Roberto Martins Searching for the Ether DIO 17
Fig. 9. According to Courvoisier, the Lorentz contraction of the Earth and of optical instruments could have a small observable influence on astronomical observations and terrestrial experiments.
Using the data he had already obtained from 1914 to 1917, and combining those results with other measurements he made in 1921-1922 and 1925-1926, with the same instrument, Courvoisier obtained the following result:
A = 74° ± 3°; [D = +40°]; v = 587 ± 48 km/s
He also analyzed measurements that had been obtained in routine observations at the Paris observatory, in the period 1899-1901. All those series of observations exhibited similar variations with a period of 12 sidereal hours. Assuming a value of 40° for the declination, he obtained the following results:
A = 70° ± 11°; [D = +40°]; v = 810 ± 166 km/s
Afterwards Courvoisier also computed the motion of the Earth using measurements from Breslau (1923-1925 and 1933-1935) and from München (1927-1931). Taking into account all the observations, he obtained the following final result:
A = 65° ± 10°; [D = +40°]; v = 574 ± 97 km/s
Searching for the Ether
Comparison between measurements from different places
The effects predicted by Courvoisier as a consequence of the Lorentz contraction of the Earth should depend on the latitude of the observatory. For that reason, if the same set of stars was observed from two observatories at very different latitudes, there should exist a systematic difference between the measured declinations of the stars, as a function of sidereal time.
To test the existence of this effect, Courvoisier analyzed the catalogues containing measurements made at Heidelberg (<|>i = + 49.24°) and at Cape Town, South Africa (§2 = - 33.48°). LetDj be the declination of some star measured from Heidelberg, andL>2 the declination of the same star measured from Cape of Good Hope. Each declination, according to Courvoisier's analysis, undergoes a periodical change:
Az\ = Vi oqPi Az2 = V2 CC2P2 (13)
Those effects are not equal; therefore, the difference between the declinations measured at the two observatories should undergo a periodical change:
Di-D2 = 1/2(aiPi-a2P2) (14)
Using the typical values A=15° andD=40° obtained in former measurements, and taking into account the latitudes of Heidelberg and Cape Town, Courvoisier predicted that there should exist a difference between the measured declinations of the stars that should depend on their right ascension a:
D\-D2 = + 0.16” - 0.18”.cos (a - 5 h) - 0.16”.cos 2(a -5 h) (15)
The amplitude was obtained by comparing the astronomical data of the two observatories, and led to v =750 km/s. Table 3 contains Courvoisier’s comparison between the observed and predicted values ofD\-D2-The third column of the table presented the observed values corrected for null declination, in order to avoid classical errors due to atmospheric refraction, etc. There is a better agreement between the theoretical prediction and the corrected values than with the raw data.
In his analysis of the second method, Courvoisier assumed that the Lorentz contraction of the Earth produces a local periodical change of the direction of the gravitational field. This effect was not compensated by changes in the direction of the astronomical instruments. Therefore, he was led to think that the effect could also be detected in an experiment using a terrestrial light source.