These words correspond to the 12 months of the year, and the first lether in each word marks the day of the week on which each cor-i responding month comes in; whence any other day may be easily found. For example, let it be required to find on what day of the week the 4th of July falis, in the year 1827, the Dominical letter for which year is G. Good answers to July; consequently, July coines in on a Sunday; wherefore the 4th day of July falls on Wednesday. Note. There are tiro Dominical letters in leap years, one for January and February, and another for the rest of the year.

65. Supposing your age to be 15 y. 19 d. 11 h. 37 m. 45 s., how many seconds old are you, allowing 365 days 6 hours to the year?

66. Reduce 475047465 seconds to years.

68. Reduce 325440 minutes to

67. How many minutes from the 1st day of January to the 14th days. day of August, inclusively?

69. How many minutes from

70. In 4079160 minutes, how

the commencement of the war many years?
between America and England,
April 19th, 1775, to the settle-
ment of a general peace, which
took place January 20th, 1783?

CIRCULAR MEASURE, OR MOTION.

Circular measure is used in reckoning latitude and longitude; also in computing the revolution of the earth and other planets round the sun. The denominations are circles, signs, degrees, minutes, and seconds.

Note. Every circle, whether great or small, is divisible into 360

equal parts, called degrees.

71. Reduce 9 s. 13° 25′ to 72. In 1020300", how many seconds.

degrees?

The following are denominations of things not included in the Tables:

6 points make 1 line, 12 lines

1 inch,

used in measuring the length of the rods of clock pendulums.

1 hand, used in measuring the height of horses.

. 1 fathom, used in measuring depths at sea.

in

1. What is reduction? 2. Of how many varieties is reduction? 3. What is understood by different denominations, as of money, weight, measure, &c.? 4. How are high denominations brought into lower? 5. How are low denominations brought into higher? 6. What are the denominations of English money? 7. What is the use of Troy weight, and what are the denominations? 8. avoirdupois weight? the denominations? 9. What distinetion do you make between gross and net weight? 10. What distinctions do you make between long, square, and cubic measure? 11. What are the denominations in long measure? 12. square measure? 13. in cubic measure? 14. How do you multiply by? 15. When the divisor contains a fraction, how do you proceed? 16. How is the superficial contents of a square figure found? 17. How is the solid contents of any body found in cubic measure? 18. How many solid or cubic feet of wood make a cord? 19. What is understood by a cord foot? 20. How many such feet make a cord? 21. What are the denominations of dry measure? 22. of wine measure? 23. of time? 24. of circular measure? 25. For what is circular measure used? 26. How many rods in length is Gunter's chain? of how many links does it consist? how many links make a rod? 27. How many rods in a mile? 28. How many square rods in an acre? 29. How many pounds make 1 cwt. ?

EXERCISES.

1. In 46 £. 4 s., how many dollars?

Ans. $154.

2. In 36 guineas, how many crowns, at 6 s. 7 d. each? Ans. 153 crowns, and 9 d. 3. How many rings, each weighing 5 pwt. 7 grs., may be made of 3 lb. 5 oz. 16 pwt. 2 grs. of gold?

Ans. 158. 4. Suppose West Boston bridge to be 212 rods in length, how many times will a chaise wheel, 18 feet 6 inches in circumference, turn round in passing over it? Ans. 189 18 times. 5. In 470 boxes of sugar, each 26 lb., how many cwt.? 222 6. In 10 lb. of silver, how many spoons, each weighing 5 oz. 10 pwt.?

7. How many shingles, each covering a space 4 inches one way and 6 inches the other, would it take to cover 1 square foot? How many to cover a roof 40 feet long, and 24 wide? (See 25.) Ans. to the last, 5760 shingles.

6*

8. How many cords of wood in a pile 26 feet long, 4 feet wide, and 6 feet high? Ans. 4 cords, and 7 cord feet. 9. There is a room 18 feet in length, 16 feet in width, and 8 feet in height; how many rolls of paper, 2 feet wide, and containing 11 yards in each roll, will it take to cover the walls? Ans. 816. 10. How many cord feet in a load of wood 6 feet long, 2 feet wide, and 5 feet high? Ans. 4 cord feet. 11. If a ship sail 7 miles an hour, how far will she sail, at that rate, in 3 w. 4 d. 16 h.?

66

12. A merchant sold 12 hhds. of brandy, at $2'75 a gallon; how much did each hogshead come to, and to how much did the whole

amount?

13. How much cloth, at 7 s. a yard, may be bought for 29 £. I s.? 14. A goldsmith sold a tankard for 10 £. 8 s. at the rate of 5 s. 4 d. per ounce; how much did it weigh?

15. An ingot of gold weighs 2 lb. 8 oz. 16 pwt.; how much is it worth at 3 d. per pwt.?

16. At 2018 a pound, what will T. 2 cwt. 3 qrs. 16 lb. of lead

come to ?

17. Reduce 14445 ells Flemish to ells English.

18. There is a house, the roof of which is 44 feet in length, and 20 feet in width, on each of the two sides; if 3 shingles in width cover one foot in length, how many shingles will it take to lay one course on this roof; if 3 courses make one foot, how many courses will there be on one side of the roof? how many shingles will it take to cover one side? to cover both sides?

Ans. 16020 shingles. 19. How many steps, of 30 inches each, must a man take in travelling 54 miles?'

20. How many seconds of time would a person redeem in 40 years, by rising each morning hour earlier than he now does?

21. If a man lay up 4 shillings each day, Sundays excepted, how many dollars would he lay up in 45 years?'

22. If 9 candles are made from 1 pound of tallow, how many dozen can be made from 24 pounds and 10 ounces?

23. If one pound of wool make 60 knots of yarn, how many skeins, of ten knots each, may be spun from 4 pounds 6 ounces of wool?

ADDITION OF COMPOUND NUMBERS.

T 29. 1. A boy bought a knife for 9 pence, and a comb for 3 pence; how much did he give for both? Ans. I shilling. 2. A boy gave 2 s. 6 d. for a slate, and 4 s. 6 d. for a book; how much did he give for both?

3. Bought one book for 1 s. 6 d., another for 2 s. 3 d., another for 7 d.; how much did they all cost? Ans. 4 s. 4 d.

4. How many galtons are 2 qts. + 3 qts. +1 qt.?

5. How many gallons are 3 qts. +2 qts. +1 qt. +3 qts. + 2 qts.?

6. How many shillings are 2 d. + 3 d. + 5 d. + 6 d. 7 d. ?

7. How many pence are 1 qr.+ 2 grs. + 3 qrs. +2 qrs. + 1 qr. ?

8. How many pounds are 4 s. + 10 s. + 15 s. + 1 s.? 9. How many minutes are 30 sec. +45 sec. + 20 sec.? 10. How many hours are 40 min. +25 min. +6 min.? 11. How many days are 4 h. +8 h. +10 h. +20 h.? 12. How many yards in length are 1 f.+2 f. 1 f.? 13. How many feet are 4 in. +8 in. +10 in. + 2 in. +1 in. ? 14. How much is the amount of 1 yd. 2 ft. 6 in. +2 yds. 1 ft. 8 in. ?

15. What is the amount of 2 s. 6d. 4 s. 3 d. 7 s. 8d.?

16. A man has two bottles, which he wishes to fill with wine; one will contain 2 gal. 3 qts. 1 pt., and the other 3 qts.; how much wine can he put in them?

17. A man bought a horse for 15 £. 14 s. 6 d., a pair of oxen for 20 £. 2s. 8 d., and a cow for 5 £. 6 s. 4 d.; what did he pay for all?

When the numbers are large, it will be most convenient to write them down, placing those of the same kind, or denomination, directly under each other, and beginning with those of the least value, to add up each kind separately.

OPERATION.
£. 8. d.
15 14 6
20. 2 8
5 6 4

Ans. 41 3 6

=

In this example, adding up the column of pence, we find the amount to be 18 pence, which being 1 s. 6 d., it is plain, that we may write down the 6 d. under the column of pence, and reserve the 1 s. to be added in with the other shillings.

Next, adding up the column of shillings, together with the 1 s. which we reserved, we find the amount to be 23 s. 1 £. 3s. Setting the 3 s. under its own column, we add the 1 £. with the other pounds, and, finding the amount to be 41 £., we write it down, and the work is done.

Ans. 41 £. 3 s. 6 d.

Note. It will be recollected, that, to reduce a lower into a higher denomination, we divide by the number which it takes of the lower to make one of the higher denomination. In addition, this is usually called carrying for that number: thus, between pence and shillings, we carry for 12, and between shillings and pounds, for 20, &c.

The above process may be given in the form of a general RULE for the Addition of Compound Numbers:

I. Write the numbers to be added so that those of the same denomination may stand directly under each other.

II. Add together the numbers in the column of the lowest denomination, and carry for that number which it takes of the same to make one of the next higher denomination. Proceed in this manner with all the denominations, till you come to the last, whose amount is written as in simple numbers.

Proof. The same as in addition of simple numbers.

Bought a silver tankard, weighing 2 lb. 3 oz., a silver cup, weighing 3 oz. 10 pwt., and a silver thimble, weighing 2 pwt. 13 grs.; what was the weight of the whole?

A man bought 5 loads of hay, weighing as follows, viz. 23 cwt. (1 T. 3 cwt.) 2 qrs. 17 lb. ; 21 cwt. 1 qr. 16 lb.; 19 cwt. 0 qr. 24 lb. ; 24 cwt. 3 qrs.; 11 cwt. 0 qr. 1 lb.; how many tons in the whole?

There are four pieces of cloth, which measure as follows, viz. 36 yds. 2 qrs. 1 na.; 18 yds. 1 qr. 2 na; 46 yds. 3 qrs. 3 na.; 12 yds. 0 qr. 2 na.; how many yards in the whole?