(18) In 2706359 seconds, how many weeks, &c.,? and prove it.

Answer: 4wks. 3 days. 7 hrs. 45 min. 59 sec.

(19) How many degrees, &c., are of equal value with 206265 seconds? and prove the converse.

Answer: 57°. 17′ . 45′′.

(20) In 340 pistoles at 17s. 6d. each, how many pounds sterling?

Answer: £297 . 10s.

(21) How many moidores of 27s. each, are equal to 198 guineas?

Answer: 154 moidores.

(22) In 12lbs. 10oz. 15 dwts. 14grs. of silver, how many grains? and prove the result.

Answer: 74294 grains.

(23) Find how many grains there are in 18 lbs. 2 oz. 4drs. 2 scr. 12 grs; and give a proof.

Answer: 104932 grains.

(24) In 20 yds. 3 qrs. 1nl., find the number of nails; and prove it.

Answer: 333 nails.

(25) What number of acres, &c., are equal in extent to 82973 square poles?

Answer: 518 ac. 2ro. 13 po.

(26) How many pints are equivalent to 987 bar. 25 gals. 3qts. 1 pt. of ale? and prove it.

Answer: 284463 pints.

(27) Reduce 21 tuns. 3hhds. 54 gals. 2 qts. of wine to pints; and the contrary.

Answer: 44284 pints.

(28) Required the number of quarts in 356 qrs. 7bu. 2 pks. 1 gal. of corn; and prove it.

Answer: 91380 quarts.

(29) In £453. 16s. 8d., how many pieces of coin valued at 3s. 4d. each?

Answer: 2723 pieces.

(30) Find how often a rod of 2ft. 10in. in length must be applied to measure 10 miles, 140 yards.

Answer: 18783 times, and 18in. over.

(31) What number of weights of 14oz. 13drs. each, are equivalent to 25 cwt. 2qrs. 14lbs?

Answer: 3100 weights, and 1 oz. 4drs. over.

(32) How many revolutions will the wheel of a carriage, 4ft. 7 in. in circumference, make in 2 mi. 4 fur.?

Answer: 2880 revolutions.

(33) If 5oz. of silk can be spun into a thread 2 fur. 20 po. long; what weight of silk would supply a thread sufficient to reach to the moon, if the distance be 240000 miles?

Answer: 107 tons. 2cwt. 3 qrs. 12lbs.

(34) A year being equivalent to 365 days 6 hours, it is required to find the number of years, &c., in 295402874 seconds.

Answer: 9yrs. 131 days. 18 hrs. 12 min. 54 sec.

62. Keeping in mind what was said in the first article of this chapter, we need no additional enquiry to inform us that the fundamental operations on Compound Quantities must be performed as in Integers, with this difference, that instead of carrying and borrowing tens, we must do the same with the different numbers which connect their parts together: and we shall therefore merely enunciate the rule for each, at the beginning of the portion of the work appropriated to it.

I. COMPOUND ADDITION.

RULE. Arrange the quantities under one another according to their denominations: add together those of the lowest, and having found the number of the next denomination to which the sum is equivalent, put down the remainder, if any, and add this number to those of the next denomination; and repeat the process till all the quantities are disposed of.

Ex. Find the sum of 142 cwt. 1qr. 21 lbs, 78 cwt. Oqr. 14lbs., 21 cwt. 2qrs. 19lbs., and 176cwt. 1qr. 15lbs.

and the method of proof is similar to that of Simple Addition in article (23).

Examples for Practice.

(1) Add together £73. 2s. 9id.; £25. 8s. 4d.; £68. 3s. 11d.; £76. 17s. 7d. and £5. 14s. 5d, and prove the result.

Answer: £249. 7s. 21d.

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

Answer: 120cwt. 2qrs. 6lbs. 2oz.

(3) Required the sum of 11 yds. 2ft. 9in.; 46yds. 1ft. 8in.; 15yds. 1ft. 10in.; 38 yds. 2ft. 9in.; 55yds. 11in., and 27 yds. 2ft. 7 in.: and prove it.

Answer: 196 yds. 6in.

(4) Collect into one quantity 49 gals. 3qts. 1pt. ; 34 gals. 1qt.; 25 gals. 1pt.; 51 gals. 3 qts. 1pt.; 30gal. 1 qt., and 58 gals. 2 qts. 1 pt.: and prove it.

Answer: 245 gallons.

(5) Determine the aggregate of 10wks. 5 days. 14 hrs. 31 min.; 18 wks. 4days. 12hrs. 38min.; 25 wks. 10hrs. 14 min.; 75 wks. 6days. 23 hrs. 59min.; 53 wks. 4 days. 19hrs. 23min., and 40wks. 17 hrs. 25min.: and prove it. Answer: 224 wks. 2 days. 2hrs. 10min.

(6) Add together 64lbs. 11 oz. 16dwts. 14grs.; 21lbs. 10oz. 12dwts. 13 grs.; 2lbs. 1 dwt. 16grs.; 12lbs. 10oz.

18grs.; 24lbs. 11oz. 12dwts., and 14lbs. 1oz. 1gr.: and prove the result.

Answer: 140lbs. 9oz. 3dwts. 14 grs.

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

Answer: 58 oz. 1 dr. 1 scr. 3grs.

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

Answer: 105 yds. 2qrs. 2nls.

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

Answer: 108lea. 2 fur. 9po.

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

II.

Answer: 585.ac. 3ro. 25 po.

COMPOUND SUBTRACTION.

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 together; and the several quantities thus obtained will be the difference required.

Ex. Let it be required to subtract 35 yds. 2ft. 8 in., from 48 yds. 1 ft. 4in.

Reductions.
in.

in.

16 = 4 + 12 borrowed,

8

8 in.

ft.

and the proof used for integers is applicable here.

Examples for Practice.

(1) Find the difference of £325. 19s. 48d. and £253. 18s. 6: and prove it.

Answer: £72. Os. 104d.

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

Answer: 31 tons. 16cwt. 26lbs. 8 oz. 12 drs.

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

Answer: 198 lea. 2 mi. 1 fur. 28 po.

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

Answer: 99gals. 1pt.

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

Answer: 19days. 17 hrs. 27 min. 39 sec.

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

Answer: 66lbs. 10oz. 16dwts. 23 grs.

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

Answer: 15lbs. 10oz. 7drs. 12 grs. (8) What is the difference between 38 ac. 31 po. and 21 ac. 3ro. 34po.?

Answer: 16ac. 37 po.

(9) Subtract 1 tun. 3hhds. 32gals. 4pts of wine from 3 tuns. 2hhds.

Answer: 1tun. 2hhds. 30 gals. 4pts.

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

Answer: 84qrs. 4bush. 1 pk. 1 gal.

III. COMPOUND MULTIPLICATION. 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