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.
Roberto Martins Searching for the Ether DIO 17
He placed a mercury mirror directly below the observatory meridian circle and pointed the telescope downward. The instrument was then delicately adjusted in such a way that it was possible to observe the reflected image of the micrometer threads superimposed to the real threads. The position of the telescope was locked, and observations were made of the relative displacement of the micrometer thread and its image. He predicted the following deflection in the East-West direction:
Az = - (l/4)(v/c)2.[sin (|).sin 2D.sin (0-A) + cos (|).cos2D.sin 2(9—^4)] (16)
Table 3. Difference between the declinations of a star (Dj-Z^), observed from two distant observatories, as a function of sidereal time a.