and the proof is the same as that of Article (23).

Examples for Practice.

(1) Add together £73. 2s. 94d.; £25. 8s. 42d.; £68. 3s. 11d.; £76. 17s. 7d., and £5. 14s. 5 d. and prove the result.

(2) Find the sum of 32cwt. 2qrs. 15lbs. 12oz.; 47cwt. 25lbs. 7oz.; 5cwt. 3qrs. 17lbs. 10oz.; 23cwt. 1qr. 19lbs. 15oz.; lcwt. 2qrs. 10lbs. 8oz., and 9cwt. 3qrs. 14oz, and prove it.

(3) Required the sum of 11yds. 2ft. 9in.; 46yds. 1ft. sin.; 15yds. 1ft. 10in.; 38yds. 2ft. 9in.; 55yds. 11in., and 27yds. 2ft. 7in.: and prove it.

(4) Collect into one quantity, 49gals. 3qts. 1pt. ; 34gals. 1qt.; 25gals. 1pt.; 51gals. 3qts. 1pt.; 30gals. 1qt., and 53 gals. 2qts. 1pt.: and prove it.

(5) Determine the aggregate of 10wks. 5days. 14hrs. 31min.; 18wks. 4days. 12hrs. 38min.; 25wks. 10hrs. 14min.; 75wks. 6days. 23hrs. 59min.; 53wks. 4days. 19hrs. 23min., and 40wks. 17hrs. 25min.: and prove it.

(6) Add together 64lbs. 11oz. 16dwts. 14grs.; 21lbs. 10oz. 12dwts. 13grs.; 2lbs. 1dwt. 16grs.; 12lbs. 10oz. 18grs.; 24lbs. 11oz. 12dwts., and 14lbs. 1oz. 1gr. and prove the result.

(7) Find the sum of 11oz. 4drs. 2scrs. 11grs.; 10oz. 3drs. 4grs.; 11oz. 1scr. 14grs.; 10oz. 1scr. 16grs.; 2drs. 2scrs. 18grs, and 14oz. 5drs. 1scr.: and prove it.

(8) Express in one sum, 21yds. 2qrs. 3nls.; 18yds. 2qrs. 2nls.; 21yds. 1qr. 2nls.; 16yds. 3qrs. 2nls.; 12yds. 1qr. 2nls., and 14yds. 2qrs. 3nls.

(9) Find the sum of 32lea. 2mi. 1fur. 21po.; 16lea. 1mi. 3fur. 26po.; 18lea. 2mi. 6fur. 21po.; 13lea. 1mi. 2fur. 12po., and 26lea. 1mi. 4fur. 9po.

(10) Find the sum of 21ac. 1ro. 34po.; 16ac. 2ro. 27po.; 214ac. 1ro. 2po.; 32ac. 1ro. 28po., and 301ac. 14po.

II. COMPOUND SUBTRACTION.

61. RULE. Having properly arranged the quantities under one another, begin at the right hand and take each number in the lower line from the corresponding one in the upper, borrowing instead of 10, when necessary, the numbers which connect the successive denominations; and the several quantities thus obtained will be the remainder or difference.

Ex. Subtract 35yds. 2ft. 8in., from 48yds. 1ft. 4in.

and the proof used for integers is applicable here.

Examples for Practice.

(1) Find the difference of £325. 19s. 4 d. and £253. 18s. 6d. and prove it.

(2) Required the excess of 59tons. 13cwt. 2qrs. 23lbs. 11oz. 10drs. above 27tons. 17cwt. 1qr. 25lbs. 2oz. 14drs.; and verify the result.

(3) Subtract 82lea. 2mi. 5fur. 38po. from 281lea. 1mi. 7fur. 26po.; and verify it.

(4) Find the difference of 140gals. 3qts. 1pt. and 240gals.; and prove it.

(5) From 24days. 14hrs. 46min. 31sec., take 4days. 21hrs. 18min. 52secs. ; and verify it.

(6) Take 14lbs. 11oz. 12dwts. 19grs. from 81lbs. 10oz. 9dwts. 18grs.

(7) Required the difference of 28lbs. 7oz. 1dr. 2scr. 4grs. and 12lbs. 8oz. 2drs, 1scr. 12grs.

(8) What is the difference between 38ac. 31po. and 21ac. 3ro. 34po. ?

(9) Subtract Itun. 3hhds. 32gals. 4pts. of wine from 2tuns. 2hhds.

(10) Required the difference of 162qrs. 1bush. 1pk. and 127qrs. 4bush. 3pks. 1gal.

III. COMPOUND MULTIPLICATION.

62. RULE. Place the multiplier under the lowest denomination of the multiplicand, and find the number of the next denomination contained in the first product : put down the remainder, if any, and carry the quotient to the second product, and repeat the process till all the denominations are multiplied.

Ex. Multiply 35gals. 3qts. 1pt. by 7.

gals. 251.0.1 the prod. qts. 3. 1 pt: gals. 6. 0 qt.

and this may be proved by reducing 35gals. 3qts. 1pt. to pints, multiplying the result by 7, and then reducing the product to gallons, &c.

When the multiplier exceeds 12, this process will be laborious, and we may use the following.

Ex. To find the product of 3days. 18hrs. 45min. by we may have either of the operations below:

da. 177. 17. 15 the prod'. da. 177. 17. 15 the prod*.

Should this method require many factors to make up the multiplier, it would be better to reduce the multiplicand to the lowest denomination contained in it, to multiply this result by the multiplier, and then to reduce the product back again.

Examples for Practice.

(1) Multiply £358. 4s. 72d. by 5 and 9.

(2) Required the products of 49cwt. 3qrs. 15lbs. by 7 and 11.

(3) Find the products of 154yds. 2ft. 10in. by 6 and 10.

(4) Multiply 58gals. 3qts. 1pt. by 8 and 12.

(5) Multiply 42wks. 5days. 23hrs. 42min. by 3 and 4.

(6) Multiply £125. 15s. 91d. by 28 and 45.
Answers: £3522. 1s. 7d., and £5660. 9s. 84d.

(7) Multiply £53. 18s. 73d. by 51 and 83.
Answers: £2750. 10s. 114d., and £4476. 7s. 74d.

(8) Multiply 17cwt. 2qrs. 19lbs. 5oz. by 36 and 73. Answers: 636cwt. 23lbs. 4oz., and 1290cwt. 9lbs.

13oz.

(9) Multiply 13lea. 2mi. 6fur. 25po. by 42 and 97. Answers: 585lea. 1mi. 6fur. 10po., and 1352lea. Imi. 2fur. 25po.

111.

(10) Multiply 15qrs. 6bush. 3pks. 1gal. by 54 and ✰

Answers: 856qrs. 3bush. 1pk., and 1760qrs. 3bush. Igal.

(11) Multiply 43days. 18hrs. 45min. by 77 and 147. Answers: 3371 days. 3hrs. 45min., and 6435days. 20hrs. 15min.

(12) Multiply 57°. 7'. 45" by 4 and 6.

Answers: 228°. 31'., and 342°. 46′. 30".

(13) What is the value of 72 reams of paper, at

13s. 8d. a ream?

Answer: £49. 4s.

(14) Find the cost of 120 ounces of silver, at 5s. 3 d. an ounce ?

Answer: £31. 17s. 6d.

(15) Find the number of yards in 40 pieces of cloth, each containing 42yds. 2qrs. 2nls.

Answer: 1705 yards.

(16) Required the price of 279cwt. at £3. 7s. 10d.

a cwt.

Answer: £946. 17s. 1d.

(17) If I spend £2. 7s. 14d. a day, how much is that in a year of 365 days?

Answer: £860. Os. 74d.

(18) What sum will purchase an estate of 2120 acres, when the price of each acre is £32. 5s. 6d. ? Answer: £68423.

(19) If each of 114 persons receive £1. 18s. 61d., what is received by them all?

Answer: £219. 13s. 9d.