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Multiplication of Denominate Numbers.

ART. 236.-1. Multiply 15 gal. 2 qts. 1 pt. by 5.

Process.

Analysis.—5 times 1 pt. is 5 pts., equal

to 2 qts. and 1 pt. We write 1 in the gal. qts. pts. 15 2 1 place of pts. and add 2 to the product of

5 qts. 5 times 2 qts, are 10 qts., and 2 qts. 78 0 1 added are 12 qts., equal to 3 gal. and

O qts. We write 0 in the place of qts., and add 3 to the product of gal. 5 times 15 gal. are 75 gal., and 3 gal. added are 78 gal., which we write in the place of gal.

Multiply:
2. 17 cwt. 75 lb. 11 oz. by 5.
3. 15 lb. 9 oz. 14 pwts. 18 gr. by 7.
4. 18 hhd. 33 gal. 3 qts. 1 pt. by 8.
5. 16 mo. 8 d. 18 h. 32 min. 30 sec. by 10.
6. 11 fb 8 3 6 3 2 D 16 gr. by 12.

7. How much. wood is there in 9 piles, each containing 11 O. 80 cu. ft. 23 cu. in. ?

8. If 30 gal. 3 qts. 1 pt. of water runs into a hogshead every hour and 10 gal. 2 qts. 1 pt. leaks out every hour, how much will the hogshead lack of being full at the end of three hours ?

9. If Lemuel walked 19 mi. 128 rds. 4 yds. each day for 11 days, and Humphrey averaged 19 mi. 200 rds. 3 yds. for 12 days, how much farther did Humphrey walk than Lemuel ?

10. Illustrate multiplication of denominate numbers by an original problem in square measure.

11. Illustrate the same subject by an original problem in time measure.

Division of Denominate Numbers.

ART. 287.-1. Divide 42 bush. 3 pks. 4 qts. 1 pt. by 5.

Process.

Analysis.- of 42 bush. is 8 bush., bu. pks. qts. pt. and 2 bush. remaining = 8 pks. 8 pks. 5)42 3 4 1

and 3 pks. 11 pks. ß of 11 pks. is 8 2 2 1

2 pks. and 1 pk. remaining = 8 qts. 8 qts. and 4 qts. = 12 qts. ☆ of 12 qts. is 2 qts. and 2 qts. remaining = 4 pts. 4 pts. and 1 pt. 5 pts. } of 5 pts. 1 pt.

Divide:
2. £45 16s. yd. by 4.
3. 54 lb. 11 oz. 12 pwts. 10 grs. by 5.
4. 118 T. 16 cwt. 81 lb. by 8.
5. 94 hhd. 38 gal. 3 qts. 1 pt. 3 gi. by 9.

6. If a pile of wood containing 12 cords 96 cu. ft. be equally divided among 5 persons, how much will each receive ?

7. If George picks 3 bush. 3 pks. 1 qts. of apples a day, how many days will it take him to pick 43 bush. 2 pks. 5 qts. ?

8. If 28 cwt. 16 lb. of sugar is put up in packages, each containing 2 lb. 8 oz., how many packages will there be?

9. If three boys gather daily 2 gal. 3 qts. 1 pt. of sap from each of 4 trees, how long will it take them to gather 23 hogsheads of sap ?

10. Illustrate division of denominate numbers by an original problem in cubic measure.

11. Illustrate the same subject by a problem in which the dividend and divisor are denominate numbers.

LATITUDE AND LONGITUDE.

ART. 238.-The Equator is an imaginary line, passing around the earth midway between the north and south poles.

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ART. 239.—The Latitude of a place is its distance north or south of the equator. Northward 90° from the equator is the north pole, and southward 90° from the equator is the south pole : consequently, no place on the globe can have more than 90° of latitude.

ART. 240.—A Meridian is a semi-circumference of great circle passing around the earth through the poles.

ART. 241.—The Longitude of a place is its distance east or west of a certain meridian.

ART. 242.—Latitude and longitude are reckoned in degrees, minutes and seconds.

Since 360° comprise the circumference of the earth, and since longitude is numbered both east and west from a given meridian, the greatest longitude a place can have is 180°.

The system of reckoning longitude in use in most parts of the world, is attended with great inconvenience. Our school atlases, as a rule, give the longitude from Washington at the top of the page, and that from Greenwich, in England, at the bottom. Germany, besides Greenwich, uses for her topographical maps, the longitude of Berlin ; Russia uses Greenwich, Paris, and St. Petersburg; the Netherlands employ Greenwich and Amsterdam ; France reckons from Paris only; Denmark from Copenhagen ; Spain uses San Fernando ; while Italy uses San Fernando, Turin, and Milan.

So urgent has become the need for a single prime

[graphic]

meridian for the world, that an International Conference was convened in Washington in October, 1884, for the purpose of fixing upon a meridian.

There were forty delegates present, representing Austria, Hungary, Brazil, Colombia, Costa Rica, Denmark, France, Germany, Great Britain, Guatemala, Hawaii, Italy, Japan, Mexico, Netherlands, Paraguay, Russia, San Domingo, San Salvador, Spain, Sweden and Norway, Switzerland, Turkey, Venezuela, and the United States. A resolution was adopted providing that longitude shall be counted from the meridian of Greenwich in two directions up to 180° east longitude plus, and west longitude minus.

The Conference also adopted a universal day for the purposes for which it may be found convenient. This day does not interfere with the use of local or other standard times where desirable.

This universal day is to be a mean solar day, and is to begin for all the world at the moment of mean midnight at the initial meridian. It coincides with the beginning of the civil day at that meridian, and is to be counted from zero up to twenty-four hours.

The earth turns entirely around every 24 hours, causing day and night. Since each circle contains 360 degrees, every part of the earth passes through 360 degrees in 24 hours. Hence, in 1 hour it passes through 4 of 360°, or 15o.

It follows, therefore, that if the position of the sun is noted at any moment it will be 15° farther west an hour later, appearing to descend the sky at that rate until it disappears below the horizon, to reappear later in the east and continue its ceaseless round.

Hence, for every 15o we move eastward, the time will be found 1 hour later, and the reverse prevails as we move westward.

From these facts we can readily ascertain the difference of time between two places whose longitude is given, and

can calculate the difference in longitude when the difference in time is known.

All know the inconvenience of computing time as indicated. A person traveling eastward or westward finds his watch continually too slow or too fast, even though he sets it every few miles of his journey. This is especially felt since the increased facilities in railroad traveling of the last few years, the variation in a single day amounting almost to an hour.

The Pacific steamers sailing westward are obliged to drop a day, which is “picked up” on the return. Thus, in going from San Francisco to China, one of the weeks, of necessity, contains only 6 days, while in coming back, a certain week must contain 8 days.

STANDARD TIME. ART. 243.—The great inconvenience attending the ordinary division of time led to the adoption throughout the United States in 1884 of what is known as Standard Time.

By general agreement and partial legislation, four standard meridians were selected, by which railway trains are run and local time regulated. These meridians are 15 degrees apart. On the equator they are 69.16 x 15 miles apart. There is a difference of just one hour in time from one meridian to another, since in the earth's circumference there are 360°, which divided by 24 hours gives 15 degrees to an hour.

The Eastern meridian, 75o W. from Greenwich, passes 4' west of New York City. The Central meridian, 90° W. longitude, passes near New Orleans and St. Louis. The Mountain standard meridian, 105° W. longitude, passes near Pike's Peak, Rocky Mountains. The Pacific meridian, 120° W. longitude, is near the coast, San Francisco being 92 miles west of it.

Standard time has been only partially adopted, and in

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