The 18th March, A. M. all having been verified, the comparisons were made as by the following Table: The four double Meter Bars were now successively put under comparison in their four possible positions, and found A = 0.044475 Changed end for end, 0.043575 0.043775 0.043794 0.0001752 0.043619 --.756381 49.8 0.043850 Changed end for end, 0.0433625 0.00017345 0.0431890 78.756811 0.043550 0.043500 50.5 The same day P. M. the comparisons were repeated as follow: 0.042525 51.8 To make these results comparable, it is necessary to reduce them all to one temperature by the difference of expan- In iron 0.000006963535 = In brass = 0.00001050903 } Difference. 0.000003545495 Decimal parts of the length. On account of the change of temperature during the comparison, and the considerable influence of this element in The standard temperature to which I find it most natural to reduce the measurements is 32° Fahr. or 0° Cen- The constant quantity of 0"000172 is also to be added to each measure taken on account of the individual value of the part of the scale made use of. The following table will therefore present the Results of all the foregoing Comparisons, with their Reductions : By the principles of the arrangement, it is obtained by a simple equation of the form; C ters accordingly. evident that the value of any one single metre compared above will be 2 ; and so any of the others, mutating the let The final results of these comparisons form therefore the following table of the values of the different meters compared at the temperature of 32° of both metre and scales, in English inches: These results might now be compared with those obtained by various comparisons made in England, these being however always stated so as taking the metre at 32°, and in value of the English scale at 62°, it is necessary to reduce them all for 30° difference of temperature full expansion of the brass. As I have not now the books in which they are related, and am ignorant, so various are they, which English standard and expansion has been used; supposing, however, that it has most generally been that of Borda, I will here only present, in a tabular shape, the different results as I have them, and reduce them to 32°, to compare them with my results. Observing, at the same time, that they are yet subject to the differences between the English standards themselves, which are in some instances greater than the differences of these results, as may be seen by the paper of Sir G. Shuckburgh, quoted above, and the account of Mr. Pictet, of Geneva, made in London in 1802. Borda's expansion for brass being 0.00000999, (though I have seen it lately stated at 0.0000101, on what ground I do not know, unless I suppose a mistake.) I do not compare by my ratio of expansion, because they were not made or known at the times of the older comparison; of course could never have been employed in them. The 21st March, I took the different standards of the toise under comparison. The toise of Canivet being half an inch French in thickness, and the brass scale half an inch English, this difference was compensated by laying four thicknesses of white paper strips under the whole length of the scale; the microscopes were adjusted to fit this toise, and then the scale adjusted to it; the other toises had rules of proper thickness to bring them to the same focus. |