5. What time elapsed between November 8th, at 11 o'clock A.M., 1847, and December 16th, at 4 o'clock, P.M., 1850?

6. What time elapsed between October 9th, at 11 P.M., 1840, and February 6th, at 9 P.M., 1853 ?

7. Mr. Johnson was born September 6th, 1771, at 9 o'clock A.M., and his first child November 5th, 1801, at 9 o'clock P.M.: what was the difference of their ages?

APPLICATIONS IN ADDITION AND SUBTRACTION.

1. From 38mo. 2wk. 3da. Thr. 10m., take 10mo. 3wk. 2da. 10hr. 50m.

2. From 176yr. 8mo. 3wk. 4da., take 91yr. 9mo. 2wk. 6da.

3. From £3, take 3s.

4. From 2lb. take 20gr. Troy.

5. From 8b, take 1b 13 23 20.

6. From 9T., take 1T. 1cwt. 2qr. 20lb. 15oz. 14dr.

7. From 3 miles, take 3fur. 19rd.

8. The revolution commenced April 19th, 1775, and a general peace took place January 20, 1783: how long did the war continue?

9. America was discovered by Columbus, October 11, 1492: what was the length of time to July 25, 1855 ?

10. I purchased 167b. 8oz. 16pwt. 10gr. of silver, and sold 98/b. 10oz. 12pt. 19gr.: how much had I left?

11. I bought 19T. 11cwt. 2qr. 2lb. 12oz., 12dr. of old ron, and sold 17T. 13cwt. 2qr. 19lb. 14oz. 10dr.: what had I left?

12. I purchased 101 11373 20 19gr. of medicine, and sold 17 23 33 10 5gr.: how much remained unsold?

13. From 46yd. 1qr. 3na., take 42yd. 3qr. 1na. 2in.

14. Bought 7 cords of wood, and 2 cords 78 feet having been stolen, how much remained?

5. A owes B £100: what will remain due after he has

paid him £25 3s. 61d.?

16. A farmer raised 136 bushels of wheat; if he sells 49bu. 2p. 7qt. 1pt., how much will he have left?

17. From 174hhd. 10gal. 1qt. 1pt. of beer, take 86hhd. 17gals. 2qt. 1pt.

18. A farmer had 576bu. 1pk. 2qt. of wheat; he sold 139bu. 2pk. 3qt. 1pt.: how much remained unsold?

19. A merchant bought 17cwt. 2qr. 147b. of sugar, of which he sold at one time 3cwt. 2qr. 20lb.; at another 6cwt. 1qr. 5lb.: how much remained unsold?

20. Sold a merchant one quarter of beef for £2 7s. 9d.; one cheese for 9s 7d.; 20 bushels of corn for £4 10s. 11d. and 40 bushels of wheat for £19 12s. 8d. : how much did the whole come to?

21. Bought of a silversmith a teapot, weighing 3lb. 4oz. 9pwt. 21gr.; one dozen of silver spoons, weighing 2lb. 1oz. 1pwt.; 2 dishes weighing 166. 10oz. 15pwt. 16gr.: how much did the whole weigh?

22. Bought one hogshead of sugar weighing 9cwt. 3qr. 2lb. 14oz.; one barrel weighing 3cwt. 1qr. 2lb., and a second barrel weighing 3cwt. Oqr. 1lb. 4oz.: how much did the whole weigh?

23. A merchant buys two hogsheads of sugar, one weighing 8cwt. 3qr. 21lb., the other 9cwt. 2qr. 6lb.; he sells two barrels, one weighing 3cwt. 1qr. 12lb. 14oz., the other, 2cwt. 3qr. 15lb. 6oz.: how much remains on hand?

24. A man sets out upon a journey and has 200 miles to travel; the first day he traveled 9 leagues 2 miles 7 furlongs 30 rods; the second day 12 leagues 1 mile 1 furlong; the third day 14 leagues; the fourth day 15 leagues 2 miles. 5 furlongs 35 rods: how far had he then to travel?

25. A farmer has two meadows, one containing 9A. 3R. 37 P., the other contains 10A. 2R. 25P.; also three pastures, the first containing 12A. 1R. 1P.; the second con-' taining 13A. 3R., and the third 6A. 1R. 39P.: by how many acres does the pasture exceed the meadow land?

26. Supposing the Declaration of Independence to have been published at precisely 12 o'clock on the 4th of July, 1776, how much time elapsed to the 1st of January, 1833, at 25 minutes past 3, P.M.?

MULTIPLICATION OF DENOMINATE NUMBERS.

122. MULTIPLICATION of denominate numbers is the operation of multiplying a denominate number by an abstract number. 1. A tailor has 5 pieces of cloth each containing 6yd. 2qr. 3na.: how many yards are there in all?

ANALYSIS.-In all the pieces there are 5 OPERATION. times as much as there is in 1 piece.

If in

yd. qr.

na.

1 piece each denomination be taken 5 times, the result will be 5 times as great as the multiplicand. Taking each denomination 5 times, we have 30yd. 10gr. 15na.

6

2

3

5

30

10

15

3

But, instead of writing the separate products, 33 1 we begin with the lowest denomination and say, 5 times 3na. are 15na. ; divide by 4, the units of the scale, write down the remainder 3na., and reserve the quotient 3gr. for the next product. Then say, 5 times 2qr. are 10gr., to which add the 3gr. making 13qr. Then divide by 4, write down the remainder 1, and reserve the quotient 3 for the next product. Then say, 5 times 6 are 30, and 3 to carry are 33 yards: hence,

RULE.-I. Write down the denominate number and set the multiplier under the lowest denomination.

II. Multiply as in simple numbers, and in passing from one denomination to another, divide by the units of the scale, set down the remainder and carry the quotient to the next product. PROOF.-The Same as in simple numbers.

122. What is multiplication of denominate numbers? Give the rule. How do you prove multiplication?

7. A farmer has 11 bags of corn, each containing 2bu. 1pk. 3qt. how much corn in all the bags?

:

8. How much sugar in 12 barrels, each containing 3cwt. 3gr. 2lb.?

9. In 7 loads of wood, each containing 1 cord and 2 cord feet, how many cords?

10. A bond was given 21st of May, 1825, and was taken up the 12th of March, 1831; what will be the product, if the time which elapsed from the date of the bond till the day it was taken up, be multiplied by 3?

11. What is the weight of 1 dozen silver spoons, each weighing 3oz. 6pwt.?

12. What is the weight of 7 tierces of rice, each weighing 5cwt. 2qr. 161b.?

13. Bought 4 packages of medicine, each containing 3 43 63 10 16gr.: what is the weight of all?

14. How far will a man travel in 5 days at the rate of 24mi. 4fur. 4rd. per day?

15. How much land is there in 9 fields, each field containing 12A. 1R. 25P.?

16. How many yards in 9 pieces, each 29yd. 2qr. 3na.? 17. If a vessel sails 5L. 2mi. 6fur. 36rd. in one day, how far will it sail in 8 days?

18. How much water will be contained in 96 hogsheads, each containing 62gal. 1qt. 1pt. 1gi.?

NOTE.-When the multiplier is a composite number, and the factors do not exceed 12, multiply by the factors in succession. In the last example 96=12×8.

19. If one spoon weighs 3oz. 5pwt. 15gr. what is the weight of 120 spoons?

20. If a man travel 24mi. fur. 4rd. in one day, how far will he go in one month of 30 days?

21. If the earth revolve 0° 15′ of space per minute of time, how far does it revolve per hour?

22. Bought 90hhd. of sugar, each weighing 12cwt. 2qr. 11b.: what was the weight of the whole?

23. What is the cost of 18 sheep, at 5s. 91d. apiece?

24. How much molasses is contained in 25hhd. each hogshead having 61gal. 1qt. 1pt.?

25. How many yards of cloth in 36 pieces, each piece containing 25yd. 3qr.?

26. A farmer has 18 lots, and each lot contains 41A. 2R. 11P.: how many acres does he own?

27. There are three men whose mutual ages are 14 times 20yr. 5mo. 3wk. 6da.: what is the sum of their ages?

28. Bought 90hhd. of sugar, each weighing 12cwt. 2qr. 147b.; what is the weight of the whole?

29. If a vessel sail 49mi. 6fur. 8rd. in one day, how far will she sail in one month of 30 days?

30. Suppose each of 50 farmers to raise 125bu. 3pk. 6qt. of grain how much do they all raise?

:

31. If a steam ship, in crossing the Atlantic, goes 211mi. 4fur. 32rd. a day, how far will she go in 15 days?

32. If 1 horse consume 2 tons 1gr. 20lb. of hay in a winter, how much will 36 horses consume?

33. How much cloth will clothe a company of 48 men, if it takes 5yd. 3qr. 2na. to clothe one man?

NOTE. Each denomination may be multiplied by the multiplier, separately, and the results reduced and added.

DIVISION OF DENOMINATE NUMBERS.

123. DIVISION of denominate numbers is the operation of dividing a denominate number into as many equal parts as there are units in the divisor.

1. Divide £25 15s. 4d. by 8.

ANALYSIS.-We first say 8 into 25, 3 times and £1 or 208. over. Then, after adding the 158. we say, 8 into 35, 4 times and 38. over. Then, reducing the 3s. to pence and adding in the 4d., we say, 8 into 40, 5 times.

OPERATION.

8)£25 15s. 4a £3 4s. 5d.

123. What is division of denominate numbers? Give the rule for division. How do you prove division? How do you divide when the divisor is a composite number? What will be the unit of each quotient figure?