Roberto Martins Searching for the Ether DIO 17
then developed an equation to account for the effect, analyzed the data using the minimum square method, and obtained his second measurement of the velocity of the Earth relative to the ether. The speed obtained in this case was about 700 km/s, in the direction of the constellation of Perseus (not very far from Auriga). Courvoisier regarded the agreement of those two earliest results as satisfactory, and this led him to further researches. There was a delay of 5 years between Courvoisier’s first positive results and his next publication on the subject.12 In this period he accumulated a series of positive results by different methods, obtained the equations required for the analysis of his data, and devised new methods for measuring the absolute speed of the Earth. This delay shows that Courvoisier was careful enough to resist publishing preliminary results before he was able to amass a large amount of evidence for his claim.
The method of the moving mirror
Courvoisier derived equations13 that related the relevant measurements to the parameters of the motion of the Earth relative to the ether.14 The main parameters that appear in his equations (Fig. 2) are:
c = the speed of light relative to the ether = 300,000 km/s
v = speed of the Earth (or the solar system) relative to the ether
A = right ascension of the apex of the absolute motion
D = declination of the apex of the absolute motion
a = North local component of v/c
P = Zenith local component of v/c
y = West local component of v/c
<|) = latitude of the terrestrial observatory
9 = sidereal time of measurement
A straightforward geometrical analysis shows that the components of v/c are:
a = (v/c) [cos <|) sin D - sin <|) cos D cos (0—^4)] (1)
P = (v/c) [sin <|) sin D + cos <|) cos D cos (9-v4)] (2)
12 Leopold Courvoisier, “Bestimmungsversuche der Erdbewegung relativ zum Lichtäther”, Astronomische Nachrichten, ccxxvi (1926), 241-64.
13 Courvoisier never published the details of his derivations - he only presented his main assumptions, a few steps and the final results. In all relevant cases, however, I have been able to confirm that his equations do follow from his assumptions.
14 Courvoisier, “Bestimmungsversuche der Erdbewegung relativ zum Lichtäther” (ref. 12).
Searching for the Ether
y = - (v/c) cos D sin (9- 4) (3) NP
Fig. 2. This diagram shows the main geometrical parameters used in Courvoisier’s theoretical analysis of ether effects. The spherical surface represents the Earth, and the observer is at /, and the local directions Z, N, W correspond to Zenith, geographical North and West. The North Pole is in the direction NP. The velocity of the
Earth is V .
In Courvoisier's first method, as described above, light was reflected by a mirror. To derive the theoretical effect, it was necessary to study the influence of the motion of the mirror through the ether upon the direction of the reflected ray. Courvoisier made use of the non-relativistic analysis developed by Adolf von Hamack,15 that predicted that the angle of reflection would be different from the angle of incidence, relative to the proper reference system of the mirror (Fig. 3). This was one of Courvoisier’s main assumptions that was incompatible with the principle of relativity.
15 Adolf von Hamack, “Zur Theorie des bewegten Spiegels”. Annalen der Physik, series 4, xxxix (1912), 1053-8.