common denomination-the lowest denomination in either-and then

divide.

2s. 8 d. 65 half-pence.

£8 6s. 3984 half-pence.

3984 half-pence÷ 65 half-pence = 613 Ans.

400. RULE.-I. To divide a compound by an abstract number, beginning at the left, divide the numbers of the several denominations in turn.

When there is a remainder, before dividing further, reduce it to the next lower denomination, add in the given number of that denomination, if any, and making this sum the dividend continue the division.

Collect the partial quotients for the entire quotient.

II. To divide one compound number by another, reduce both to the lowest denomination in either, and divide as in simple numbers.

401.-EXAMPLES FOR PRACTICE.

1. What is the sum of Cong. 5 0.7 f 13 £36 m 43 and 0.5 f 15 m 59? What is their difference? How much is 19 times the latter number? Find of the former number. What is the sum of the four answers?

Ans. Cong. 26 0.4 f31 f 35 m 441. 2. Find of the sum of the following: 1 sq. mi. 15 sq. } rd. 15 sq. yd. 5 sq. ft. 23 sq. in.; 23 sq. yd. 15 sq. ft. 56 sq. in.; and 29 sq. rd. 19 sq. yd. 17 sq. ft.

Ans. 71 A. 22 sq. rd. 26 sq. yd. 8 sq. ft. 963 sq. in.

3. By how much does of

ceed of 3 34 gr. 17? Ans.

17 37 37 02 gr. 9 ex

3 35 36 1 gr. 251.

4. Two pieces of cloth measure together 93 yd. 1 qr. 2 nails, and one is 4 yd. 3 nails longer than the other. Required, the length of each.

5. A surveyor, measuring a road with a broken chain containing 73 links, will find its length repeated how many times in going 2 mi. 236 rd. ?

6. If a person's income is £50 8s. 84d. each calendar month, how much will it be in 4 years?

7. From March 31st to June 17th, both inclusive, a miner dug on an average 3 pwt. 17 gr. of gold a day; how much did he dig in all ? Ans. 1 lb. 2 oz. 12 pwt. 23 gr.

8. How many miles, etc., in the mean equatorial diameter of the earth, which is 41848380 ft. in length? How many in the polar diameter, which is 41708710 ft. long? What is their difference of length, in miles, etc.?

Last ans. 26 mi. 3 fur. 24 rd. 4 yd. 2 ft. 9. By how much do 12 lunar months fall short of 1 solar year? Ans. 10 da. 21 h. 15.62 sec.

10. A farmer's crop from one meadow is 5 T. 19 cwt. of hay; from another, 4 T. 3 cwt. 16 lb.; and from a third, 7 cwt. 70 lb. more than from the second. How many loads of 1 T. 5 cwt. 48 lb. will the whole make?

11. What must be the length of a bin 4 ft. wide and 6 ft. high, to receive 2 Cd. 6 cd. ft. 8 cu. ft. of pine and 15 Cd. of hickory? Ans. 99 ft.

12. Eighteen persons dig, on an average, 13 bu. 3 pk. 6 qt. 1 pt. of potatoes each. From the quantity thus dug, how many sacks, each holding 2 bu. 1pk. 3 qt. pt., can be filled? Ans. 1064 sacks. 13. How many angles of 2° 51' 25" will exactly fill the space of two right angles?

Ans. 63. 14. How much alloy must be mixed with 1 lb. 2 oz. 15 pwt. 19 gr. of pure gold, to make gold 18 carats fine? Ans. 4 oz. 18 pwt. 14 gr.

15. A mirror 16 ft. 2 in. by 8 ft. 4 in., the largest at that time in the world, was made a few years since at St. Petersburg. What would it cost to coat this mirror

with amalgam, if it would require 11⁄2 lb. of amalgam for each square yard of surface, and the amalgam cost $1.50 per pound?

16. How many plots 80 ft. wide by having an equivalent area, can be laid out 33 sq. rd. 11 sq. yd.?

Ans. $33.68. 150 ft. deep, or

from 4 A. 3 R. Ans. 18 plots.

17. H. Hudson bought of Roe & Co., of London, July 3d, 1873, 15 reams of paper, at £1 3s. 6d. a ream; 28 gross of steel-pens, at 3s. 10d. 1 far. a gross; and 3 doz. dictionaries, at 5s. 8d. apiece. Make out and receipt Hudson's bill. Ans. £33 5s. 2 far. 18. A silversmith, having on hand 1 lb. 10 oz. 3 pwt. 15 gr. of silver, bought 3 times as much more, and then melted up some old scraps weighing 7 oz. 19 pwt. 18 gr. How much was left of the whole, after making up from it 3 dozen spoons weighing 1 oz. 4 pwt. 5 gr. each ?

Ans. 4 lb. 5 oz. 2 pwt. 18 gr.

19. From a cask containing 34 gal. 1 qt. 1 pt. of vinegar, there leaked out 3 qt.gi. A pail holding 2 gal. 2 qt. 1 pt. 1.25 gi. was filled eight times from what remained; how many times would what was then left in the cask fill a half-gallon measure? Ans. 241 times.

20. Light moving 185000 miles in a second, how long before a flash of lightning would reach the eye from a cloud 3 mi. 80 rd. distant?

21. A person having a quarter-section of land, laid off from it three farms, each containing 20 A. 3 R. 24 sq. rd., and divided the rest into seven equal parts. What was

the area of each of these parts?

22. In the coinage of Great Britain, 24 pennies are made out of 1 lb. avoir. of copper. How many drams avoir. in 1 penny, and how many grains Troy? How many pennies will 6 oz. Troy of copper make?

23. What is the difference of capacity between 5 bins,

each containing 3 cu. yd. 26 cu. ft. 15933 cu. in., and 1 rectangular bin, 7 yd. long, 2 yd. 1 ft. 6 in. wide, and 14 in. high? Ans. 13 cu. yd. 4 cu. ft. 14893 cu. in. 24. How much pure silver is there in 25 lb. 4 oz. 3 pwt. 15 gr. of silver alloyed for coinage at the Philadelphia mint? Ans. 22 lb. 9 oz. 15 pwt. 63 gr.

25. A and B, leaving the same point, walk in opposite directions, A averaging 3 mi. 1 fur. 20 rd. 6 yd. 2 ft. 6 in. an hour, and B averaging a furlong in 2 min. 20§ sec. far apart are they at the end of 4 hours?

How

Ans. 25 mi. 4 fur. 20 rd. 5 yd. 1 ft.

26. A clock loses a second every hour and a half. If it is right at 20 min. past noon on the 1st of May, on what day and at what hour, etc., will it be ten minutes Ans. June 8th, 20 min. 20 sec. after 12, A. M. How much too slow will it be at noon, July 4th?

slow?

27. Allowing 1.15 statute miles to 1 geographical mile, how much less than a nautical league is the sum of 1 stat. mile 5 rd. 3 yd. 2 ft., 6 fur. 4 yd. 9 in., 1 rd. 5 yd. 3 in., and 2 fur. 4 yd. 2 ft. ?

Difference of Time and Longitude.

402. Latitude and Longitude.—The position of places on the earth's surface is determined by their Latitude and Longitude.

Latitude is distance north or south from the equator, -that is, from the great circle that runs round the earth midway between the poles. It is expressed in degrees (up to 90), minutes, and seconds.

Longitude is distance east or west of some given meridian; in this country, it is reckoned from the meridian of Greenwich (near London) or of Washing

ton. It is expressed in degrees (up to 180), minutes,

403. Difference of Longitude.-When two places are both in east, or both in west, longitude, their difference of longitude is found by subtracting; when one is in east and the other in west longitude, by adding.

This is apparent from the diagram. The difference of longitude between the points C and D, both on the same side of the meridian of Greenwich, would be found by subtracting C's longitude from D's; whereas the difference of longitude between C and F would clearly be the sum of their several distances from the meridian.

So of latitude. How would the difference of latitude between two places both north, or both south, of the equator, be found? How can we find the difference of latitude between two points like D and Q, one north of the equator and the other south of it?

404. Difference of Time.-The earth turns on its axis from west to east. Places east of a given point are, therefore, brought within sight of the sun before that point is, and consequently have their noon-that is,