The value of 240 yards, etc., at any number of pence per yard, etc., is evidently an equal number of pounds, and consequently the value of the same number at any fraction of a penny gives the same fraction of a pound.

Therefore, according to this mode of calculation, the number of pence in the price being reckoned as so many pounds (that is, the value of 240), is to be multiplied by whatever number of times 240 may be contained in the given number of the quantity to be valued, and then the valuation of the remainder is to be made in dozens or scores, and in odd yards and fractions.

III. FOR THE VALUATION OF CWT. QRS. AND LB. AT 20s. PER CWT.

RULE.-Reckon every cwt. as £1, every quarter as 5s., and double the number of the lb. as pence; with the addition of 1d. for every 7 lb., and 14-100ths of a penny for each remaining lb. At 20s. per cwt., or 15d. for 7 lb., 1 lb. is worth 2 1-7d., or 2 pence and 14-100ths of a penny. The addition of 1 or 2 extra 100ths is made in order to allow for the remaining fraction of 2-7ths of 1-100th in the value of each pound at 20s. per cwt.

If great precision is required, there may be 1 part or 1-100th added in for 2, 3, 4, or 5 lb., and 2 parts or 2-100ths for 6 lb.

Example 4.

To find the amount of 73 cwt. 1 qr. 17 lb. at 47s. 6d.

This valuation as 20s. per cwt. is thus made: 73 cwt. give £73, twice 17d. with 2d. (because there are 2 seven pounds in 17 lb.) give 36d., or 3s., which with 5s. for 1 qr. give 8s.; and as there are 3 lb. above the 2 sevens, 14 lb., we add 3 times 14 parts, with 1 more (making 43) and obtain, for the amount, the above valuation, £73 8s. 0.43d.

or

IV. FOR THE VALUATION OF TONS CWT. QRS. AND LB. AT 20S. PER TON.

RULE.-Reckon every ton as £1, every cwt. as 1s., every qr. as 3d., and every 7 lb. as d.; then multiply by the £s and parts of a £.

Example 5.

To find the amount of 37 tons 17 cwt. 3 qrs. 14 lb. at £24 10s. per ton.

N.B.-When the lb. are given otherwise than in 7 lb., 14 lb., or 21 lb., the preceding rule for the cwt. may be used, if the shillings in the price per ton make a fraction of a £, for which a corresponding fraction can be taken of а shilling, thus:

3 tons 13 cwt. 1 qr. 17 lb. at £47 10s. per ton, are

73 cwt. 1 qr. 17 lb. at 47s. 6d. per cwt.

1 Otherwise the extra pounds may be valued at 20s. per ton, which is at the rate of 107, or 107-1000ths of a penny per ib.

V.-FOR VALUATION OF Oz. DWTS. AND GRAINS TROY AT 20S. PER OZ.

RULE.-Reckon every oz. as £1, every dwt. as ls., and half the number of grains as so many pence.

Example 6.

To find the value of 341 oz. 11 dwts. 17 grains of gold, at £3 17s. 10 d. per oz.

VI.-FOR FINDING THE AMOUNT OF A RATE PER £.

RULE.—Take the given sum as the amount at 20s., take parts of 20s. for the given rate.

Example 7.

To find the amount of £679 9s. 4d. at 4s. 101d. per £.

and

VII.-FOR FINDING THE AMOUNTS OF RATES PER CENT.

RULE 1.—Take parts for the rate out of the given amount. RULE 2.-Multiply the variable term of the rate expressed in pounds by the number of hundreds of pounds in the given sum, and take parts for the remainder of the sum out of £100.

RULE 3.-Multiply the given sum by the variable term of the rate, and divide the product by 100.

Example 8.

To find the amount of £649 at 83 per cent.

Or take 10 per cent., and subtract 1-8th for 11 per cent., producing 83 per cent.

The student is to observe that, in rates per cent. without any valuations being given, the two terms are of the same kind or value: thus 83 per cent. may be 8 of a £ out of £100, or 8 s. out of 100s.; and so with any other matter of weight, measure, or quantity, as 8 yards out of 100 yards, or 8 things out of 100 things; but when a value is given to the variable part of the rate in money, the words "per cent." always mean to be out of £100; as 12s. 6d. per cent. means 12s. 6d. out of £100. In any other case both terms of the rate are valued.

Example 9.

To find the amount of £652 10s. at 651 per cent.

To find the amount of £1,187 10s. 6d. at 123 per cent.

CHAPTER XXIV.

GOVERNMENT STOCKS.

CASE 1.

To find the cost or the net proceeds of Government stocks. RULE. Find the value of the stock by one of the rules in page 393 supra, and add 1-8th per cent. for brokerage upon buying, or subtract the same upon selling.

The brokerage is on the amount of stock, and not on its

value.