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In these measures and weights the principal and subordinate units are arbitrary; but, when chosen, it is necessary to have some standard of comparison by which their accuracy may be tested.

The length of a mean solar day is supposed to be invariable. This is conceived to be divided into 86,400 equal parts or seconds. The length of a pendulum which beats 86,400 times in a mean solar day, or which beats seconds, is also supposed to be invariable, the place, conditions of temperature, &c. being the same. Therefore, so long as the duration of a mean solar day, and the length of a pendulum which makes 86,400 vibrations during this portion of time, can be measured, the same constant length can be found.

The length of the seconds' pendulum, in London, has been determined with great care. This length and the length of the standard yard, previously in use, having been compared, it was found that of such equal parts or inches as the yard contains 36, the pendulum contains 39-13929. This relation supplies the means of restoring the standard yard and other standard measures, should they happen (as in 1834 when the Houses of Parliament were burnt) to be injured or destroyed.

Extension is measured by the application of a measuring rod, cord, chain, or other convenient instrument, to the thing which is measured.

The measures of surface are square inches, square feet, &c., a square inch being a square of which the side is 1 inch; a square foot, a square of which the side is 1 foot, &c.

Measures of bulk are of two kinds.

In the first kind, which is called cubic or solid measure, the object measured is considered as having length, breadth, and

thickness. The measures are cubic inches, cubic feet, &c. the cubic inch having the form of a die, the edges of which are each 1 inch in length.

In the second kind, the measure, which is called a measure of capacity, is made in the form of a hollow vessel, and the substance to be measured is placed in the measure.

The standard measure of capacity is the gallon. This is made to depend on a measure of extension -- the inch-in the following manner. An empty vessel, the interior of which is a cubic inch, is weighed. Being filled with pure water at the temperature of 62° Fah., it is weighed again. The difference between the two weights-that is, the weight of a cubic inch of water-is divided into 252-458 equal parts, of which one part is called a grain. Seven thousand of these grains make a pound avoirdupois weight: and it is required that the gallon measure shall contain precisely 10 lb. avoirdupois of such water.

Since the gallon contains 7000 × 10=70000 grains' weight of water, and I cubic inch of water weighs 252-458 grains, it follows that the capacity of the gallon is 70000÷252·458= 277-273844, or 277-274 cubic inches, nearly.

The standards of weight are two-the pound troy, and the pound avoirdupois. Both are multiples of the same elementary weight as the gallon, namely, the grain.

The standards of measures and weights, and their multiples and parts, are described by an Act of Parliament passed in 1835. By this act, also, the use of measures and weights, equivalent to these standards, was made compulsory after the 1st of January, 1836.

a. The Report of a committee of the House of Commons recommending the adoption of a decimal coinage has been mentioned. (Art. 142.) In this report are contained the following observations respecting a decimal system of weights and measures:- "The attention of your committee has been incidentally directed, in the course of their inquiries, to the advantage of applying the decimal system to weights and measures as well as to coinage. This being a question not embraced in their order of reference, your committee do not feel themselves in a position to do more than express their sense of the importance of further inquiry into that interesting subject." (p. viii.) As any reform which does not comprehend weights and measures

as well as money, must be incomplete, it is to be hoped that the committee will be reappointed with power to inquire into the whole subject.

The irregular form of a compound number, and not the absolute value of the principal unit, being the thing which requires alteration, the existing principal units should be preserved; but their multiples, or the denominations greater than the principal units, ought to be tens, hundreds, &c.; and their parts, or the denominations less than the principal units, tenths, hundredths, &c. of their respective units.

For the sake of simplicity, the principal units ought to be as few in number as possible.

The standard yard for measures of length; the square yard for measures of surface; the cubic yard for measures of volume; the imperial gallon for measures of capacity; and the pound avoirdupois for weights, ought to be sufficient.

The several decimal multiples and parts of these units might each have the name of its appropriate number, followed by the name of the principal unit, or (which seems less rational) new names might be given to those decimal multiples and parts of a principal unit which appear likely to be much used as measures or weights.

The use of Cloth Measure, Troy Weight, and Apothecaries Weight ought to be discontinued.

The following tables contain the decimal equivalents of the existing British coins, measures, and weights; and also the values of proposed new coins, measures, and weights, expressed in terms of the existing system of compound numbers.

Table for converting Farthings, Pence, and Shillings into Mils, Cents, Florins, and Pounds.

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Table for converting Mils, Cents, and Florins, into Shillings, Pence, and

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Farthings.

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5=4.80=1 03

6=5-76=1 1

6=144=1 2 13

= 12

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7=16.8=1 4 3

7

= 14

8=7-68=1 317

8=19.2=1 7 0

8

= 16

9-864-2

9=21.6=1 9 23

= 18

Table for converting Lines, Inches, and Feet into Decimal Parts of a Yard.

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83.33 = 8.333 = '8333 = ⚫08333

4 = 111'11 - 11.111 = 1.1111 = •11111

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