squares and cubes based upon that; (b) the standard pound of 7000 grains, with all weights based upon that, with the troy pound of 5760 grains for trade purposes; (c) the standard gallon (and multiples and fractions of it), declared to contain 10 pounds of water at 62 F., being in volume 277·274 cubic inches, which contain each 252·724 grains of water in a vacuum at 62°, or 252·458 grains of water weighed with brass weights in air of 62° with the barometer at 30 in. Of the metric units international definitions have been stated as follows:—
(a) The unit of volume for determinations of a high degree of accuracy is the volume occupied by the mass of 1 kilogram of pure water at its maximum density and under the normal atmospheric pressure; this volume is called litre.
(b) In determinations of volume which do not admit of a high degree of accuracy the cubic decimetre can be taken as equivalent to the litre; and in these determinations expressions of volumes based on the cube of the unit of linear measure can be substituted for expressions based on the litre as defined above.
(c) The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram.[1]
(d ) The term “weight” denotes a magnitude of the same nature as a force; the weight of a body is the product of the mass of the body by the acceleration of gravity; in particular, the normal weight of a body is the product of the mass of the body by the normal acceleration of gravity. The number adopted for the value of the normal acceleration of gravity is 980·965 cm/sec2.
2. Standards.—The metre (mètre à traits) is represented by the distance marked by two fine lines on an iridio-platinum bar t＝0° C.) deposited with the Standards Department. This metre (m.) is the only unit of metric—extension by which all other metric measures of extension—whether linear, superficial or solid—are ascertained.
The kilogram (kg.) is represented by an iridio-platinum standard weight, of cylindrical form, by which all other metric weights, and all measures having reference to metric weight, are ascertained in the United Kingdom.
From the above four units are derived all other heights and measures (W. and M.) of the two systems.
The gallon is the standard measure of capacity in the imperial system as well for liquids as for dry goods.
In the United Kingdom the metric standard of capacity is the litre, represented (Order in Council, 19th May 1890) by the capacity of a hollow cylindrical brass measure whose internal diameter is equal to one-half its height, and which at 0° C., when filled to the brim, contains one kg. of distilled water of the temperature of 4° C, under an atmospheric pressure equal to 760 millimetres at 0° C. at sea-level and latitude 45°; the weighing being made in air, but reduced by calculation to a vacuum. In such definition an attempt has been made to avoid former confusion of expression as to capacity, cubic measure, and volume; the litre being recognized as a measure of capacity holding a given weight of water.
For the equivalent of the litre in terms of the gallon, see below III. Commercial.
In the measurement of the cubic inch it has been found that[2] the specific mass of the cubic inch of distilled water freed from air, and weighed in air against brass weights (∆ = 8·13), at the temperature of 62° F., and under an atmospheric pressure equal to 30 in. (at 32° F.), is equal to 252·297 grains weight of water at its maximum density (4° C). Hence a cubic foot of water would weigh 62·281 ℔ avoir., and not 62·321 ℔ as at present legally taken.
For the specific mass of the cubic decimetre of water at 4° C., under an atmospheric pressure equal to 760 mm., Guillaume and Chappuis of the Comité International des Poids et Mesures at Paris (C.I.P.M.) have obtained 0·9999707 kg.,[3] which has been accepted by the committee.
The two standards, the cubic inch and the cubic decimetre, may not be strictly comparable owing to a difference in the normal temperature (Centigrade and Fahrenheit scales) of the two units of extension, the metre and the yard.
For the weight of the cubic decimetre of water, as deduced from the experiments made in London in 1896 as to the weight of the cubic inch of water. D. Mendeléeff (Proc. Roy. Soc., 1895) has obtained the following results, which have been adopted in legislative enactments in the United Kingdom:—
| Temperature on the Hydrogen Thermometer Scale. |
Weight of Water in vacuo. | |||
| Of a Cubic Decimetre in Grammes. |
Of a Cubic Inch in Grains. |
Of a Cubic Inch in Russian Dolis. | ||
| C. | F. | |||
| 0° | 32°·0 | 999·716 | 252·821 | 368·686 |
| 4 | 39·2 | 999·847 | 252·854 | 368·734 |
| 15 | 59·0 | 998·979 | 252·635 | 368·414 |
| 1623 | 62·0 | 998·715 | 252·568 | 368·316 |
| 20 | 68·0 | 998·082 | 252·407 | 368·083 |
In this no account is taken of the compressibility of water—that is to say it is supposed that water is under a pressure of one atmosphere. The weight of a cubic decimetre of water reaches 1000 grammes under a pressure of four atmospheres, but in vacuo, at all temperatures, the weight of water is less than a kilogram.
Fig. 1.—Present Imperial Standard Yard, 1844.
Totals length of bronze bar, 38 m.; distance a a′, 36 m., or the imperial yard a a′, wells sunk to the mid depth of the bar, at the bottom of each of which is inserted a gold stud, having the defining line of the yard engraved on it.
 |
| Fig. 2.—Imperial Standard Pound, 1844. |
| Platinum pound avoirdupois, of cylindrical form, with groove at a for lifting the weight. |
3. National Standards.—National standards of length are not legally now referred to natural standards to physical constants[4] but it has shown by A. A. Michelson that a standard of length might be restored, if necessary, by reference to the measurement of wave-lengths of light. Preliminary experiments have given results correct to ±0·5 micron, and it appears probable that by further experiments, results corrected to ±1·0μ may be obtained. That is to say, the metre might be redetermined or restored as its length within one ten millionth part, by reference to, e.g. 1553163·5 wave lengths of the red ray of the spectrum of cadmium, in air at 15° C. and 760 mm.
In all countries the national standards of weights and measures are in the custody of the state, or of some authority administering the government of the country. The standards of the British Empire, so far as the relate to the imperial and metric systems, are in the custody of the Board of Trade. Scientific research is not, of course, bound by official standards.
For the care of these national standards the Standards Department was developed, under the direction of a Royal commission[5] (of which the late Henry Williams Chisholm was a leading member) to conduct all comparisons and other operations with reference to weights and measures in aid of scientific research or otherwise which it may be of duty of
the state to undertake. Similar standardizing offices are established- ↑ Troisième Conférence Générale des Poids et Mesures (Paris, 1901). Metric Units Com. Roy. Soc. (1898).
- ↑ Phil. Trans. (1892): and Proc. Roy. Soc. (1895), p. 143.
- ↑ Proc. Verb. Com. Intern, des Poids et Mesures (1900), p. 84. Congrès International de Physique réuni à Paris en 1900.
- ↑ Valeur du Mètre, A. A. Michelson (Paris, 1894); Units Everett, Illustrations of C.G.S. System; Unites et Étalons, Guillaume (Paris, 1890); Lupton’s Numerical Tables 1892; Metric Equivalent Cards, 1901; Dictionary of Metric Measures, L. Clark (1891); Glazebrook and Shaw’s Physics (1901).
- ↑ Report Standards Commission 1870.
