6. Baltimore is 76° 37′ west, and Berlin is 13° 23′ 45′′ east longitude. When it is 9 o'clock A. M. at Baltimore, what time is it at Berlin?

363. To find the difference in longitude between two places when the difference in time is given.

1. The difference in time between two places is 4 hr. 15 min. What is the difference in longitude?

25 sec.

EXPLANATION.-Since there are 15 times as many degrees, minutes, and seconds of longitude as there are hours, minutes, and seconds of time, 15 times 4 hr. 15 min. 25 sec., is the difference in degrees, minutes, and seconds of longitude. Hence, the difference in longi

RULE.-Multiply the difference of time expressed in hours, minutes, and seconds, by 15. The result will be the difference of longitude respectively in degrees, minutes, and seconds.

EXAMPLES.

2. The difference in time between two places is 5 hr. 13 min. What is their difference in longitude?

17 sec.

3. The difference of time between Denver, Colo., and Greenwich is 6 hr. 59 min. 47.6 sec. What is the longitude of Denver?

4. If the exact difference in time between Chicago and Washington is 42 min. 15 sec., what is their difference in longitude?

5. When the solar time in San Francisco is 10 min. past 6 o'clock P. M., the solar time in Calcutta is 13 min. 3 sec. past 8 o'clock A. M. If the longitude of San Francisco is 122° 26' 15" west, what is the longitude of Calcutta?

6. The difference in time Cuba, is 5 hr. 29 min. 26 sec.

between Greenwich and Havana, What is the longitude of Cuba?

7. The difference in time between New York and Astoria, Ore., is about 3 hr. 19 min. 25 sec. The longitude of New York is 74° 3' west. What is the longitude of Astoria?

8. Yokohama, Japan, time is about 7 hr. 17 min. 26 sec. faster than St. Petersburg time. The longitude of the latter city is 30° 19' east. What is the longitude of Yokohama ?

9. A captain of a vessel finds on observation that by solar time it is 9 A. M., but by his chronometer, Greenwich time, it is 10 min. past 12 o'clock P. M. What is the longitude of his ship?

METRIC SYSTEM OF WEIGHTS AND MEASURES.

364. The Metric System is a decimal system of denominate numbers, which has for its basis a certain unit of measure called the meter.

1. The length of the meter was originally intended to be one ten, millionth part of a quadrant of the earth's circumference, or of the distance from either pole to the equator; but later calculations have shown the meter to be a very little less than that.

2. The system derives its name from the meter, because all the units of measure in the system are derived from it.

365. The Primary Units of the metric system are the following:

366. Lower Denominations than the primary units are denoted by prefixing the following from the Latin: milli (10 of a primary unit); centi (1 of a primary unit); deci ( of a primary unit).

367. Higher Denominations than the primary units are denoted by prefixing the following from the Greek: deka (10 primary units); hekto (100 primary units); kilo (1000 primary units); myria (10000 primary units).

1. In the prefixes deka and hekto, the letter k is usually changed to c; as decameter, hectometer, decaliter, etc.

2. The Metric System of weights and measures is based wholly upon the decimal method of notation. All the divisions and multiples are by 10. This is so great an improvement upon the old methods that it has been adopted or legalized by most of the civilized nations of the world. It is authorized by law in the United States.

368. The following tables give all the denominations, but many of them are not in common use. Those usually employed in business or science are printed in bold-faced type.

369. Abbreviations beginning with small letters indicate divisions of the unit; those beginning with capital letters denote multiples of the unit.

MEASURES OF LENGTH, SURFACE AND VOLUME.

METRIC TABLES.

MEASUREMENTS OF LENGTH.

159

370. The unit of length is the meter. It equals 39.37079 inches, or about 3.28 feet.

1. The meter is a little over 3 feet 3 inches and 3-tenths of an inch in

length.

2. The 5-cent piece is about of a meter in diameter, or 2 centimeters.

MEASURES OF SURFACE.

371. The unit of surface is the square meter. It equals about 1.196 square yards.

In measuring land, the square meter is called a centâre (ca), the square decameter an are (a) and the square hectometer a hectare (Ha). The hectare equals very nearly 24 acres, and is the metric denomination commonly employed in expressing the quantity of land in farms.

MEASURES OF VOLUME.

372. The unit of volume is the cubic meter. It equals 35.317 cubic feet, or 1.308 cubic yards, or .2759 cord.

TABLE.

cm).

1000 Cu. Millimeters (cu mm) 1 Cu. Centimeter (cu cm)

1000 Cu. Centimeters

1000 Cu. Decimeters

a decistere, etc.

In measuring wood the cubic meter is called a stêre (3), † of a cubic meter

MEASURES OF CAPACITY.

373. The unit of capacity in both liquid and dry measure is the liter. It is a cylinder whose volume is equal to that of a cube whose edge is a decimeter. The liter equals .9081 qt., dry measure, or 1.05673 qt., liquid measure.

In measuring grains, fruits, vegetables, etc., the hectoliter, like the bushel, is used for measuring large quantities, and the decaliter, liter, or deciliter for small quantities.

MEASURES OF WEIGHT.

374. The unit of weight is the gram. It is the weight of a cubic centimeter of distilled water in a vacuum, and at its greatest density. The gram equals 15.4324874 Troy grains.

1. The equivalents in ounces and pounds are Avoirdupois.

2. The tonneau, like our ton, is used to express the weight of very large qnantities; the kilogram (generally abbreviated to kilo) like our pound, to express the weight of moderate quantities; and the gram, and centigram, like our pennyweight and grain, to express the weight of minute quantities, such as precious jewels, medicines, etc.; the milligram for exceedingly minute quantities.

3. The silver dollar weighs about 26 grams; the dime about 21 grams; and the five-cent piece, called the nickel, 5 grams.

NOTATION AND NUMERATION.

375. In the Metric System any quantity, except surfaces and solids, is written according to the decimal system by placing the decimal point between the unit and its divisions, making each denomination occupy that order of the decimal scale which is denoted by its prefix.

Thus, 5g 7Dg 68 4dg 8mg are written 576.4088, or 576.408 grams.

376. A metric quantity is commonly read like any other decimal; but the fractional part may be read as an integer of the denomination of its right-hand order.

Thus 576.4088, instead of being read 5Hg 7Dg 6o 4de 8mg, is commonly read 576 and 408 thousandths grams. It may also be read 576 grams and 408 milligrams.

377. In the Metric System surfaces are based upon the scale of 100, and solids upon the scale of 1000. Hence each denomination of these measures must occupy as many decimal places as there are O's in the scale of its measure.

Thus, 158qm 68q dm are written 15.068qm; and 87cu m 9cu dm 150u cm 135cu mm are written 87.009015135cu m

EXERCISES.

378. 1. Copy and read the expression 325.164.

EXPLANATION.-The expression is read 325 and 164 thousandths meters; or 325 meters and 164 millimeters; or 3Hm 2Dm 5m 1dm 6cm 4mm

Copy and read the following metric quantities :

14. Write 7Dm 6m 13cm as a mixed decimal of meters.

15. Write 41 5D1 21 3d as a mixed decimal of liters.

16. Write 7Kg 8He 6DE 58 4mg as a mixed decimal of grams.

19. Write 78 8Kg 6Dg 40g 5mg as a mixed decimal of grams. sq cm 16891 20. Write 75sqm 13sq dm 24sq sq mm decimeters.

as a mixed decimal of square