11. A merchant bought 4 barrels of potash of the following weights, viz.: 1st, 3cwt. 2qr. Olb. 12oz. 3dr.; 2d, 4cwt. 1qr. 21lb. 4oz.; 3d, 4cwt; 4th, 4cut. Oqr. 2lb. 15oz. 15dr.: what was the entire weight of the four barrels ?

19. There are 4 fields, the 1st contains 12A. 2R. 38P. ; the 2d, 4A. 1R. 26P.; the 3d, 85A. OR. 19P.; and the 4th, 57A. 1R. 2P.: how many acres in the four fields?

NOTE. Since 12 signs make a circumference of a circle, we write down only the excess over exact 12's.

APPLICATIONS IN ADDITION.

1. Add 46lb. 9oz. 15pwt. 16gr., 87lb. 10oz. 6pwt. 14gr., 100lb. 10oz 10pwt. 10gr., and 56lb. 3pwt. 6gr. together.

2. What is the weight of forty-six pounds, eight ounces, thirteen pennyweights, fourteen grains; ninety-seven pounds, three ounces; and one hundred pounds, five ounces, ten pennyweights and thirteen grains?

3. Add the following together: 29T. 16cwt. 1gr. 14lb. 12oz. 9dr., 18cwt. 3qr. 1lb., 50T. 3qr 4oz., and 2T. 1qr. 14dr.

4. What is the weight of 39 T. 10cwt. 2qr. 2lb. 15oz. 12dr., 17cwt. 6lb., 12cwt. 3qr., and 2qr. 8lb. 9dr.?

5. What is the sum of the following: 314A. 2R. 39P. 200sq. ft. 136sq. in., 16A. 1R. 20P. 10sq. ft., 3R. 36P. and 4A. 1R. 16P.?

6. What is the solid content of 64tons 33ft. 800in., Itons 1200in., 25ft., 700in., and 95tons 31ft. 1500in.

7. Add together, 96bu. 3pk. 2qt. 1pt., 46bu. 3pk. 1qt. lpt., 2pk. 1qt. 1pt. and 23bu. 3pk. 4qt. 1pt.

8. What is the area of the four following pieces of land; the first containing 20A. 3R. 15P. 250sq. ft. 1168q. in.; the second, 194. 1R. 39P.; the third, 2R. 10P. 60sq. ft.; and the fourth, 54. 6P. 50sq. in.?

9. A farmer raised from one field 37bu. 1pk. 3qt. of wheat; from a second, 41bu. 2pk. 5qt. of barley; from a third, 35bu. 1pk. 3qt. of rye; from a fourth, 43bu. 3pk. 1qt. of oats; how much grain did he raise in all?

10. A grocer received an invoice of 4hhd. of sugar; the first weighed 11cwt. 15lb.; the second, 12cwt. 3qr. 15lb.; the third, 9cwt. 1qr. 167b.; the fourth, 12cwt. 1qr.: how much did the four weigh?

11. A lady purchased 32yds. 3qrs. of sheeting; 31yds. 1qr. of shirting; 14yds. 2qrs. of linen; and 6yds. 2qrs. of cambric: what was the whole number of yards purchased?

12. Purchased a silver teapot weighing 23oz. 17pwt. 11gr.; a sugar bowl, weighing 8oz. 13pwt. 19gr.; a cream pitcher, weighing 5oz. 11gr.: what was the weight of the whole?

13. A stage goes one day, 87m. 6fur. 24rd.? the next, 75m. 3fur. 17rd.; the third, 80m. fur. 10rd.; the fourth, 78m. 5fur.: how far does it go in the four days?

14. Bought three pieces of land; the first contained 17 acres 1R. 35rd.; the second, 36 acres 2R. 21rd.; and the third, 46 acres ÓR. 37rd.: how much land did I purchase?

SUBTRACTION OF DENOMINATE NUMBERS.

120. The difference between two denominate numbers is such a number as added to the less will give the greater. SUBTRACTION is the operation of finding this difference.

1. What is the difference between £27 16s 8d and £19 17s. 9d.?

OPERATION.

£27

20 12

16s. 8d.

19

17 9

7 18 11

ANALYSIS.-We cannot take 9d. from 8d.; we therefore add to the upper number as many units as are contained in the scale, and at the same time add 1, mentally, to the next higher denomination of the subtrahend. We then say, 9 from 20 leaves 11. Then, as we cannot subtract 18 from 16, we add 20 and say, 18 from 36 leaves 18. Now, as we have taken 1 pound=20 shillings, from the pounds, and added it to the shillings, there are but 26 pounds left. We may then say, 19 from 26 leaves 7, or 20 from 27 leaves 7. The latter is the easiest in practice.

The first step is called borrowing, the second, carrying : hence,

RULE.-I. Set down the less number under the greater, placing units of the same value in the same column.

II. Begin with the lowest denomination, and subtract as in simple numbers, borrowing and carrying for each operation according to the scale.

PROOF.-The same as in simple numbers.

TIME BETWEEN DATES.

121. To find the time between any two dates.

1. What time elapsed between July 5th, 1848, and August 8th., 1850?

NOTE. In the first date, the number of the year is 1848; the number of the month 7, and the number of the day, 5. In the second date, the number of the year is 1850, the number of the month 8, and the number of the day, 8.

Hence, to find the time between two dates:

OPERATION.

yr. mo. da. 1850 8 8 1848 7 5

2 1 3

Write the numbers of the earlier date under those of the later, and subtract according to the preceding rule.

NOTE.-1. In finding the difference between dates, as in casting interest, the month is regarded as the twelfth part of a year, and as containing 30 days.

2. The civil day begins and ends at 12 o'clock at night.

2. What is the difference of time between March 2d, 1847, and July 4th, 1856?

3. What is the difference of time between April 28th, 1834, and February 3d, 1856?

4. What time elapsed between November 29th, 1836, and January 2d, 1854 ?

120. What is the difference between two denominate numbers? Give the rule for subtraction. How do you prove subtraction?

121. Give the rule for finding the difference between two dates. How is the month reckoned? At what time does a civil day begin?