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The 18th March, A. M. all having been verified, the comparisons were made as by the following Table:

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The four double Meter Bars were now successively put under comparison in their four possible positions, and found

A =

0.044475

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0.043575

0.043775

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0.043794

0.0001752

0.043619

--.756381

49.8

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0.043850

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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:

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0.042525

51.8

To make these results comparable, it is necessary to reduce them all to one temperature by the difference of expan-
sion between iron and brass. I shall for this make use of my own results of the pyrometrical experiments made im-
mediately after the comparison, and published in the philosophical transactions of Philadelphia of the same year,
the results of which gave the expansion for one degree of temperature of Fahrenheit's scale,

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 results, it is necessary to take for each comparison the proportional temperature corresponding to it between the
readings of the thermometer, the work proceeding regularly, each single comparison will correspond to the propor-
tional time.

The standard temperature to which I find it most natural to reduce the measurements is 32° Fahr. or 0° Cen-
tesimal & Reaumur, it being adopted for the meter and toise. I shall reduce the results of the iron to brass, so that
the numbers will express the length of the meters in English inches of the brass scale, both at the temperature of 32°,
which appears to me most naturally, being possible to obtain by actual experiment, while the giving of the meter at
32° in length, on the scale at 62°, is impossible to produce and verify in nature, therefore always a result of calcula-
tion in which the ratio of expansion used has too much influence. The brass metre is therefore considered as need-
ing no reduction.

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.

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The following table will therefore present the Results of all the foregoing Comparisons, with their Reductions :

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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
(c+b) + (c+l)—(b+1)

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:

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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.)

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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.

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