Page:MajoranaEmission1.djvu/11

We have, therefore,

$n'=n\left(1+{\frac {2k\pi dg\ \cos \alpha \ \cos \theta }{c}}\right)$

and, by the hypothesis of the invariability of c,

$\lambda '=\lambda \left(1-{\frac {2k\pi dg\ \cos \alpha \ \cos \theta }{c}}\right)$

If l is the difference of path of two interfering rays in Michelson's apparatus, the number of fringes which are seen to cross the micrometer thread of the telescope when λ becomes λ' (that is to say when the velocity of rotation varies between zero and g turns per second) is

$f={\frac {l}{\lambda }}{\frac {2k\pi dg\ \cos \alpha \ \cos \theta }{c}}$.

If the observation is made by noting the position of the fringes when the wheel turns in one sense with the velocity g, and that corresponding to an equal and contrary velocity, the number of fringes crossing the micrometer thread will be 2f.

Now, in my apparatus d = 38 cm., α = 29°, θ = 27°, k = 4 (as in the figure); if λ is put equal to 0.546μ (green mercury line), l = 13 cm., c = 3·10¹⁰ cm., and g = 60 (turns of R per second in one sense and afterwards in the other), we may expect, according to the preceding formula, a fringe displacement 2f = 0.71.

Experiment gives, for the case mentioned, a displacement of between 0.7 and 0.8 fringes; and it is not possible, for reasons of visibility, to carry the precision of the observations further. But, as is seen, the agreement between the predicted result and observation is sufficient; this agreement is confirmed by observations made by choosing other convenient values of l and g, of which for brevity's sake I shall not speak here.

Experiment, therefore, authorizes the conclusion that reflexion of light by a moving metallic mirror does not alter the velocity of propagation of the light itself, in air, and consequently, with great probability, also in vacuo; at least, in the conditions of the experiment above described. This experimental result, as to which no doubt can be entertained, is contrary to the hypothesis of some physicists who, like Stewart^[1], basing themselves upon the electromagnetic emission theory of Thomson, maintain the possibility that

1. Phys. Rev. xxxii. p. 418 (1911).