The actual relation of our prototype metre No. 16 is as follows: Here μ means one micron, or one-thousandth of a millimetre (or nearly 000004 inch), so that metre 16 may be said to have been verified with an accuracy of one part in five millions. The "end" standard bar, or mètre-â-bout has been verified μ also with great accuracy, with a probable error of ±0·3. In the verification of the end standard, MM. Cornu and Benôit originally introduced a method of reflection, by means of which it was unnecessary to bring the ends of a bar into contact with any touching surfaces, and thus the measuring ends of a bar might be carefully preserved and used. The Kilogram. The unit of mass of the kilogram (Fig. 21) is determined by a solid piece of iridio-platinum in the form of a cylinder, the height and diameter of which are equal (39 millimetres). The kilogram, No. 18, supplied to Great Britain has a faint distinguishing mark, and is highly polished. On analysis, the metal showed very faint traces of ruthenium, rhodium, and iron. Its volume (18) was found to be at 0° Centigrade millilitres. 18 46 414. corresponding to a density of— 21.5454. After its final adjustment it was found to be in vacuô at 0° Centigrade. kg. milligram. Prototype 18 = 1 + 0·070 ± 0·002. So that it may be said that the kilogram (kg.) has been verified with a probable accuracy of 0.002 parts in a million. Besides the primary metric standards, we have also Standard iridio-platinum standard weights (1895) below the kilogram, as follows:- 500 grams. Weights below the Kilogram. In order to obtain the true weight of each weight in the series 500, 200, 200', 100, &c. it is of course necessary to compare all four weights with the kilogram prototype (1,000 grams); and then the 50, 20, 20', and 10 with the the 100 grams, and so on down to the 0.001 gram. For such purpose a separate series of weighings is required ; and the six weighings (1) to (6) when obtained are reduced according to the formula given opposite (p. 100). The equivalents of the metric trade weights and measures, in terms of the Imperial system, are (Weights and Measures Act, 1878, sections 18 and 21) as follows: With reference to the above trade equivalents it may be stated that the equivalent of the metre, 39-37079 inches, is based on a comparison made at Paris in 1818 by M. Arago, the Astronomer, and Capt. H. Kater, F.R.S. (“Phil. Trans. Roy. Soc." London, 1818), of two platinum metres for the Royal Society. These metres were made in consequence of a resolution of the House of Commons of 15th March 1816, moved by Mr. Davies Gilbert, M.P., and one on 14th May 1817, by which the Standard Yard (Bird's, 1760), in the custody of the Clerk of the House, was required to be delivered to the Royal Society, so that it might be compared "with the ten-millionth part of the quadrant of the meridian." Capt. Kater, however, did not base his equivalent on Bird's yard, but on Sir G. Shuckburgh's subdivided standard scale of 1795, which was deposited with the Royal Society. One of the earliest official attempts to define the English equivalents of Imperial weights and measures was that made at Paris by an officer of the Army of Occupation for the convenience of the individuals composing it, which calculations were published at Paris on 1st January 1817, having been printed at the headquarters of the army. A direct comparison of the Imperial Yard with the new international standard metre has now been made under the directions of the Board of Trade and the International |