Roberto Martins Searching for the Ether
Fig. 7. Courvoisier’s coupled mirror device for measuring the motion of the Earth through the ether.
Courvoisier’s new experiment was probably suggested by a similar arrangement that had been used by Esclangon in 192 7.23 The French astronomer used two mirrors, but light underwent three reflections (Fig. 8). The maximum effect occurred at 3 h or 15 h sidereal time, corresponding to A = 45° or 225\ Esclangon did not compute the speed of the Earth through the ether - indeed, he did not even provide a definite interpretation of the phenomenon.
The second method: Lorentz contraction
As described above, Courvoisier's second attempt to measure the absolute velocity of the Earth was grounded upon his analysis of the Lorentz contraction of the Earth (Fig. 9). In this case, Courvoisier supposed that the local vertical would undergo a change, due to the Lorentz contraction of the Earth, and this change would be observable as a periodical fluctuation in the angle between the North Pole and the zenith, as a function of the sidereal time.
Courvoisier's theoretical analysis led him to predict that the variation of the zenithal distance Az of a star close to the North Pole would obey the approximate relation:
Az = Vi ap (11)
23 Ernest Esclangon, “Sur la dissymétrie optique de l'espace et les lois de la réflexion", Comptes rendus de Yacadémie des sciences de Paris, clxxxv (1927), 1593-5 ; idem, “Sur l'existence d'une dissymétrie optique de l'espace", Journal des observateurs, xi (1928), 49-63.
Searching for the Ether
There are some special observational difficulties in this second method. If it were possible to observe a star laying exactly in the direction of the celestial North Pole, the observation would be quite simple. However, if the star is not exactly in the direction of the pole, its zenithal distance will depend on the sidereal time of the observation. This classical large effect would have, therefore, a period of one sidereal day and would interfere with any attempt to measure any influence due to the motion through the ether with a period of one sidereal day. Other interfering effects, such as temperature changes, vary with a period of about one solar day, and they are very large and irregular. For those reasons, Courvoisier gave up the attempt of finding the amplitude of the sidereal day effect, and only computed the half sidereal day effect. It was impossible, therefore, to find all parameters, and he assumed a value of 40° for the declination, and computed the speed and right ascension of the motion of the Earth relative to the ether. Dropping out the component corresponding to the period of one sidereal day, he obtained the following equation:
Az = - (lMXv/c^.sin2<|) (const. - cos2D.cos2(9-4)] (12)
Fig. 8. Esclangon’s coupled mirror device for measuring the motion of the Earth through the ether (a), and a graphical representation of his results (b), showing the observed angular fluctuations as a function of sidereal time.