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The 18th March, A. M. all having been verified, the comparisons were made as by the following Table:
Standards Microscope Read. Mean of the four Correction for Mi Corrected Result Final Value. Mean Tempera-
0.039643 -760357 Mc+=
Mc+= 0.040475 M3+(=
0.040525 Changed ends for middle, > 0.040850
$ 0.000003545495 Decimal parts of the length.
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 values
The following table will therefore present the Results of all the foregoing Comparisons, with their Reductions :
Date of compari
Temperature of the
Result of the com
78.7558085 17.2 0.00480286 78.76078336
0.00488162 -.76186502 49.8 -.7563810
0.00497040 -.76152340 50.2 -.7568110
0.00508204 -.76206509 18th March, Mc+
78.7553503 18.5 0.00516567 78.76068797 P. M. Mc+i
-75.93134 19.0 0.00530555 -.76479095
(c+b) + (c+1)—(6+1) .
; and so any of the others, mutating the letters accordingly.
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 : Date of the com
Mj. parison. 15th March,
39.37992415 S9.379854162 18th March, A.M. -.3809641
39.3840606 P. M. -.37955601
-.3836290 Means 39.381022708 39.37972015
39.3838448 Correction of the brass metre by the certificate
. +0.00039381 which applied, gives the metre corrected - - - 39.38024797
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.)
Difference with my
tee metre. The Roy. Soc. accepted 39.370572 39.38126801 +0.0002453
- in 1800 -.3702 -.380896 -0.0001267 Mr. Pictet in 1802
381696 +0.0006733 Mr. Kater on S. G.
Shuckburgh's scale, lately, 1818
-.37079 .381486 + 0.0004633 The same on Bird's scale -.37062 -.381316 + 0.0002933 (Unknown wbich of Bird's
scales, there being a difference.)
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.