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Find how many times the divisor is contained in the fewest left-hand figures of the dividend that will contain the divisor, and place this number in the quotient at the right.

Multiply the divisor by this quotient figure; place the product under that part of the dividend from which it was obtained.

Subtract this, roduct from the figures above it; to the remainder bring down the next figure of the dividend, and divide as before until all the figures of the dividend are brought down.

If at any time after bringing down a figure the number thus formed is too small to contain the divisor, place a cipher in the quotient and bring down another figure, after which divide as before.

PROOF: Same as in short division.

In 147,095 days, how many years, each of 365 days?

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Solution.-Taking 147 (thousands) for the first partial dividend, we find it will not contain the divisor; hence we use four figures.

Again, after multiplying and subtracting, as in the preceding example, and bringing down the 9 tens, the partial dividend, 109 (tens), will not contain the divisor; hence, write a cipher (no tens) in the quotient, and bring down the 5 units. The last partial divisor is 1095 (units), which contains the divisor three times.

The product must never be greater than the partial dividend from which it is to be subtracted; when so, the quotient figure is too large, and must be diminished.

After subtracting, the remainder must always be less than the divisor. When the remainder is not less than the divisor the last quotient figure is too small and must be increased.

The order of each quotient figure is the same as the lowest order in the partial dividend from which it was obtained.

Divide 78,994 by 319:

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Answer, 328.
Answer, 567,4824.

8. Divide 4,049,160 by 12,345. 9. Divide 552,160,000 by 973. 10. The President of the United days). How much is that per day? $205173.

973

States receives $75,000 a year (365
Answer, $205 and $175 over, or

DIVISION OF SIMPLE NUMBERS.

1. A cistern is supplied by two pipes which supply 1,200 and 2,250 gallons per hour, respectively; the capacity of the cistern is 32,500 gallons. How many hours will it take to fill it? Answer, 928 hours.

2. The stroke of an engine is 4 feet, and there are two strokes to a revolution; the engine makes 187 revolutions per minute. How many minutes will it take the piston to travel a mile? Answer, 3 minutes.

3. In coming on watch the revolution counter at midnight registered 432,765 revolutions, at 1 o'clock it registered 442,905 revolutions; the engine ran throughout the hour without stopping. What was the revolutions per minute? Answer, 169.

4. During the first hour of a watch the engine averaged 171 revolutions per minute; second hour, 169 revolutions; third hour, 167 revolutions; fourth hour, 173 revolutions. What was the average revolutions per minute for the four hours? Answer, 170 revolutions.

5. In a mile there are 5,280 feet, how many pipes 14 feet long would it take to lay a pipe a mile long? Answer, 377 pipes.

6. How many rivets will be required for a longitudinal seam of a steam drum of a boiler, the joint being a triple riveted butt joint, and the rivets being spaced 4 inches apart, boiler being 20 feet long? Answer, 360 rivets.

NOTE.-A triple riveted butt joint would be a joint having three rows of rivets on each side.

7. A bunker contains 84 tons of coal and the average consumption of coal per watch being 10,560 pounds, how many hours will the coal in the bunker supply the fireroom? Answer, 17 hours.

NOTE. Use long ton, 2,240 tons.

8. The unit of work is the foot-pound. It is the energy expended in raising 1 pound through a space of 1 foot; thus, 5 pounds raised through a space of 10 feet equals 50 foot-pounds, and 10 pounds raised through 5 feet of space equals 50 foot-pounds. How many footpounds are developed in raising 492 pounds through a distance of 67 feet? Answer, 32,964 foot-pounds.

9. The unit of power is the horsepower. The unit of power takes into conside: ation the element of time and is equivalent to the energy expended in raising 33,000 pounds 1 foot in 1 minute or 1 pound 33,000 feet in 1 minute. How many horsepower are developed in raising 2,145 pounds through a space of 1,000 feet in 1 minute? Answer, 65 horsepower.

11. Four men shoveled 64 tons of coal from a bunker in 8 hours. How many tons did each man shovel in 1 hour? Answer, 2 tons.

12. The revolution counter of an engine registered 10,140, showing that that number of revolutions of the shaft had been made in 1 hour. What was the average number of revolutions per minute? Answer, 169.

13. A ship steamed 10,368 miles in 36 days. How many miles did it steam in 1 day? Answer, 288 miles.

14. In weighing coal to find the average weight of coal contained per bucket, there were 50 buckets weighed, the total weight of the coal was 4,800 pounds. What was the weight per bucket? Answer, 96 pounds.

15. A tank contained 2,976 gallons of water when full. How many barrels whose capacity is 31 gallons will the water in the tank fill? Answer, 96.

TABLES OF DENOMINATE NUMBERS.

MEASURES OF EXTENSION.

Measures of extension are used in measuring lengths, distances, surfaces and solids.

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The length of a degree of latitude varies; 69.16 miles is the average length, and is that adopted by the United States Coast Survey. The standard unit of length is identical with the imperial yard of Great Britain.

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Scale..

Sq. ft.

Sq. in.

1 = 640=102,400=3,097,600=27,878,400=4,014,489,600.

.640, 160, 301, 9, 144.

Cubic measure.

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In determining the capacity of cisterns, reservoirs, etc., 31 gallons are considered a barrel (bbl.), and 2 barrels, or 63 gallons, a hogshead (hhd.). In commerce, however, the barrel and hogshead are not fixed

measures.

Casks of large size, called, tierces, pipes, butts, tuns, etc., do not hold any fixed quantity. The capacity is usually marked upon them The standard gallon of the United States contains 231 cubic inches, and will hold a little over 83 pounds of distilled water. The imperial gallon, now adopted by Great Britain, contains 277.274 cubic inches, or 10 pounds, of distilled water, temperature 62° F., the barometer standing at 30 inches.

Water, in large quantities, is measured by the barrel (bbl.) of 31 gallons, by the cubic foot, and by the ton. A gallon is equivalent to 231 cubic inches; hence, 1 cubic foot (1,728 cubic inches) equals 7.48 plus gallons or nearly 74 gallons.

In ordinary calculations, the weight of a cubic foot is taken as 62 pounds or 1,000 ounces.

Then, since 231 cubic inches equals of a cubic foot, a gallon of 128 231 water weighs 232 of 624 pounds or 8.335 pounds, about 8 pounds. The following measures and approximate weights will be used in the following examples, unless otherwise stated:

1 gallon equals 231 cubic inches.

1 cubic foot equals 7 gallons.

1 barrel equals 31 gallons.

1 cubic foot fresh water weighs 62 pounds.

1 gallon fresh water weighs 83 pounds.

Dry measure.

Dry measure is used in measuring grain, vegetables, fruit, etc.

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In delicate weighing, a small unit of weight called a grain, originally the weight of a grain of wheat, is used.

The grain is the same for both avoirdupois and troy weight, and is therefore the connecting link between them.

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Avoirdupois weight is used in weighing bulky articles, such as coal, machinery, water, etc. Troy weight is used in weighing gold, silver, platinum, and some kinds of jewels. The apothecary's weight is used in filling prescriptions, although druggists buy and sell by avoirdupois weight.

AVOIRDUPOIS WEIGHT.

Avoirdupois weight is used in measuring all coarse and heavy articles, as hay, grain, groceries, coal, etc., and the metals, except gold and silver. At the customhouse (and in some trades) 2,240 pounds are considered a ton; this is known as a long ton.

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Troy weight is used in weighing gold, silver, and jewels.

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In weighing diamonds, pearls, and other jewels, the unit commonly employed is the carat, which is equal to 4 carat grains, or 3.168 troy grains.

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The term carat is also used to express the fineness of gold, and means part. Thus, gold that is 18 carats is gold and alloy. The standard unit of weight is the troy pound. It is equal to the weight of 22.7944 cubic inches of distilled water at its maximum density, the barometer being at 30 inches. It is identical with the troy pound of Great Britain.

APOTHECARIES WEIGHT.

Apothecaries weight is used by apothecaries and physicians in weighing medicine for prescriptions.

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It will be observed that the pound is identical with the troy pound, as are also the ounce an the grain, though the ounce is differently

divided.

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