XV.

AN EXAMINATION OF THE STANDARDS OF LENGTH CONSTRUCTED BY THE SOCIÉTÉ GÉNEVOISE.

BY PROFESSOR W. A. ROGERS.

Communicated December 10th, 1884.

SEVERAL physical laboratories in this country have recently received from the Société Génevoise instruments of precision of various kinds, which appear to have decided merit, both in regard to design and workmanship. The Society has among other things undertaken the construction of standards of length, and of a cathetometer, which is designed to take a high rank as an instrument of precision. Through the kindness of Professor Wright of Yale College, the writer has been permitted the opportunity of a somewhat extended study of one of the standard meters of the Society. Through the courtesy of J. W. Queen & Co. of Philadelphia, the opportunity was at the same time offered of an examination of three other standard meters, and of the meter graduated upon the upright bar of a cathetometer.

On account of the somewhat extended introduction of these standards, it has seemed to the writer worth while to place upon record the results of this examination.

EXAMINATION OF METERS.

The meter belonging to Professor Wright is designated W. The meter of similar form and dimensions received from J. W. Queen & Co. is designated Q1. A second meter, in which the graduations are nearly along the centre of gravity of a cross section of the bar, is designated Q. The graduations upon W, Q, and Q, are upon silver inlaid in the brass, which is the material of the bars. A third meter, designated Q, has the graduations upon the brass. cathetometer is designated Q

2

The meter of the

COMPARISON OF METER W WITH BRONZE STANDARD METER Ra2 AND STEEL STANDARD METER R2,

in which, designating the Mètre des Archives by A。,

The coefficient of expansion of R2 for 1° C. in 1 metre is assumed to be 17.17 μ.* The coefficient of R, for 1° C. is assumed to be 10.28 μ. At 0° C. these relations become, with these coefficients,

The values R-W and R-W are given in divisions of the micrometer of the microscope employed, in which

The thermometer employed is No. 8612 Baudin, and the readings have been reduced to the Yale standard.

The observations extend from November 15 to December 3, 1884.

* Proceedings of the American Academy, Vol. XVIII. p. 341.

It appears from these observations, that the coefficient of W for 1° C. from comparison with R, is

17.17 μ +0.92 μ = 18.09 μ;

and that the coefficient of W for 1° C. from comparison with R, is

10.28 μ7.82 μ= 18.10 μ.
μ

On account of the large deviation from the value communicated by the Society, viz. 19.155 μ, a series of comparisons was instituted beween Wand a steel end-meter S immersed in melting ice, according to the method described in the Proceedings of the American Academy, Vol. XVIII. p. 341.

Combining this value with the values 18.09μ derived from R., and 18.10μ derived from R,, we have:

Coefficient of expansion of bar Win one meter =

degree Centigrade.

18.19μ for each

For the relation between Wand 4 at 16°.67 C. 62°.0 Fahr., we have:

W-263.0 μ=R, A,+1.6μ W-263.6μ-R=A+1.2 μ

W-264.6μA。

And finally,

Reducing to 0° C., with the coefficient 18.19μ, we have at 0°

A slightly different but probably more accurate value of this relation will be obtained by selecting only those comparisons which were made From these data we have:

near 0°.

COMPARISON OF STANDARD Q1 WITH STANDARDS R2 AND R2.

COMPARISON BETWEEN STANDARDS Q2, R2, AND Rg.

EQUATIONS OF CONDITION BETWEEN R2 AND Q2.