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These are the denominations of Troy Weight when used for weighing gold, silver, and precious stones (except diamonds). But Troy Weight is also used by Apothecaries in compounding medicines, and by them the ounce is divided into 8 drams, and the dram into 3 scruples, so that the latter is equal to 20 grains.

For scientific purposes the grain only is used; and sets of weights are constructed in decimal progression from 10,000 grains downwards to of a grain.

By comparing the number of grains in the Avoirdupois and Troy pound and ounce respectively, it appears that the Troy pound is less than the Avoirdupois, in the proportion of 144 to 175; but the Troy ounce is greater than the Avoirdupois, in the proportion of 192 to 175.

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The carat, used for weighing diamonds, is 3 grains. express the fineness of gold, has a relative meaning only.

The term, however, when used to Every mass of alloyed gold is supposed to be divided into 24 equal parts: thus the standard for coin is 22 carats fine; that is, it consists of 22 parts of pure gold and 2 parts of alloy. What is called the new standard, used for watch cases, &c. is 18 carats fine.

5. ANGULAR MEASURE; OR, DIVISIONS OF THE CIRCLE.

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Formerly, the subdivisions were carried on by sixties; thus, the second was divided into 60 thirds, the third into 60 fourths, &c. At present, the second is more generally divided decimally into 10ths, 100ths, &c. The degree is frequently so divided.

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365 Days, 5 Hours, 48 M. 45 Seconds

In 400 years, 97 are leap years, and 303 common.

= 1 Hour.

= 1 Day.

= 1 Week.

1 Lunar Month.

= 1 Calendar Month.

1 Year.

= 1 Common Year.

= 1 Leap Year.

1 Julian Year.

1 Solar Year.

The same remark, as in the case of angular measure, applies to the mode of subdividing the second of time.

COMPARISON OF MEASURES.

The old ale gallon contained 282 cubic inches.

The old wine gallon contained 231 cubic inches.

The old Winchester bushel contained 21503 cubic inches.
The imperial gallon contains 277-274 cubic inches.

The corn bushel, eight times the above.

Hence, with respect to Ale, Wine, and Corn, will be expedient to possess a

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N.B. For reducing the prices, these numbers must all be reversed.

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24 Cubic feet of sand, or 18 cubic feet of earth, or 17 cubic feet of clay, make 1 ton.

1 Yard cube of solid gravel or earth contains 18 heaped bushels before digging, and 27 heaped bushels when dug.

27 Heaped bushels make 1 load.

FRENCH AND ENGLISH WEIGHTS AND MEASURES COMPARED.

The following is a comparative Table of the Weights and Measures of England and France, which was published by the Royal and Central Society of Agriculture of Paris, in the Annuaire for 1829, and founded on a Report made by Mr. Mathieu, to the Royal Academy of Sciences of France, on the bill passed the 17th of May, 1824, relative to the Weights and Measures termed Imperial," which are now used in Great Britain.

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I. When the Numbers are to be reduced from a Higher Denomination to a Lower : MULTIPLY the number in the highest denomination by as many of the next lower as make an integer, or 1, in that higher; to this product add the number, if any, which was in this lower denomination before, and set down the amount. Reduce this amount in like manner, by multiplying it by as many of the next lower as make an integer of this, taking in the odd parts of this lower, as before. And so proceed through all the denominations to the lowest; so shall the number last found be the value of all the numbers which are in the higher denominations, taken together *.

EXAMPLE.

1. In 12347 15s 7d, how many farthings?

£ S d

1234 15 7

20

24695 Shillings.

12

296347 Pence.

4

Answer 1185388 Farthings.

II. When the Numbers are to be reduced from a Lower Denomination to a Higher: DIVIDE the given number by as many of that denomination as make 1 of the next higher, and set down what remains, as well as the quotient.

Divide the quotient by as many of this denomination as make one of the next higher; setting down the new quotient, and remainder, as before.

Proceed in the same manner through all the denominations to the highest; and the quotient last found, together with the several remainders, if any, will be of the same value as the first number proposed.

*The reason of this rule is very evident; for pounds are brought into shillings by multiplying them by 20; shillings into pence, by multiplying them by 12; and pence into farthings, by multiplying by 4; and the reverse of this rule by division. And the like, it is evident, will be true in the reduction of numbers consisting of any denominations whatever.

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