runs only 16 rods while the hound runs 20; how far will the hound run before he overtakes the hare?

63. What is the interest of $72.50 from Aug. 8, 1871, to July 20, 1872?

64. A, B, and C engage to do a piece of work; A can do it in 20 days, B in 24, and C in 30. In what time can the three together do the work?

1

65. A gentleman left his son an estate, of which he spent in year and of the remainder in 6 months more, when he had only $1400 remaining; what was the value of the estate?

66. The commander of a besieged fortress has 2 lb. of bread per day for each soldier for 45 days, but wishes to prolong the siege to 60 days; what must be the allowance per day?

67. A man sold a watch for $60, which was of its cost: what was lost by the transaction?

68. If a bar of silver 1 ft. 6 in. long, 4 in. wide, and 2 in. thick, is worth $1240, what is the value of a bar of gold 1 ft. 3 in. long, 8 in. wide, and 1 in. thick, the weight of a cubic inch of silver being to the weight of a cubic inch of gold as 10 to 19, and the valuc per ounce of silver being to that of gold as 2 to 33?

69. Jan. 1, 1871, A, B, and C form a partnership for 1 year, and each furnishes $2000. May 1, A furnishes $1000 more; June 1, B furnishes $1500 and C withdraws $500; Oct. 1, A withdraws $500, and B and C furnish $1000 each. Having gained $3000, at the close of the year the partnership is dissolved. What is each partner's share of the gain?

70. How many gallons of wine at 6, 10, 15, and 20s. per gal. may be taken to form a mixture of 95 gallons worth 12s. per gallon?

71. Find the difference in time due to a difference of 17° 20' 40" in longitude.

72. The difference in the time of two places is 3 h. 18 m. 15 sec.; what is the difference in longitude?

73. A merchant bought a number of bales of velvet, each containing 12917 yd., at the rate of $7 for 5 yd., and sold them out at the rate of $11 for 7 yd., and gained $200 by the bargains; how many bales were there? Ans. 9.

74. The trans-Atlantic telegraph laid in 1857 from St. Johns, Newfoundland, to Valentia, Ireland, 1640 miles in a straight line, consisted of 7 copper wires, twisted together, imbedded in gutta percha, and surrounded by 18 bundles of iron wire. Each bundle of iron wire consisted of 7 wires which were twisted together, and the bundles ran spirally round the cable. Now, to allow for deviations from a straight course, inequalities of the seabottom, etc., suppose the cable was 143 times as long as would be required for a straight course, and that it was necessary to increase the wire 1 mile in every 20 in consequence of twisting the wires, and 1 mile in every 24 because of the bundles running spirally, what length of wire was required for the cable? Ans. 362906 miles.

75. By the census of 1860, the number of inhabitants of Alabama was 964296; of Arkansas, 435427; of California, 380016; of Connecticut, 460151; of Delaware, 112218; of Florida, 140439; of Georgia, 1057329; of Illinois, 1711753; of Indiana, 1350941; of Iowa, 674948; of Kansas, 107110; of Kentucky, 1155713; of Louisiana, 709290; of Maine, 628276; of Maryland, 687034; of Massachusetts, 1231065; of Michigan, 749112; of Minnesota, 172022; of Mississippi, 791396; of Missouri, 1182317; of New Hampshire, 326072; of New Jersey, 672031, of New York, 3880735; of North Carolina, 992667; of Ohio, 2339599; of Oregon, 52464; of Pennsylvania, 2906370; of Rhode Island, 174621; of South Carolina, 703812; of Tennessee, 1109847; of Texas, 602432; of Vermont, 315116; of Virginia, 1596079; of Wisconsin, 775873; of the District of Columbia, 75076; and of the Territories, 220143; what was the population of the United States in 1860? Ans. 31443790.

THE METRIC SYSTEM OF WEIGHTS AND
MEASURES.

403. Besides the Weights and Measures in common use, which are contained in the several tables in Articles 94-107, the Weights and Measures of the Metric System need explana

tion.

In this System the scales are all decimal, like that of United States money.

LONG MEASURE.

404. The principal unit of length is the Meter, which is 39.37 inches long.

1=10=100 = 1,000 = 10,000 = 100,000 = 1,000,000

NOTE 1. About twenty-five (more exactly 25.4) millimeters make one inch. The meter is about three feet, three inches, and three eighths of an inch, which may be remembered as the rule of the three threes.

NOTE 2. The kilometer is the common unit for road measure, and is about two hundred rods, or five eighths of a mile. Five meters make about one rod.

403. What of all the scales in the Metric System? 404. The principal unit of length? Length of the meter? Table? Scale? How many millimeters to an inh? Common unit for road measure?

The accompanying scale exhibits one decimeter divided into ten centimeters, each centimeter being divided into ten millimeters. With it is a four inch scale divided into eighths of an inch.

These measures, as well as all the other metric measures and weights, are written like whole numbers and decimals. Thus, 3 kilometers, 8 hectometers, 7 meters, and 5 decimeters, are written 3807.5m. Large distances, as in road measure, are given as kilometers and decimals. Thus, 47.34km stands for 4 myriameters, 7 kilometers, 3 hectometers, and 4 dekameters. Small distances are usually expressed in millimeters, or in centimeters.

The names of the several larger units of length are formed from the word Meter, by prefixing Myria for 10,000, Kilo for 1000, Hecto for 100, and Deka for 10. The smaller units are denoted by Deci for To, Centi for Too, and Milli forro. In the same way, as will be seen hereafter, are formed the names of weights and of measures of surface and capacity.

NOTE 1. The first series of prefixes is from

the Greek, the second from the Latin language.

NOTE 2. The terms Dime, Cent, and Mill, in United States money, for the tenth, hundredth, and thousandth parts of a dollar, are analogous to the terms Decimeter, Centimeter, and Millimeter.

405. To reduce a larger denomination in the Metric System to a smaller, or a smaller to a larger:—

Multiply or divide by 10, 100, 1000, &c., as the case may require (Art. 161).

404. How are metric measures and weights written? What prefixes indicate the larger denominations? What the smaller? 405. How is reduction performed?

406. Metric measures and weights are added, subtracted, multiplied, and divided like whole numbers and decimals.

Ex. 1. Add 7.25m, 14.056m, 1850mm, and 1.6m. Ans. 24.756m. 2. From 7km added to 1750m take 3256521mm. Ans. 5493.479m. 3. Multiply 7 kilometers 823 meters and 125 millimeters by 5.12. 7823.125m X 5.12 40054.4m, = Ans.

SQUARE MEASURE.

407. The principal units of square measure are the Are and the Square Meter. The Are is a square whose side is 10 meters, and therefore contains 100 square meters.

Sq. 1= 100= 10,000

Kilom.

1 Hectare (ha).

1 Sq. Kilometer.

Sq. Decim.
1=

100:
10,000 =

1,000,000

Sq. Centim. 100 10,000 1,000,000

100,000,000

1100 10,000 1,000,000 100,000,000 10,000,000,000

NOTE 1. The hectare, which is a common unit for land measure, is a square whose side is a hundred meters; hence it is equal to 10,000 square meters. It is 2.471 acres.

NOTE 2. Since the scale in square measure is 100 (two dimensions, 1010), there will be two figures for each denomination. Thus, 25 hectares, 7 ares, 17 centares, and 20 square decimeters, would be written 2507.172 ares, or 250717.2 square meters.

406. How are addition, subtraction, multiplication, and division performed? 407. Unit of square measure? What is an are? Table? Scale? Unit of land measure? What is a hectare? Equal to how many acres? How many figures are required for each de nomination? Why?