plates let into the granite step along the back of Trafalgar Square. As this is a practically invariable earth-fast standard, and most convenient for reference, it is important to know the minute errors of it, as determined by the Standards Department.[1] Starting from 0 the errors are in inches—
| at | 0 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | feet. | ||||||||||
| error | 0 | − | .007 | − | .019 | − | .022 | − | .015 | − | .008 | − | .007 | + | .011 | + | .021 | + | 0.17 | − | .008 | inches. |
The mean uncertainty in these values is .003, and the greatest uncertainty .01. The total length of the chain standard is − .019 inch from the truth. There is also a public balance provided at Greenwich observatory, which shows the accuracy of any pound weight placed upon it, For important scientific standards comparisons are made gratuitously, as a matter of courtesy, by the officials of the Standards Office, 7 Old Palace Yard, Westminster. The most delicate weighings are all performed in a vacuum case with glass sides, which is so constructed that the weights can be exchanged from one arm to the other without opening the case, so as to obtain double weighings.
The toleration of error in copies for scientific purposes, by the Standards Department, is .0005 inch on the yard or lesser lengths, about equal to 15 divisions of the micrometer; on the pound .0025 grain, about 12 a division of the official balances; on the ounce .001 grain; on the gallon 1 grain; and on the cubic foot 4 grains. The toleration for commercial copies is .005 on the yard, .001 on the foot and under, and .1 grain on weights of 1 ounce to 1 pound.[2] The Standards Commission of 1851 recommended a limit of 1 in 20,000.
For practical work of moderate accuracy the most convenient forms of measures are—for lengths under a foot, feather-edge metal scales divided to 150 inch (finer divisions are only confusing, and 11000 of an inch can be safely read by estimation); for lengths of 1 to 10 feet, metal tubes or deep bars bearing line-divisions, and with permanent feet attached at 21 per cent. from either end, so that the deformation by flexure is always the same; for long distances a steel tape with fine divisions scratched across it and numbered by etching. The most accurate way of using such a tape is not to prepare a flat bed for it, but to support it at points not more than 50 feet apart; then by observing the distances and levels of these points, and knowing the weight of the tape, the correction for the sloping distance between the points and the difference of the catenary length of the tape from the straight distance can be precisely calculated; the corrections for stretching of the tape (best done by a lever arm with fixed weight), and for temperature, are all that are needful besides.
The first French standard metre (of 1799) is a platinum bar end-standard of about 1 inch wide and 17 inch thick; the new standard of the International Metric Commission is a line-standard of platino-iridium, 40 inches long and .8 inches square, grooved out on all four sides so that its section is between × and ʜ form; this provides the greatest rigidity, and also a surface in the axis of the bar to bear the lines of the standard. The new standard kilogramme, like the old one, is a cylinder of platinum of equal diameter and height. These new standards are preserved in the International Metric Bureau at Paris, to which seventeen nations contribute in support and direction, and in which the most refined methods of comparison are adopted. For lineal comparisons the alternate substitution of the measures on a sliding bed beneath fixed micrometer microscopes is provided as in the British office, and a bath for the heating of one measure in a liquid to ascertain its expansion. For weighing four balances are provided, each with mechanism for the transposition of the weights, and the lowering of the balance into play on its bearings, so that weighings can be performed at 13 feet distance from the balance, thus avoiding the disturbance caused by the warmth of the observer. The readings of the balance scale are made by a fixed telescope, the motion being observed by the reflexion of a fixed scale from a mirror attached to the beam of the balance. In this bureau are also an equally fine hydrostatic balance for taking specific gravities by water weighing, a standard barometer, and an air thermometer, with all subsidiary apparatus. The special work of the bureau is the construction and comparison of metric standards for all the countries supporting it, and for scientific work of all kinds.
The legal theory of the British system of weights and measuresis—(A) the standard yard, with all lineal measures and their 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 ℔ 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 inches.
The legal theory of the metric system of weights and measures is—(A) the standard metre, with decimal fractions and multiples thereof; (B) the standard kilogramme, with decimal fractions and multiples thereof; (C) the litre (with decimal fractions and multiples), declared to be a cube of 116 metre, and to contain a kilogramme of water at 4° C. in a vacuum. No standard litre exists, all liquid measures being legally fixed by weight. The metre was supposed, when established in 1799, to be a ten-millionth of the quadrant of the earth through Paris; it differs from this theoretical amount by about 1 in 4000.
The legal equivalents between the British and French systems are—metre = 39.37079 inches; kilogramme = 15432.34874 grains. By the more exact comparisons of Captain Clarke (1866) the metre (at 0° C., 32° F.) is equal to 39.37043196 inches of the yard at 62° F.; but Rogers in 1882 compared the metre as 39.37027. It must always be remembered that a French metre of perfect legal exactitude will, by expanding from 32° to 62° F., become equal to a greater number of inches when the two measures are placed together; thus a brass metre is equal to 39.382 inches when compared with British measures at the same temperature, and this is its true commercial equivalent. The kilogramme determination above is that of Professor Miller (1844), against the kilogramme des Archives, but in 1884 the international kilogramme yielded 15432.35639.
For further details, see H. W. Chisholm, Weighing and Measuring (Nature series), 1877, and Reports of the Warden of the Standards, subsequently of the Standards Department (all in British Museum Newspaper Room), for all practical details,—especially reports on metre (1868–9), errors of grain weights (1872), principles of measuring (long paper of German Standards Commission, translated 1872), Trafalgar Square standards (1876), density of water (1883), toleration of error, British and international (1883), standard wire and plate gauges in inches (1883), besides numerous practical tables, mainly in the earlier numbers before the wardenship was merged in the Board of Trade.
II. Historical.
Though no line can be drawn between ancient and modern metrology, yet, owing to neglect, and partly to the scarcity of materials, there is a gap of more than a thousand years over which the connexion of units[3] of----
- ↑ Report of Warden of the Standards, 1875.
- ↑ Report of Warden, 1868, see also 1872.
- ↑ In the absence of the actual standards of ancient times the units of measure and of weight have to be inferred from the other remains; hence unit in this division is used for any more or less closely defined amount of length or weight in terms of which matter was measured.
