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 (z1) are:
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 sin2 z (9)
Replacing a and p by their values in Eqs. (1) and (2),17 one obtains:
z' - z = [(v/c)2 sin2 z].[sin 2(|).sin2D + cos 2(|).sin 2D.cos (d-A) -
- sin 2<|).cos2D.cos2(9-^4)] (10)
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 [cos2 (9-^4)]. Therefore, from a suitable analysis of the data it should be possible to obtain the speed (v/c), the declination (D) and the right ascension (A) of the motion of the Earth relative to the ether.
Repetition of the Leyden measurements
The 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
17 From this point onward, 9 is used again to represent sidereal time.
Searching for the Ether
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.18 He confirmed the existence of a systematic effect of the same order of magnitude, and computed the values oL4=69° andD=44° Esclangon did not publish the estimated errors of his evaluation, nor the estimated speed of the Earth.
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
18 Ernest Esclangon, “Sur la dyssimétrie mécanique et optique de l'espace en rapport avec le mouvement absolu de la Terre”, Comptes rendus de l'academie des sciences de Paris, clxxxii (1926), 921-3.
19 In some of his analysis, Courvoisier found that the effect with one sidereal day period was not clearly noticeable. In those cases, he assumed the value of 40° for the declination, and computed the right ascension and speed of the Earth.