A stone is 14 pounds: 8 stones, a hundredweight.

"

All ordinary articles are weighed by this weight, which is known as the imperial standard, and is in universal use in this country.

Gold, silver, and precious stones, are weighed by troy weight. In determining the purity of gold, the gold is supposed to be divided into 24 carats, and if pure, is said to be 24 carats fine; if there be 23 carats of. pure. gold, and 1 of alloy, it is said to be 23 carats fine; and so on.

The ounce and pound are the same as in the troy weight. This weight is used only in preparing medicines.

For smaller lengths than an inch, eighths and sixteenths of an inch, also tenths, are used.

This is the ordinary measure for dimensions of all kinds. Distances are measured by miles: depth by fathoms: the height of horses by hands. The chain used for measuring land = 66 feet, and consists of 100 links, each of them 7.92 inches.

The yard in this measure is of the same length as that in Lineal Measure.

36 square yards are 1 rood of building: 100 square feet, 1 square of flooring: 2724 square feet, 1 rood of Bricklayer's work: 10,000 square links, 1 square chain: 10 square chains, l'acre.

Superficial measure refers to breadth as well as length. For instance, a superficial foot, usually called a square foot, is either a square of a foot in length and a foot in breadth-in other words, a foot each way-or it is any dimension in which the length multiplied by the breadth will form a foot, or 12 inches, each way: thus, 12 times 12 inches 144 inches, is a square foot; or 6 times 24 inches 144, is also a square foot. Sometimes the term square feet is confounded with that of feet square, which is quite a different thing. A piece of cloth said to measure six square feet, consists of six squares of a foot each; but a piece said to measure six feet square would be six feet along each side, and comprise thirty-six squares of a foot each. Inattention to these distinctions has often led to awkward errors and disputes.

It will now be understood, that the square of any number is that number multiplied by itself; thus-the square of 3 is 3 times 3, or nine; the square of 4 is 16; and so on. On this principle is formed the table of square measure, for the measurement of breadth and length: it is commonly used for measuring land, walls, &c.

40 Cubic feet of rough timber, or 50 of hewn timber, is a load.

Solid measure is computed by multiplying the length by the breadth, and the product by the thickness. This measure is used in calculating the solid contents of masses of earth, &c.; in measuring the holds of vessels, to ascertain the tonnage; and in all cases where length, breadth, and thickness are reckoned.

A hogshead (hhd.) contains 63 gallons. A pipe is 2 hogsheads, and 2 pipes form a tun. But in trade these measurements are not rigidly adhered to, as casks differ in capacity. 1 gill = 5 oz. avoirdupois of water, or about 83 cubic inches. All liquids are measured by this table.

The gallon is the same as in Liquid Measure. By this table, grain, seeds, flour, &c., are measured.

The year is also divided into 12 Calendar Months; namely

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1 week.

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1 ordinary year.

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1 solar year.

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1 leap year.

The number of days in each month may be easily remembered from the following well-known lines:

:

Thirty days have September,
April, June, and November;
All the rest have thirty-one,

Excepting February alone,

Which hath but twenty-eight days clear,
And twenty-nine in each leap-year.

As the true solar year is nearly 6 hours more than 365 days, every fourth year, termed leap-year, is reckoned as consisting of 366 days, in order to make allowance for the excess; the additional day being given to February.

To ascertain if a given year is leap-year, divide it by 4, and if there is no remainder, it is leap-year; if there be a remainder, the number over indicates how many years it is after leap-year. Thus, 1852 is leap-year, because divisible by 4 without a remainder; and 1854 is two years after leap-year, because there is a remainder of 2, after dividing it.

C

The degree is divided into 60 minutes (marked'), and the minute into 60 seconds (marked "). This measure is used for geographical purposes, and in reckoning distances at sea. At the equator, a degree of longitude is 693 imperial miles.

In Scotland, a quire consists of 24 sheets of folio paper, but of 48 sheets of quarto and octavo size.

TERMS FOR LEASES, ETC.

5 to 7 cwt.

"

sugar

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When a Scottish Term falls on Sunday, the Monday following is considered Term-day.

Lammas
Martinmas

February 2
May
August

15

REDUCTION.

REDUCTION is the method of converting sums in Compound Numbers from a higher to a lower denomination, or from a lower to a higher; as, for instance, from pence to pounds, or from pounds to pence. The calculations are made by means of the preceding Arithmetical Tables, which shew how many pence there are in a certain number of pounds, or pounds in a certain number of pence; the number of feet in so many yards, or yards in so many feet; and so on.

I. TO CONVERT NUMBERS FROM A HIGHER TO A LOWER DENOMINATION.

RULE.-1. Multiply the highest denomination in the given sum, by the number of times that the next lower denomination is contained in one of the higher, adding to the product any of the lower denomination in the given sum: thus-to convert £3, 15s. Od. into shillings, multiply the 3 pounds by 20, the number of shillings in a pound, and add the 15s. to the product, making in all 75s.

2. If the reduction is to be carried further, convert this product into the next lower denomination, by multiplying, &c., in a similar way: thus-to convert 75s. 3d. into pence, multiply the 75s. by 12, the number of pence in a shilling, adding the 3d. to the product, making 903 pence; and so on with each denomination, till the whole has been reduced to the lowest given term.

Example 1.-Reduce £4 to shillings.

£4

20

80 shillings.
12

960 pence.

Here there being 20 shillings in one pound, we multiply by 20; the answer is 80 shillings, which is the number contained in £4. If it should be required further to reduce the shillings to pence, we multiply 80 by 12, as there are 12 pence in one shilling; the result is 960, which is the number of pence in 80 shillings, or £4.

Example 2.-Reduce £3, 14s. 74d. to farthings.

£ S. d.
14 74

20

74 shillings.
12

895 pence.
4

3581 farthings.

Here the pounds are brought first to shillings, then the shillings to pence, and the pence to farthings; and as, besides the £3, there are 14s. 74d., these are to be added at the successive reductions: in multiplying the pounds by 20, we include the 14s., making 74 shillings; multiplying these again by 12, we include the 7d., making 895 pence, and these are reduced to farthings by multiplying by 4, and including the 1, making 3581 farthings.

NOTE. To convert guineas into pounds, multiply the number of guineas by 21, as there are 21 shillings in a guinea, and divide the product by 20, the number of shillings in a pound.