NOTE. We divide the sum of the signs, in these questions, by 12, and write down the remainder, because it is Circular Motion.

SECTION XI.

COMPOUND SUBTRACTION.

COMPOUND SUBTRACTION teaches to find the difference between two numbers of different denominations.

RULE.

Write the smaller compounil number under the greater, in the order of the different denominations, as pounds under pounds, shillings under shillings, &c. Begin with the lowest denomination and subtract each lower number from the one above it, and write the difference underneath. If, in any denomination, the lower number be greater than the one above it, add to the upper number the number required of this denomination to make one of the next higher; and, from the number thus obtained, subtract the lower number and set down the remainder underneath. Carry one to the next denomination in the subtrahend, and proceed in like manner with the subtraction, till the operation has been performed in all the columns, setting down the entire difference between the upper and lower numbers of the highest denomination, and the result will be the difference required.

NOTE. The reason for increasing the number of the minuend by the number required of a lower denomination to make one of the next higher, is precisely the same as that for which we add ten to a figure of the minuend, in Simple Subtraction. In both cases we add the number denoting the ratio between the denomination in question, and the next higher number of the minuend. In Simple Subtraction, the ratio of increase from right to left being uniformly tenfold, we add ten, while in the case of farthings, pence, and shillings, we add 4, 12, and 20.

NOTE..

As half a foot is equal to 6 inches, we add them to the 5 inches, which make 11 inches. The same principle is adopted in the 14th, 15th, and 16th examples.

1. What is the sum of 16. 5s. 8d. 2qr. 31£. 16s. 1ld. 3qr.-21. 11s. 1qr. — 19£. Os. 10d. 3qr.- 13£. 13s. 7d. 3qr. and 28£. 17s. 5d. 1qr.? Ans. 131£. 5s. 84d.

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

Ans. 20£. 17s. 10d.

3. Bought a silver tankard, weighing 1lb. 8oz. 17dwt. 14gr., a silver can, weighing 1lb. 2oz. 12dwt., a porringer, weighing 11oz. 19dwt. 20gr., and three dozen of spoons, weighing 1lb. 9oz. 15dwt. 10gr.; what was the whole weight?

Ans. 5lb. 9oz. 4dwt. 20gr. 4. What is the weight of a mixture of 3lb 43 23 29 14gr. of aloe, 2lb 73 63 19 13gr. of picra, and 1tb 103 13 29 17gr. of saffron ? Ans. 7b 103 33 19 4gr. 29 14gr.; 13 73 63 19 13gr. ;

5. Add 32lb 93 13 and 16b 113 73 19 12gr. together.

Ans. 631b 43 73 29 19gr. 6. Sold 4 loads of hay; the first weighed 27cwt. 3qr. 18lb.; second, 31cwt. 1qr. 15lb.; third, 19cwt. 1qr. 15lb.; and fourth, 38cwt. 2qr. 27lb.; what is the weight of the whole ?

Ans. 117cwt. 1qr. 19lb.

7. Bought 5 pieces of broadcloth; the first contained 17yd. 3qr. 2na.; second, 13yd. 2qr. 1na.; the third, 87yd. 1qr. 3na.; the fourth, 27yd. 1qr. 2na.; and the fifth, 29yd. 1qr. 2na.; what was the whole quantity purchased?

Ans. 175yd. 2qr. 2na.

8. A pedestrian travelled, the first week, 371m. 3fur. 37rd. 5yd. 2ft. 10in.; the second week, 289m. 2fur. 18rd. 3yd. 1ft. 9in.; and the third week he travelled 399m. 7fur. 3ft. 11in.; how many miles will he have travelled?

Ans. 1060m. 5fur. 16rd. 5yd. 1ft. 9. A man has 3 farms; the first contains 186A. 3R. 14p.;