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was constructed from authentic copies of the old, the size of the standard being at the same time changed to the pound avoirdupois. Four parliamentary copies of the new standard pound were

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prepared, and deposited along with those of the yard. A fifth copy has been prepared to be used instead of the imperial pound in all ordinary comparisons.

According to the Weights and Measures Act, the comparison of any other mass with the standard of mass is to be done by weighing in vacuo.

ART. 126.-Derived Units of Mass. The other units of mass in the Imperial system which have a special name (see table appended), such as the ton, ounce, grain, are defined as a multiple or a sub-multiple of the pound. The avoirdupois denominations form the principal legal system; the ounce troy and its decimal

derivatives form the legal system for weighing bullion, and may be used in the sale of precious articles. For the retail trade in drugs, apothecaries' denominations may be used.

Local standard weights are constructed by the Standards. Department, and distributed along with the local standard measures. The figure represents the form of the modern local standard avoirdupois weights.

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ART. 127. Metric Standard of Mass. In the Metric system the kilogramme was originally defined as the mass of a cubic decimetre of distilled water at the temperature of its maximum

density (about 4° C.). Distilled water is very suitable for a standard substance on account of its being obtainable everywhere in a state of purity, its homogeneity, and the invariability of its density at a given temperature. By weighing and measurement the mass contained in a cubic decimetre of water at its standard state was found, and a piece of platinum was constructed to represent that mass. The piece of platinum is called the kilogramme des archives; it, or rather

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standard kilogramme subsequently constructed, is now the ultimate standard for the kilogramme in the same way as a piece of platinum is the ultimate standard for the pound. In the Standards Department there is a standard kilogramme of platinum, which is similar to the kilogramme des archives.

English Standard Platinum Kilogramme.

The gramme is the one-thousandth part of the kilogramme, and therefore the mass of a cubic centimetre of water at its temperature of maximum density.

In the C.G.S. system the gramme is chosen for the unit of

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480 grains = 31·10 grammes.

1 "pennyweight"=24 grains. 1 "pound troy "=5,760 grains.

APOTHECARIES'.

1 "scruple"=20 grains; 1 “drachm"= 3 scruples;

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The authorized abbreviation for gramme is g., but it is customary with English writers to use gm., in order to distinguish between gramme and grain.

EXAMPLES.

Ex. 1. Find the rate connecting franc per kilogramme with pence per lb., when the course of exchange is 25 fr. 20 c. per £.

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The reciprocal rate is

100

432

franc per kgm. = penny per lb.,

i.e., 231 franc per kgm. = penny per lb.

Ex. 2. From the definitions of the gallon and of the litre deduce the relation of the former to the latter.

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1. Express a pound avoirdupois as the decimal of a pound troy, and an ounce avoirdupois as the decimal of an ounce troy.

2. Express 22 kilogrammes in pounds, and 25 pounds in kilogrammes.

3. Reduce 50 kilogrammes to hundredweights, and 1,000 kilogrammes to tons.

4. Express 4d. per lb. in terms of shilling per cwt. and pound per ton.

5. Reduce 1 franc per kilogramme to pence per lb. when the course of exchange is 25'10 francs = pound.

6. Reduce 100 francs per quintal to shillings per cwt. when the rate of exchange is 25'60 francs-pound.

7. Convert 5s. 6d. per lb. into francs per kilogramme when the course of exchange is 25 fr. 20 c. per pound.

SECTION XXIII.-DENSITY.

ART. 128. General Unit. By the density of a substance is meant the rate connecting the mass with the volume. It is expressed in terms of M per V, the systematic unit being M per L3. The reciprocal idea is V per M, which is denominated by Clerk-Maxwell the rarity,* and by Rankine the bulkiness.† + Rules and Tables, p. 147.

* Heat, p. 82.

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