801. The following Table is of great use in facilitating calculations where the quantity is an even number of tens or of hundreds. Note. It will easily be seen that the above might have been calcuJated mentally, and set down in one line. The same observation will apply to these other examples. £. s. d. at 0 4 32 6. 870 at 1 0 13 27. 590 at 2 at 0 11 68. 680 at 1 803. To divide pounds, shillings, and pence mentally. 804. To divide pounds, shillings, and pence, by 100. The hundreds in the pounds give the pounds, of the tens and 20 units, give the shillings, because = ; if 1, 2, 3, or 4 100, 5 remain, they are 240 480 720 960 of a penny respec tively, the shillings and pence must be reduced to farthings, to which add the remainder from the pence, and the sum divided by 100 will give the farthings. See paragraphs 395-6. Divide 36721. 12s. 4d. by 100*| Divide 36841. 3s. 4d. by 100 In reducing shillings to farthings, call every shilling 50 farthings, and deduct 2 for every shilling from the amount, viz : 12s. ⇒ 600 24 576. 805. To divide by 200. Each figure in the place of hundreds in the pounds is 10s., each in the place of tens is 1s., each in the place of units is 1d., 10s. = jd., 6s, 8d. = 4d., &c. Note. Dividing by 200 gives per cent. 806. To divide by 400. Each figure in the place of hundreds is 5s., in the place of tens it is 6d., and in the units place it is ĝd. Note. Dividing by 400 gives a per cent. 807. To divide by 800. Each figure in the place of hundreds is 2s. 6d., in the place of tens it is 3d., and in the place of units it is d. Note. Dividing by 800 gives per cent. 808. EXAMPLES. 1. Divide 36741. 5s. by 100. 2. Divide 78601. 4s. by 200. 3. Divide 89671. 5s. by 400. 4. Divide 368971. 6s. by 200. 5. Divide 3684961. by 800. 6. Divide 5874921. by 200. 7. Divide 5874921. by 100. 8. Divide. 5874921. by 400. How many lbs. 809. To reduce cwts., qrs., and lbs. into lbs. in 2 cwt. 2 qrs. 5 lbs. As 112 lbs. is 1 çwt. 200+ (2 × 12) =2242 cwt. 56lb. 2 qrs. Therefore 224 + 56 + 5 = 285 lbs. 810. To find the value of a compound quantity. As 5s. is of a pound, if we multiply quarters of a cwt. by 5s. we have their amount at 20s. per cwt.; and as 1lb. is of a quarter, and 24d. is of 5s., if we multiply the pounds by 2 we have their amount in pence at 20s. Therefore, if we multiply the cwts. by 1, the quarters by 5, and the lbs. by 24, we have the amount at 20s. per cwt. Acres, roods, and perches may be calculated on the same principle 1 rood = of an acre, 1 perch of a rood, 5s. = ≥ of a £., l¿d. = 4 of 5s: Troy weight may be calculated by the same plan: 1 dwt. of an ounce, 1 gr. of a dwt., ls. ʊ of a £, 4d. = 2 of a shilling. 5. 85 27 at 2 5 0? 6. 12 oz. 8 dwt. 6 gr. of silver at 4s. 9d. per oz. ? 7. 6 16 20 gold at 41. 811. To find the price of a quart or pint, having the price of a hogshead given, or vice versa. 63 X 4 = 252 the number of quarts in a gallon. 252d.guinea. Therefore I'd. per quart is 11. Is. per hogshead. 4s. 48d. per quart 48 guineas 501. 8s. per hhd. 3s. 6d. 42d. 42 441. 2s. CHAPTER XXIX. INVOLUTION, OR THE RAISING OF POWERS. 812. Involution is the multiplication of a quantity into itself a certain number of times, as 6 X 6 36, which is called the second power or square of 6, 6 X 6 X 6 = 216, which is called the third power, or cube of 6, &c. So far as involution of quantities expressed in whole numbers is concerned, the matter has already been so fully treated of in paragraphs 124, 221, 443 to 455, 463, 485, 486, 493, and 494, that nothing further need be added. It is simply the act of multiplication, and a very easy affair; but when the question to be involved is expressed by a mixed number, or by a fraction, it is then a different matter, and requires some explanation. |