Roberto Martins Searching for the Ether DIO 17 In those equations, the speed of the mirror is P=v/c, in the direction perpendicular to the mirror. Any motion of the mirror parallel to its surface would have no influence upon the direction of light. In the case of the mercury mirror, the relevant direction if the local vertical, and therefore p, here, has the same general meaning ascribed by Courvoisier to this symbol. Relative to the proper reference system of the mirror there is an aberration effect, and the angles of incidence (z) and reflection (z z = 9 + a cos 9 - p sin 9 (6) z' = 9' + a cos 9' + p sin 9' (7) where a is component of the velocity v/c of the mirror parallel to its surface. Notice that this is the classical aberration effect. A relativistic analysis would lead to a different result. The measured effect is the difference between z' and z: z' - z = (9' - 9) + a (cos 9' - cos 9) + p (sin 9' - sin 9) (8) Taking into account the above equations and making suitable substitutions, one obtains the approximate result: z' - z = 2aP sin Replacing a and p by their values in Eqs. (1) and (2), z' - z = [(v/c) - sin 2<|).cos Notice that this equation contains a constant term and two periodical components with different periods - one sidereal day [cos (9-^4)] and half a sidereal day [cos ## Repetition of the Leyden measurementsThe Leyden measurements had used four stars close to the North Pole. The difference z-z' was measured in a series of observations, at the times of upper and lower culmination of each star. The observed values of the periodical components of z-z' amounted to less than 1 ", varying from 0.04" for one of the stars to about 0.5" for another. The error of the measurements was estimated as 0.01 ", therefore the effect was regarded as significant. From the Leyden data Courvoisier obtained the results: A = 104° ± 21°; D = +39° ± 27°; v = 810 ± 215 km/s
- 13- | Roberto Martins Searching for the Ether DIO 17 The estimated error of the speed amounted to about 25%. The errors of the right ascension and declination amounted to about 1/15 of the full circle. Between 1921 and 1922 Courvoisier repeated the Leyden measurements, but with a slight change of method. Instead of a meridian circle he used a Wanschaff vertical circle that enabled him to make measurements of the stars at any time during the night. Therefore his measurements were not limited to two sidereal times for each star. From 4 June to 14 December 1921 he made a series of 142 measurements of the polar star BD +89.3°, and from 18 March to 23 May 1922 he made further 64 determinations of z-z'. From those measurements Courvoisier obtained: A = 93° ± 7°; D = +27° ± 12°; v = 652 ± 71 km/s The estimated relative error of the speed was reduced to about 10% and the errors of the right ascension and declination amounted to less than 1/30 of the full circle. Courvoisier’s work called the attention of a French astronomer, the director of the Strasbourg observatory, Ernest Esclangon, who repeated those measurements. Other evaluations were later obtained by Courvoisier using measurements made at München (1930-1931) and Breslau (1933-1935), with the following results:
The results obtained in the second Breslau series presented the smallest errors. In 1945, after his retirement, Courvoisier made a final series of observations from Basel. He obtained the following results: A = 60° ± 14°; D = +40° (estimated); v = 656 ± 157 km/s
- 14- |