0.87μ; hence the necessity of a uniform temperature in the inside brass box.

Microscopes.-The microscopes have a magnifying power of very nearly 50 diameters, the objective and eyepiece each contributing equally to the power. The objectives were of the compound type, the illumination being secured by mounting small prisms in the principal focus of the lower lens of the objective. Diffused light from incandescent lamps was thrown through a screen of thin ground glass upon the prisms, from which the light was reflected vertically downward on the meter bars.

The micrometer screws were carefully studied for periodic errors about ten years ago, and a number of determinations of the screw values have been made since. They were again determined in August, 1903, and the values found were used to reduce the observations made at this period.

The values for one turn of the micrometer screws at different dates are tabulated below:

The foregoing values indicate a very satisfactory agreement in the screw values at widely different dates. Only one, namely, that of micrometer No. 5, made in 1896, shows an appreciable deviation from the others. The reason for this unusually large value is not known, nor is it important for the present purpose.

Observations.-An observation consisted of the following operations, which consumed about fifteen minutes:

1. Reading of thermometers in inner case.

2. Reading on No. 21.

3. Reading on No. 27.

4. Reading on No. 21.

5. Reading on No. 27.

6. Reading on No. 21.

7. Reading of thermometers in inner case.

Every time a bar was brought under the microscope the micrometers were read simultaneously four times, the observers exchanging places after the second reading to eliminate personal equation.

To insure thermal equilibrium at the beginning of the observations at least three hours was allowed to elapse between the observations. A series consisted of eight observations, with the bars occupying as many different positions with respect to the observer and the microscopes. The positions were as follows:

The other four positions were obtained by substituting one bar for the other in each of the above diagrams.

By this procedure each bar was in front, and hence nearer to the observer during half of the observations; also each end of both bars was brought under each microscope twice. The result of a series of observations is, therefore, independent of any possible affect of peculiar conditions.

The observations were all reduced to zero centigrade by means of the differential expansion deduced from the equations of the meter bars as furnished by the International Bureau.

In the comparison now described three series of observations were made, making a total of twenty-four observations. The results will be found in the following table, in which the first column gives the number and the second the date of the observation. The third gives the reading of the left-hand microscope on No. 21; the fourth gives the reading of the same microscope, on No. 27; the fifth gives the difference, in revolutions, of the readings of the micrometer; the sixth, the difference in microns. The seventh column gives the reading of the right-hand microscope on No. 21; the eighth, the reading of the same microscope on No. 27; the ninth, the difference in the readings of the micrometers; the tenth, the difference in microns; the eleventh, the sum of the differences of the two microscopes, in microns; the twelfth gives the mean corrected reading of the two thermometers, and the thirteenth gives the residuals for the individual observations when referred to the mean temperature of observation, namely, 23.50° C. All of the observations at the Bureau of Standards were made with the bars in air.

The relation of the two bars, as determined in 1888, was

No. 27-No. 21 -4.00μ at 0.00 C.

If we assume that the length of No. 27 has remained constant, then No. 21 shows a decrease in length of 0.33μ. The evidence is, however, too meager to draw reliable conclusions from, and hence a discussion of this question is postponed until further observations have been made.

After the above observations had been completed, No. 27 was carefully packed in its case and transported to the International Bureau of Weights and Measures. During the transportation the bar was handled with the greatest care and received no shocks, nor was it subjected to any sudden changes of temperature. Upon the arrival of No. 27 at the International Bureau of Weights and Measures, it was immediately placed in the Brunner comparator with meter No. 26, and M. Maudet, one of the assistants at the International Bureau, was delegated to assist in the comparisons, which were begun the following day.

THE BRUNNER COMPARATOR.

The essential features of the Brunner comparator, which is fully described in Vol. 4, Travaux et Mémoires of the International Bureau, are two massive stone piers on which are mounted the two micrometer microscopes, and a double-walled box in which are placed the bars and which can be displaced laterally so as to bring the ends of the two standards successively under the microscopes. The trough is supported on a foundation which is only connected to the microscope piers through the earth. None of the piers are in contact with the floors of the laboratory. All the comparisons at the International Bureau were made with the bars submerged in water, which was thoroughly stirred before each observation. The temperature of the water and of the bars was determined by means of four symmetrically disposed Tonnelot thermometers, which had been used in the 1888 comparisons. These thermometers, numbered 4246, 4247, 4248, and 4249, respectively, are perhaps better known in terms of the hydrogen scale than any other mercury thermometers in existence, though in this case, as before stated, the actual temperature was of little importance.

Micrometers.-The micrometers used are the regular micrometers belonging to the Brunner comparator, and they will be found described in the volume above referred to. Their values have been carefully determined from time to time, and the values adopted for this period by the International Bureau were used. Merely as a check a determination of the values was made by the writer after the observations had

been completed, and the results obtained agreed almost perfectly with those used.

STANDARDS OF THE INTERNATIONAL BUREAU.

The comparison of No. 27 was made with the two standards of the International Bureau, namely, No. 26 and T.

Meter No. 26, which is the principal standard, was included in the 1888 comparisons, and it was again directly compared with the international meter in 1892. T,, which is the secondary standard, was compared directly with the international meter in 1892, and a number of times with No. 26 between 1892 and 1894.

It might be well at this point to give the equations of all of the bars involved in the comparisons, both at the Bureau of Standards at Washington, and at the International Bureau of Weights and Measures. They are as follows:

The corrections to Nos. 21 and 27 at 0° C. are given one place further than the value furnished in their certificates, the values in the certificates having been rounded off to the nearest tenth of a micron. It was deemed advisable, in view of the small difference that might be looked for, to take the actual values found in 1888 to the nearest 0.01 of a micron. For the same reason the values of No. 26 and T, were taken to the nearest 0.01 of a micron. The above values of No. 26 and T, are the values at present accepted by the International Bureau as the result of the comparisons made in 1892 and 1894. In the first two equations T means temperature in degrees of the hydrogen scale. In the last three equations t means temperature in degrees of the hard glass scale of the International Bureau." In the observation made at Washington the thermometer readings were reduced to the hydrogen scale, while the observation made at the International Bureau was referred to the hard glass temperature scale. The second equation of No. 27 was therefore used in the latter observations.

OBSERVATIONS.

Following the method in use at the International Bureau, an observation made there consisted of five pointings on one bar and four on the other, the pointings being alternately on the two, but always beginning and ending on the same bar. A series of observations was a Nouvelles déterminations des Metres Étalons: Travaux et Mémoires, Vol. 11, p. 6.