If U, the lost standard, be supposed to have the same density as V, the comparisons of Sp and RS with U by Captain v. Nehus in 1829, give, Sp=U-0.52959 a The Commissioners for the Restoration of the Standards of Weight and Measure, in their Report, dated December 21, 1841, recommended that the avoirdupois pound of 7000 grains be adopted instead of the troy pound of 5760 grains, as the New Parliamentary Standard of Weight, and that the new standard and four copies of it be constructed of platinum. In accordance with this recommendation, five weights were made by Mr. Barrow, a little in excess of 7000 grains, of platinum prepared by Messrs. Johnson and Cock. The form of these pounds is that of a cylinder, nearly 1.32 inch in height and 1.15 inch in diameter, with a groove round it, the middle of which is about 0.34 inch below the top of the cylinder, for insertion of the prongs of a forked lifter of ivory. They are marked PS 1844 i lb. ; PC No. 1 1844 i lb. ; P CNo. 2 1844 1 lb.; PC No. 3 1844 1 lb.; PC No. 4 1844 1 lb., respectively. The weights of 7000 grains might have been derived from that of 5760 grains, by the use of either a decimal or a binary system of weights. In either case, however, the number of weights to be compared with one another and with the weights of 7000 and 5760 grains would have been large, and the errors of their comparisons among themselves might, by their accumulation, sensibly affect the resulting weight of 7000 grains. Also, the repeated comparison of weights made up of the sum of several others, was a very troublesome process, previous to the use of the detached pans, already described, which had not been thought of when the weights were ordered. These two evils were in a great measure avoided by the use of a platinum weight T of about 5760 grains, or more correctly very nearly equal to Sp or RS, and of the following auxiliary weights, also of platinum, and all constructed by Mr. Barrow: A, B, C, D each of 1240 grains; F of 800 grains; G of 440 grains; H of 360 grains; K, L, M, N each of 80 grains ; R, S each of 40 grains, nearly. The numbers of the weights of each denomination, and their values, are given by the quotients and divisors obtained in the conversion of 1960 into a continued fraction. The errors of these weights are found by the following comparisons :—Sp and RS with T; T with A+B+C+D+F; each of the weights A, B, C, D with F+G; F with G+H; G with each of the weights H+K, H+L, H+M, H+N; H with K+L+M+N+R and K+L+M+N+S; each of the weights K, L, M, N with R+S. Sp and RS, instead of being true troy pounds, and, consequently, equal to U in a vacuum, had been adjusted so as to appear nearly as heavy as U when weighed in air of ordinary density, and are therefore lighter than U by about 0.53 grain, the weight of the air contained in the space equal to the difference between the volume of U and that of Sp or RS. A space equal to the difference between the volume of 7000 grains of metal of the assumed density of U, and 7000 grains of platinum, contains about 0:645 grain of air. Calling this Q, PS may be compared with each of the weights T+A+Q, T+B+Q, T+C+Q, T+D+Q. In order to determine Q with the greatest precision, Mr. Barrow supplied ten weights Q of about 0.645 grain each, so accurately adjusted that no appreciable difference could be detected between them; a weight V of 6.451 grains, and a weight W of 12.901 grains, all of platinum. Then Y and Z being two platinum weights of 20 grains each, the following comparisons became possible :-each of the weights R and S with Y+Z; each of the weights Y and Z with W+V+ each of the weights Q in turn; W with V+ sum of ten weights Q; V with the sum of the ten weights Q. In comparing PS with each of the weights T+A+Q, T+B+Q, T+C+Q, T+D+Q, the weight Q was changed at the end of every four comparisons, and thus each of the ten weights Q used in turn in a series of forty comparisons. By numerous weighings in air and in water the densities of the several weights were found to be as follows : By 286 comparisons of T with Sp and 122 comparisons of T with RS, assuming the density of U to have been the same as that of V, T=5759.47141 grains, of which U contained 5760. By numerous comparisons of the auxiliary weights with each other and with T, A=1239.88621, B=1239.88604, C=1239-88596, D=1239-88579, Q=0.64509. By 80 comparisons of PS with each of the weights T+Q+A, T+Q+B, T+Q+C, and 100 of PS with T+Q+D, gr. t. 19:47 19:19 18.83 19.63 b. 758.38 759.31 754.38 764:43 Mean gr. PS: T+Q+}(A+B+C+D)=0:00177 19.28 759.12 whence, supposing U to have the same density as V, PS=7000.00090 grains, of which U contained 5760. Results of comparisons of PC No. 1, PC No. 2, PC No. 3, PC No. 4 with PS : gr. No. of Comparisons. 200 216 PC No. 3=PS-0.00178 204 PC No. 4=PS-0.00316 204 The weights Sp, Sb, K were returned to Professor Schumacher accompanied by a weight V such that, by a mean of 200 comparisons, Sp+V-PS-0.00071 grain in air (t=13:1, b=759.09). By the good offices of M. Arago, permission was obtained from the French Government to compare the new English weights with the standard kilogramme of platinum, known as the kilogramme des Archives, and which will be denoted by the letter A. The comparison was made by two perfectly independent methods. In one of these a was compared sixty times with PC No. 1 + PC No. 2 + auxiliary weight B+ a platinum weight V of nearly 192.436 grains. In the other, a was first compared 200 times with the platinum kilogramme E, purchased for the British Government. E was afterwards compared with PS + each of the four platinum copies of the VOL, VIII. pound in succession, together with a platinum weight of about 1432.324 grains, the weight of which was found with great precision by a process to be described presently. A had never been weighed in water. By observations made with the stereometer, it was found that at 0° C. the volume of a exceeded that of E by a quantity equal to the volume of 21.119 grains of water at its maximum density. By weighing E in air and in water, it was found that AE=20:54877. Some time after these observations were made, the Committee received from Professor Schumacher some observations of his own in manuscript, and a copy of Professor Steinheil's paper, entiled “Das Bergkrystall-kilogramm,' from the fourth volume of the Transactions of the Bavarian Academy of Sciences, containing the determination of the volume of A, by comparing its linear dimensions with those of a platinum kilogramme of his own S, the density of which had been found by weighing it in air and in water. The two weights being cylinders, and the linear dimensions measured with an extremely delicate instrument constructed by Gambey, this kind of observation admitted of being made with great accuracy. The resulting difference between the volume of A and that of E, was found to be equal to the volume of 20.933 grains of water at its maximum density. On account of the large number of observations, and the extreme care with which they were made, this value of the volume A – volume E is to be preferred to that which was obtained by the stereometer, and has accordingly been used in reducing the observations for comparing the weights of A and E. E was compared with PS by the method which had proved so satisfactory in deducing the avoirdupois pound from the troy pound. Let I, K, L, M, N denote PS and its four platinum copies, A, B, C, A, platinum weights of about 1432.322 grains each, Z a weight of about 1270 708 grains, 0 a weight of 161.629 grains, made up of weights the values of which had been carefully determined. E was compared with each of the weights I+K+ A, I+L+B, I+M+T, I+N+A, each of the lbs. K, L, M, N having been previously compared with I; I with A+B+r+A+Z; each of the weights A, B, C, A with Z+0. In this manner it was found that the kilogramme des Archives weighed 15432-34874 grains, of which the new Imperial Standard pound contains 7000, or kilogramme = 2.20462125 lb. This is pro bably the best determination of the weight of A in terms of the English standard of weight. The value of A, as deduced from the direct comparison of A with K+L+B+V, is subject to some uncertainty, arising from the circumstance that the platinum, of which A, B, C, F were made, had been very badly prepared and contained cavities filled with some hygroscopic substance which rendered the weight of B slightly variable, according to the greater or less amount of moisture present in the atmosphere. According to these observations, the kilogramme des Archives = 15432.31816 grains. By the observations of Schumacher and Steinheil on the ratio of the weight of a to that of Sp, subject to an uncertainty of 0.00139 grain, on account of an error of the press, and the comparison of Sp with PS, the weight of a is either 15432-34873 or 15432-35012 grains, of which PS contains 7000. The French standard of commercial weight is a brass kilogramme L, known as the kilogramme type laiton. It is deposited at the Ministère de l'Intérieure. According to a comparison of L with a the result of which is published in the 25th volume of the Modena Transactions, the apparent weight of L, when weighed in air at Somerset House, the mercury in the barometer, reduced to the freezing-point, standing at 29.75 inches, and the thermometer at 65 66 F. (b=755.64 mm., t=18.7 C.), is 15432.344 grains, of which the English commercial standard contains 7000. The Society then adjourned to Thursday, May 8. |