s, where the sun hardly shines in winter. It abounds with falls, the most remarkable of which is the Staubbach, which falls over the Balm precipice in a drizzling spray from a height of 925 feet; best viewed in the morning sun or by moonlight. In general, it is like a gauze veil, with rainbows dancing up and down it, and when clouds hide the top of the mountain, it seems as poured out of the sky.

In Canada, the falls of Montmorenci are 250 feet high, the falls of Niagara (the Horse Shoe Falls) are 158 feet high and 2,000 feet wide, the American Falls arc 164 feet high and 900 feet wide. The Yosemite Valley Falls are 2,600 feet high, and the Ribbon Falls of the Yosemite are 3,300 feet high. The waterfall of the Arve, in Bavaria, is 2,000 feet.

THE PERIODS OF GESTATION are the same in the horse and a.s.s or eleven months each, camel 12 months, elephant 2 years, lion 5 months, buffalo 12 months, in the human female 9 months, cow 9 months, sheep 5 months, dog 9 weeks, cat 8 weeks, sow 16 weeks, she wolf from 90 to 95 days.

The goose sits 30 days, swans 42, hens 21, ducks 30, peahens and turkeys 28, canaries 14, pigeons 14, parrots 40 days.

AGES OF ANIMALS, ETC.--Elephant 100 years and upward, Rhinoceros 20, Camel 100, Lion 25 to 70, Tigers, Leopards, Jaguars and Hyenas (in confinement) about 25 years, Beaver 50, deer 20, wolf 20, Fox 14 to 16, Llamas 15, Chamois 25, Monkeys and Baboons 16 to 18 years, Hare 8, Squirrel 7, Rabbit 7, Swine 25, Stag under 50, Horse 30, a.s.s 30, Sheep under 10, Cow 20, Ox 30, Swans, Parrots and Ravens 200, Eagle 100, Geese 80, Hens and Pigeons 10 to 16, Hawks 36 to 40, Cranes 24, Blackbird 10 to 12, Peac.o.c.k 20, Pelican 40 to 50, Thrush 8 to 10, Wren 2 to 3, Nightingale 15, Blackcap 15, Linnet 14 to 23, Goldfinch 20 to 24, Redbreast 10 to 12, Skylark 10 to 30, t.i.tlark 5 to 6, Chaffinch 20 to 24, Starling 10 to 12, Carp 70 to 150, Pike 30 to 40, Salmon 16, Codfish 14 to 17, Eel 10, Crocodile 100, Tortoise 100 to 200, Whale estimated 1,000, Queen Bees live 4 years, Drones 4 months, Working Bees 6 months.

The melody of singing birds ranks as follows: The nightingale first, then the linnet, t.i.tlark, sky lark and wood lark. The mocking bird has the greatest powers of imitation, the robin and goldfinch are superior in vigorous notes.

The condor of Peru has spread wings 40 feet, feathers 20 feet, quills 8 inches round.

In England, a quarter of wheat, comprising 8 bushels, yields 14 bushels 2-1/2 pecks, divided into seven distinct kinds of flour, as follows: Fine flour, 5 bushels 3 pecks; bran, 3 bushels; twenty-penny, 3 bushels; seconds, 2 pecks; pollard, 2 bushels; fine middlings, 1 peck; coa.r.s.e ditto, 1 peck.

The ancient Greek phalanx comprised 8,000 men, forming a square battalion, with spears crossing each other, and shields united.

The Roman legion was composed of 6,000 men, comprising 10 cohorts of 600 men each, with 300 hors.e.m.e.n.

The ancient battering ram was of ma.s.sive timber, 60 to 100 feet long, fitted with an iron head. It was erected under shelter to protect the 60 or 100 men required to work it. The largest was equal in force to a 36-lb. shot from a cannon.

Pile Driving on Sandy Soils.--The greatest force will not effect a penetration exceeding 15 feet.

Various Sizes of Type.--It requires 205 lines of Diamond type to make 12 inches, of Pearl 178, of Ruby 166, of Nonpareil 143, of Minion 128, of Brevier 112-1/2, of Bourgeois 102-1/2, of Long Primer 89, of Small Pica 83, of Pica 71-1/2, of English 64.

Wire ropes for the transmission of power vary in size from 3/8 to 7/8 inch diam. For from 3 to 300 horse power; to promote flexibility, the rope, made of iron, steel, or copper wire, as may be preferred, is provided with a core of hemp, and the speed is 1 mile per minute, more or less, as desired. Tho rope should run on a well-balanced, grooved, cast iron wheel, of from 4 to 15 feet diam., according as the transmitted power ranges from 3 to 300 horse; the groove should be well cushioned with soft material, as leather or rubber, for the formation of a durable bed for the rope. With good care the rope will last from 3 to 5 years.

Cannon b.a.l.l.s go furthest at an elevation of 30 degrees, and less as the b.a.l.l.s are less; the range is furthest when fired from west to east in the direction of the earth's motion, which for the diurnal rotation on its axis, is at the rate of 1,037 miles per hour, and in its...o...b..t, 66,092 miles.

The air's resistance is such that a cannon ball of 3 lbs. weight, diameter, 2.78 ins. Moving with a velocity of 1,800 feet per second, is resisted by a force equal to 156 lbs.

Bricklayers ascend ladders with loads of 90 lbs., 1 foot per second.

There are 484 bricks in a cubic yard, and 4,356 in a rod.

A power of 250 tons is necessary to start a vessel weighing 3,000 tons over greased slides on a marine railway, when in motion, 150 tons only is required.