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and 1far. 1d. 2far., and 1far. 1d. 3far., and 2far. 2d. 1 far. Writing the far. under the column of farthings, we carry the 2d. to the column of pence; and add, 2d. (carried) + 1 3d., and 9d. 12d. 1s., and 11d. 1s. 11d., and 6d. = 2s. 5d., and 9d. - 3s. 2d. Writing the 2d. under the column of pence, we carry the 3s. to the column of shillings; and add, 3s. (carried) + 17s.

20s. =1£., and 19s. 1£. 198., and 11s. 2£. 10s., and 16s. 3£. 6s., and 17s. 4£. 3s. Writing the 3s. under the column of shillings, we carry the 4£. to the column of pounds, and so find the whole amount to be, as before, 147£. 38. 2d. Ifar.

The last method of operation may be rendered more concise, as it should always be in practice, by merely naming results as the adding is performed (Art. 45).

From the illustrations given, it is evident that the adding of compound numbers is like that of simple numbers, except in carrying ; which difference holds also in subtracting, multiplying, and dividing compound numbers.

RULE. — Write all the given nu so that units of the same denomination may stand in the same column.

Add as in addition of simple numbers ; and carry, from column to column, one for as many units as it takes of the denomination added to make a unit of the denomination next higher.

Proof. — The proof is the same as in addition of simple numbers.

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NOTE. — As half a mile is equal to 4 furlongs, we add them to the 1 furlong, which makes 5 furlongs. And as half a foot is equal to 6 inches, we add them to the 7 inches, which makes 13 inches; and these are equal to 1 foot 1 inch.

10. Add together 37 yd. 3qr. 3na. 2in.; 61yd. 3qr. Ina. lin.; 13yd. 2qr. 2na. 2in. ; 32yd. lqr. Ina. lin.; 61yd. 2qr. 2na. 2in.; and 22yd. lqr. 3na. Ans. 229yd. 3qr. 3na. 14in.

11. Add together 671E.E. 1qr. Ina. lin.; 161E.E. 3qr. 3na. 2in.; 617E.E. 3qr. Ina. 2in.; 178E.E. 3qr. 2na. lin.; 717 E.E. 2qr. Ina. 2in.; and 166 EE. 3qr. 2na. lin.

12. Add together 761A. 3R. 37p. 260ft. 125in.; 131A, 2R. 16p. 135ft. 112in.; 613A. 1R. 14p. 116ft. 131in.; 161A. 3R. 13p. 116ft. 123in. ; 321A. 2R. 31p. 97ft. 96in.; and 47A. 3R. 19p. 91ft. 48in.

Ans. 2038A. 1R. 13p. 2ft. 95in. 13. Add together 38A. 1R. 39p. 272ft.; 61A. 3R. 38p. 167ft.; 35A. 3R. 19p. 198ft.; 47A. 3R. 16p. 271ft.; 86A. 2R. 13p. 198ft. ; and 46A. 1R. 14p. 269ft. 14. Add together 17m. 7fur. 9ch. 3p. 241. ; 16m. 3fur. 4ch.

1p. 15l. ; 27m. 4fur. 6ch. 2p. 171. ; 18m. Gfur. 3ch. 3p. 211.; 61m. 7fur. 7 ch. 2p. 161. ; and 17m. 1fur. 8ch. 2p. 191.

Ans. 160m. Ofur. Ich. 1p. 121. 15. Required the sum of 27m. 4fur. 3ch. lp. 211.; 29m. 3fur. 1ch. 3p. 231. ; 67m. 3fur. 3ch. lp. 191. ; 21m. 7fur. 1ch. 3p. 161. ; 16m. 7fur. Ich. 3p. 131. ; and 31m. 4fur. 8ch. lp. 201.

16. Required the value of 29T. 36ft. 1279in. + 69T. 19ft. 1345in. + 67T. 18ft. 1099in. + 71T. 14ft. 1727in. + 43T. 35ft. 916in. + 53T. 17ft. 1719in.

Ans. 335T. 23ft. 1173in. 17. Add together 61C. 127ft. 1161in.; 37C. 89ft. 1711in. ; 61C. 98ft. 1336in. ; 43C. 56ft. 1678in. 91C. 119ft. 1357in. and 81C. 115ft. 1129in.

18. Required the value of 61 tuns 3hhd. 62gal. 3qt. 1pt. + 39 tuns 2hhd. 16gal. Iqt. 1pt. + 68 tuns 3hhd. 57gal. 2qt. 1pt. + 87 tuns 3hhd. 45gal. 3qt. 1pt. + 47 tuns 2hhd. 59gal. 3qt. 1pt. + 47 tuns 3hhd. 39gal. 2qt. 1pt.

Ans. 354 tuns Ohhd. 30gal. Iqt. 19. Required the value of 67 hhd. 15gal. 3qt. 1pt. + 16hhd. 16gal. 3qt. + 39hhd. 16gal. 3qt. + 47hhd. 62gal. lqt. 1pt. + 43hhd. 57gal. 3qt. + 71hhd. 61gal. 3qt. 1 pt.

20. Add together of beer measure 161 hhd. 53gal. 3qt. 1 pt. ; 371hhd. 52gal. 3qt. 1pt. ; 98hhd. 19gal. Iqt.; 47hhd. 43gal. 1qt. Opt. ; 61 hhd. 43gal. Iqt. 1 pt.; and 42hhd. 27gal. 3qt. 1 pt.

21. Find the amount of 37bu. 3pk. 5qt. lpt. + 61bu. 2pk. 7qt. 1pt. + 32bu. 3pk. 2qt. + 71bu. 1pk. 6qt. 1pt. + 61bu. 1 pk. 3qt. lpt. + 32bu. 3pk. 3qt. lpt.

Ans. 298bu. Opk. 4qt. 1 pt. 22. Required the value of 3lbu. 3pk. 3qt. + 31bu. 3pk. 1qt. + 16bu. 3pk. Iqt. + 15bu. 3pk. + 17 bu. 3pk. lqt. + 14bu. 3pk. 1qt.

23. Required the value of 57y. 11mo. 27d. 23h. 29m. 55s. + 31y. 11mo. 18d. 19h. 19m. 39s. + 46y. Imo. 23d. 17h. 28m. 56s. + 43y. 10mo. 16d. 18h. 17m. 48s. + 32y. Imo. 190. 16h. 23m. 28s. + 14y. 1mo. 29d. 21h. 28m. 16s.

Ans. 227y. 7mo. 16d. 21h. 28m. 2s. 24. Required the value of 23w. 6d. 23h. 59m. 585. + 5lw. 3d. 18h. 51m. 175. + 29w. 5d. 21h. 47m. 49s. + 28w. 4d.

23h. 56m. 18s. + 19w. Gd. 10h. 18m. 53s. + 86w. 1d. 20h. 40m. 51s.

25. Add together 4S. 29° 59' 59' ; 6S. 17° 17' 29"'; 11S. 16° 56' 58"; 9S. 13° 46' 51"; 5S. 27° 16' 42"; and 2S. 25° 17' 17".

Ans. 5S. 10° 35' 16". 26. Add together 11S. 11° 16' 51"; 6S. 6° 6' 16"; IS. 14° 56' 56''; 3S. 29° 29' 49''; 9S. 17° 18' 58"; and 6S. 13° 13' 52".

Note. — We divide the sum of the signs, in the last two questions, by 12, and write down the remainder only. Since the circumference of a circle cannot exceed 12 signs (Art. 143).

27. Bought of a London tailor a vest for 1£. 13s. 4d., a coat for 7£. 12s. 9d., pantaloons for 2£. 3s. 9d., and surtout for 9£. 8s. Od. ; what was the whole amount?

Ans. 20£. 17s. 10d. 28. Bought a silver tankard, weighing llb. 8oz. 17pwt. 14 a silver can, weighing llb. 2oz. 12pwt., a porringer, weighing 11oz. 19pwt. 20gr.; and 3 dozen of spoons, weighing llb. 9oz. 15pwt. 10gr. ; what was the whole weight?

Ans. 5lb. 9oz. 4pwt. 20 gr. 29. What is the weight of a mixture of 3lb 43 23 23 14gr. of aloe, 2 lb 73 63 13 13gr. of picra, and ilb 103 13 23 17gr. of saffron ?

Ans. 71b 103 33 13 4 gr. 30. Sold 4 loads of hay; the first weighed 27cwt. 3qr. 181b. ; the second, 31cwt. lqr. 15lb.; the third, 19cwt. lqr. 15lb. ; and the fourth, 38cwt. 2gr. 241b.; what is the weight of the whole?

31. Bought 5 pieces of broadcloth; the first contained 17yd. 3qr. 2na.; second, 13yd. 2qr. Ina.; the third, 87yd. lqr. 3na. ; the fourth, 27yd. lqr. 2na.; and the fifth, 29yd. lqr. 2na. ; what was the whole quantity purchased ?

Ans. 175yd. 2qr. 2na. 32. A pedestrian travelled, the first week, 371m. 3fur. 37rd. 5yd. 2ft. 10in.; the second week, 289m. 2fur. 18rd. 3yd. Ift. Iin.; and the third week, 399m. 7fur. 3ft. llin. ; how many miles did he travel ? Ans. 1060m. 5fur. 16rd. 5yd. 1ft.

33. A man has three farms; the first contains 186A. 3R. 14p.; the second, 286A. 17p.; and the third, 115A. 2R. ; how much do they all contain ?

Ans. 588 A. 1R. 31 p.

34. The Moon is 5S. 18° 14' 17'' east of the Sun; Jupiter is 7S. 10° 29' 28" east of the Moon; Mars is 11S. 12° 11' 56' east of Jupiter; and Herschel is 78. 18° 38' 15" east of Mars ; how far is Herschel east from the Sun ?

Ans. 7S. 29° 33' 56".

SUBTRACTION OF COMPOUND NUMBERS.

OPERATION.
£

8.

d.

146. SUBTRACTION of Compound Numbers is the process of finding the difference between two compound numbers. Ex. 1. From 617£. 11s. 8d. take 181£. 15s. 5d.

Ans. 435£. 16s. 3d. Having placed the less number un

der the greater, pence under pence, Min. 617 11 8

shillings under shillings, &c., we beSub. 181 15 5 gin with pence, thus: 5d. from 8d.

leaves 3d., which we set under the Rem. 435 16 3

column of pence. As we cannot take

15s. from 11s., we add 20s. 1£. to the 11s., making 31s., and then subtract the 15s. from it, and set the remainder, 16s., under the column of shillings. Then, having added 1£. = 20s. to the 181£., to compensate for the 20s. added to the 11s. in the minuend, we subtract the pounds as in subtraction of simple numbers, and obtain 435£. for the remainder, and as the result complete, 435£. 16s. 3d.

RULE. Write the less compound number under the greater, so that units of the same denomination shall stand in the same column.

Subtract as in subtraction of simple numbers.

If any number in the subtrahend is larger than that above it, add to the upper number as many units as make one of the next higher denomination before subtracting, and carry one to the next lower number vefore subtracting it.

Proof. The proof is the same as in simple subtraction,

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2. £

d. 87 16 3 1 19

17 91 67 18

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