43. How many seconds have elapsed from the Christian era to the beginning of 1853?

44. In what time would sound travel from the earth to the moon, the distance being 240000 miles, and sound moving about 1143 feet per second?

45. How long would it take a cannon ball, at the velocity of 1960 feet per second, to travel from the earth to the sun, the distance being 95 millions of miles ?

46. The piston of a steam engine moves at the rate of 240 feet per minute. What is the rate in miles, per day of 16 hours? 47. If 7 yds. 3 qrs. of cloth make a suit of clothes, how many suits can be made from 24 pieces, each of 45 yards?

48. How many times does a clock, which strikes the hours and quarters, strike, between noon on the 20th of June, and midnight on the 31st of December, of the same year?

49. An indolent youth loses 8 minutes per hour. How much time will he lose from August 12th to December 17th, reckoning 10 hours work per day?

50. A wheel is 5 yards in circumference. How long is that part of the circumference which measures 48° 24'?

51. If a person counts 80 sovereigns per minute for 15 hours each day, in how many days will he count a million?

52. How many canisters of tea can be filled out of 8 cwt. 2 qrs., the canisters holding respectively 2 lbs., lb., lb., and there being the same number of each?

ADDITION OF COMPOUND QUANTITIES.

237. Little need be said upon the principles of performing the fundamental operations of compound quantities; references to the corresponding operations of simple quantities will suffice. The former differ from the latter in this, that the subdivisions of the unit are not uniform, as they do not follow the decimal system.

238. A owes to B £564. 2s. 73d.; to C, £324. 16s. 11d.;

to D, £216. 14s. 104d.; and to E, £949. 15s. 6d. How much does he owe in all?

Having written the numbers under each other, taking care that the units of the same kind are under each other, begin by adding together the farthings, which amount to 7f., or lad., set down the under the farthings; the sum of the pence with the 1 penny resulting from the addition of the farthings, is 35 pence, or 2s. 11d., set down 11d. under the pence; the sum of the shillings, with the 2s. resulting from the addition of pence, is 49 shillings, or £2. 9s., the 9s. are set down under the shillings, and the £2 carried to pounds, the sum of which is £2055.

The same method of proof may be employed as for simple `addition.

When the quantities are of any other sort, the same method is followed. The tables render the process easy.

239. EXERCISES.

1. Find the sum of £3489. 11s. 63d.; £267. 7s. 74d; £5671. 14s. 10d.; £367. 19s. 114d.; and £1304. 19s. 11 d. 2. The expenses of building a house were: surveyor, £340; bricklayer, £5696 17s. 4d.; mason, £2740. 16s. 7d.; carpenter, £4169. 17s. Od.; plumber, £1565. 15s. 3d.; glazier, £473. 10s. 6d.; painter, £375. 18s. 6d.; paper-hanger, £124. 1s. 4d.; and locksmith, £275. 19s. 8d. What did the house cost?

3. The distance from A to B is 24 mi. 7 fur. 20 p.; from B to C, 35 mi. 4 fur. 28 po. 3 yds.; from C to D, 47 mi. 6 fur. 31 po. 4 yds.; from D to E, 15 mi. 3 fur. 16 po. 2 yds. What is the distance between A and E ?

4. Of five pieces of timber, the first contains 3 cub. yds. 24 ft 416 in.; the second, 5 cub. yds. 16 ft. 94 in.; the third, 4 cub. yds. 18 ft. 1014 in.; the fourth, 2 cub. yds. 12 ft. 96 in.; and the fifth, 3 cub. yds. 10 ft. 184 in. How many cubic yards, &c., are there in all ?

5. What is the weight of 6 bales of cotton, weighing respectively 5 cwt. 3 qrs. 19 lbs. ; 7 cwt. 0 qrs. 16 lbs.; 3 cwt. 2 qrs. 24 lbs.; 5 cwt. 2 qrs. 18 lbs. ; 6 cwt. 1 qr. 10 lbs. ; and 4 cwt. 3 qrs. 25 lbs. ?

6. How many yards are contained in 3 pieces of cloth, the first of which contains 542 yds. 3 qrs. 3 nls. ; the second, 643 yds. 3 qrs. 2 nls.; and the third, 576 yds. 1 qr. 3 nls.?

7. An apothecary weighs several parcels of drugs: one weighs 17 lbs. 7 oz. 2 scr. 17 grs.; another, 14 lbs. 10 oz. 8 dr. 1 scr. 15 grs.; another, 11 lbs. 9 oz. 5 dr. 1 scr. 19 grs. ; another, 21 lbs. 10 oz. 6 dr. 2 scr. 10 grs.; and another, 16 lbs. 8 oz. 6 drs. 2 scr. 16 grs. What is the weight of the whole?

8. A was born on the 24th of November, 1845, and died when 8 yrs. 6 mo. 11 days old. What was the exact date of his death?

9. B was born at 58 minutes after 5 p.m., April 14th, 1820, and lived 27 yrs. 10 mo. 22 days 22 hrs. 46 min. When did he die ?

10. A farmer has sown 23 bu. 1 pk. 4 gals. 4 pts. of corn; 13 bu. 0 pk. 6 gals. 3 pts. of oats; 12 bu. 1 pk. 5 gals. 6 pts. of rye. How much corn has he sown altogether?

11. A jeweller used 1 lb. 10 oz. 18 dwts. 21 grs. of silver for the manufacture of a piece of plate; for a second piece, 1 lb. 8 oz. 16 dwts.; and for a third, 1 lb. 9 oz. 14 dwts. 20 grs. How much silver was used?

12. A landowner, possessing 216 ac. 3 ro. 32 po. of land, bought two fields, one of which contained 15 ac. 2 ro. 31 po., and the other 19 ac. 3 ro. 32 po. How much land has he at present?

SUBTRACTION OF COMPOUND QUANTITIES.

240. The subtraction of compound quantities is performed by subtracting the units of the same kind from each other; and the principle laid down in simple subtraction is equally true here.

From £576. 16s. 91d. subtract £267. 18s. 10 d.

These quantities are written under one another, thus:

As cannot be taken from, add 1d. to both quantities, it does not alter the difference, and we have from leaves, which is set down under the farthings; 1d.+10 make 11d., now since 11d. cannot be subtracted from 9d., to each quantity 1s. is added, and we take 11d. from 9d.+12d., or 21d., the difference is 10d., which is set down under the pence; 1s.+18s., or 19s., subtracted from 16s., cannot be effected, £1 is added to each quantity, and 19s. taken from 16s.+20s., or 36s., leaves 17s., which is set down under the shillings; now, £1+£7, or £8, taken from £6 cannot be done, but by adding 1 tens to each quantity, we have £8 from £6+£10, or £16 leaves £8; and 6 tens +1 tens, or 7 tens, leaves 0 tens; 2 hundreds taken from 5 hundreds leaves 3 hundreds. Thus, the whole difference is £308. 17s. 104d.

The operation explained is represented below:

The proof is the same as in simple subtraction.

241. The same method is applied for the subtraction of quantities in the tables.

6. From a sugar loaf, weighing 5 stones 11 lbs. 13 oz., a grocer sold 2 stones 12 lbs. 14 oz. How much had he left?

7. I am 54 yrs. 7 mo. 18 days old, and my son is 28 yrs. 8 mo. 26 days old. What was my age at my son's birth?

8. A man is 6 ft. 2 in. in height; another is 83 in. shorter. What is the height of the latter?

9. Charles XII. was born January 27th, 1682, and died Dec. 11th, 1718. How old was he at his death?

10. B died 35 min. after 5 o'clock p.m., on March 7th, 1853, when he was 17 yrs. 10 mo. 21 days 43 min. old. he born?

When was

11. A man received the following sums: £369. 14s. 7d., £564. 17s. 8d., £273. 19s. 6d. ; and paid the following debts £176. 18s. 2d., and £144. 13s. 8d. How much has he left?

12. Four towns are represented by A, B, C, and D respectively; a man travels from A to B in 7 hrs. 20 min. 30 sec.; from B to C in 11 hrs. 14 min. 38 sec.; from A to D in 34 hrs. 36 min. 40 sec. How long will it take him to go from B to D, and from C to D?

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13. A man being asked the age of his daughter, said, I am yrs. 3 mo. old; my wife is 45 yrs. 5 mo. 15 days old; and my daughter's age is 77 yrs. 5 mo. 8 days less than the sum of her parents'. Find her age.

14. A landowner has two farms, one of 740 ac. 3 ro. 30 pl. and the other of 675 ac. 2 ro. 24 pl.; from the first he sells 245 ac. 3 ro. 36 pl., and from the second 396 ac. 3 ro. 30 pl. How much land has he left?

15. A bankrupt owes to A £135. 17s. 8d., to B £196. 11s. 6d., to C £214. 16s. 8d., to D £144. 17s. 8d. At the time, he has in cash, £123. 9s. 6d.; in wares, £53. 11s. 4d.; in