NOTE.-The multiplicand may be reduced to pence, or the shillings and pence to the decimal of a pound, before multiplying; or, it may be multiplied as it stands, by the whole number, and then by the fraction.

6. What is the length of a fence which incloses a square field, each side of which is 37 rd. 7 yd. 24 ft. long?

7. The tropical or solar year is exactly 365 da. 5 h. 48 m. 49.7 sec. What time is lost in the calendar in 4 years by reckoning 365 days as one year? What time will be gained or lost in 100 years, if every fourth year be reckoned 366 days?"

Ans. Lost in 4 years, 23 h. 15 m. 18.8 sec.

Gained in one hundred years, 18 h. 37 m. 10 sec.

8. Bought of Markland & Wells, London, 2 cases Worcestershire sauce, pints, each 5 doz., at 22s. per doz.; 3 cases do., pints, each 10 doz., at 12s. per doz. The charges added were, for 5 cases, 17s. 6d. ; commission, 11s. 5d.; consul's certificate, 11s. 6d.; and a discount was allowed of £6 12s. 3d.: what was the total amount of the invoice?

9. Multiply 17 T. 5 cwt. 3 qr. 13 lb. by 18.

10. Multiply 9 lb. 3 z. 4 3. 2 9. by 7.

11. Multiply 112° 15′ 15′′ by 40.

12. How many pounds Troy are equal to 100 lbs. Avoirdu pois ?

DIVISION OF COMPOUND NUMBERS.

253. EXAMPLE. Divide 57 mi. 3 fur. 36 rd. 14 ft. 6 in. by 6.

OPERATION.

mi. fur. rd.

ft. in. 14 6

6)57 3 36

9 4 26 2

5

ANALYSIS.-Commencing with the highest denomination, we divide 57 mi. by 6, and get 9 as the quotient, with 3 remainder. Writing the 9 under the number divided, we reduce the remainder to the next lower denomination; 3 mi. = 24 fur. To this we add the 3 in the dividend, and divide their sum, obtaining the quotient 4, with 3 remaining. Continuing the division in this way to the lowest denomination, the entire quotient is found to be 9 mi. 4 fur. 26 rd. 2 ft. 5 in.

254. When the divisor is large, the work may be performed by long division; or, if it is a composite number, by dividing by its factors in succession.

EXAMPLE. Divide £437 10s. 9d. equally among 32 persons.

255. When the divisor is a mixed number, both dividend and divisor must be reduced to the same denomination as the fraction of the divisor, before dividing, But, in multiplying the dividend by the denominator of the fraction, it is not necessary to carry, as in other cases. Each denominate number may be multiplied as a simple number.

1. Divide 37 T. 1400 lb. 13 oz. by 8.

2. Divide 17 lb. 11 z. 4 3. 2 9. 7 gr. by 17.

3. Divide 18 A. 2 R. 7 rd. 3 yd. 3 ft. by 6.

4. Divide 372 da. 21 h. 134 m. by 75.

5. If 1777 acres of land be equally divided between 7 persons, how much will each receive?

6 Divide 54 lb. 10 oz. 19 pwt. 23 gr. by 91.

7. How many cords of wood are there in a pile 24 feet long, 6 feet wide, and 4 feet 6 inches high?

8. Divide 242 cu. ft. 6 cu. in. by 3.

9. Divide 48 d. 11 h. 30 m. 10 sec. by the decimal .5.

MISCELLANEOUS EXAMPLES IN COMPOUND NUMBERS.

1. Reduce 1 mile to feet.

2. How many statute miles are there in the circumference of the earth?

3. Reduce 76 ch. 14.5 1. to inches.

4. A certain tract of land is 75 ch. 3 1. long, and 18 ch. 20 1. wide: how many acres does it contain?

5. How many square feet are there in a board 14 feet long and 18 inches wide?

6. How many bricks 8 in. long, 4 in. wide, and 2 in. thick, will it take to pave a yard 16 ft. 8 in. long by 8 ft. 4 in. wide?

7. What is the value of .3 of 12 cwt.?

8. Divide 17 d. 3 h. 30 m. by 4.

9. Divide 13 S. 15° 40' by 44.

Ans. 625.

10. Suppose the temperature on a certain day at St. Petersburg to be 8° R.: what is it on the scale of Fahrenheit?

Ans. 50°. 11. If the Fahrenheit thermometer marks the temperature at 13° below zero, what will be the corresponding degree on Thermometre Centigrade? Ans. 25° below zero.

12. Suppose a clock to mark the correct time at 10 o'clock A.M. on Monday, and gain 2 seconds per hour: how much too fast will it be the next Saturday at 7 o'clock P.M.?

Ans. 4 min. 18 sec.

13. What is the difference between .025 of a ton and .6 of a pound?

14. Reduce 13s. 6d. to the decimal of £1.

15. Reduce 7 oz. 12 pwt. 16 gr. to the decimal of a pound.

16. Reduce .16 of a year of 365 days to integers of lower denominations.

17. If a horse consume 3 bushels of oats per week: how many bushels will he require from the 9th day of November to the 15th day of April in a leap-year? Ans. 79.

18. A grocer sold 2 cwt. 3 qr. of sugar, at retail, and weighed it on scales which gave oz. short of the true weight on every pound of how much money did he defraud his customers, reckoning the sugar at 15 cts. per pound? Ans. $1.33

"

19. If the wheel of a carriage be 15 ft. 6 in. in circumference, how many revolutions will it make in running a mile?

20. The velocity of sound is 1142 feet per second: how far distant is a cloud from which a flash of lightning comes 12 seconds before the thunder is heard?

THE METRIC SYSTEM.

256. The Metric System of Weights and Measures, first adopted by France, was in 1866, by Act of Congress, authorized, or made lawful in the United States. It has also been legalized in Great Britain, Spain, Belgium, Portugal, Holland, Austria, Greece, Italy, Turkey, Norway, Sweden, Switzerland, and in some of these countries exclusively adopted; and, also in Mexico, Guatemala, Venezuela, Ecuador, United States of Colombia, Brazil, Chili, San Salvador, and the Argentine Republic.

257. The cosmopolitan character of the system, and the importance of a uniform standard of weights and measures among the civilized nations, will, it is believed, in time, lead to its universal use over a large portion of the globe.

258. The Metre, or unit of length, on which the system is based, and from which its name is derived, is, or was originally intended to be, a ten-millionth part of a quadrant of the earth's circumference, or the distance from either pole to the equator. It is equal to 39.37079 United States inches.

This distance was computed from a very accurate survey of the length of an arc of the meridian ́ between Dunkirk and Barcelona, made by MM. Delambre and Mechain, and other surveys and measurements, and the metre derived from this natural base was marked by two very fine parallel lines on a platinum bar, at the temperature of the maximum density of water (or 4° Centigrade nearly), which was deposited in the national archives of France.

Investigations made since the metre was thus fixed, seem to show that it is not absolutely correct, when referred to the natural standard, being a minute fraction too small. For the standard, therefore, as now established, reference must be had to the bar on which it is preserved.