Page:TolmanPostulate.djvu/10

 $$\frac{1.5}{300000}\times10=.5\times10^{-4}$$ cm.

We obtain double the effect, or 10-4 cm., in changing from the approaching to the receding limb of the sun, and considering $$5\times10^{-5}$$ as an average wave-length, we should expect a shift of about two fringes. Since no shift was observed, we have strong evidence that the velocity of light is independent of the velocity of its source.

To complete the discussion, it is necessary to consider the effect of the lens (and the earth's atmosphere) through which the light has to pass before reaching the slit. At first sight, it might seem as if an original difference between the velocities of light from the two sources would be obliterated by passage through a stationary medium. The experiments of Fizeau and of Michelson, however, give us data for calculating the effect upon the velocity of light of relative motion between the source of light and a transmitting medium.

If c is the velocity of light in vacuo, μ the index of refraction of the medium and v the velocity with which the medium is moving towards the source, we have the velocity of light in the medium equal to $$c/\mu\mp v\theta$$, where θ is some fraction which must be determined experimentally. The considerations of Fresnel and others have led to the expression for any medium θ=(u²-1)/μ², an equation which was very closely verified for water in the experiments referred to. The velocity of light in the lens may now be calculated.

$$c/\mu\mp v\theta$$ is the velocity of light with respect to the source; with respect to the medium, it will be $$c/\mu\mp v(1-\theta)$$. For glass, putting μ=1.5, we have θ=(u²-1)/μ²=0.51. The velocity of light from the approaching limb will be c/μ+0.49v and from the receding limb c/μ-0,49v, where v may be taken as 1.5 km. per second. We now see that, even if the light after leaving the lens did not regain its original velocity, the difference in the velocities of the light from the two limbs of the sun would still be about 1.5 km. per second, which would give a shift of one fringe in the experiment performed.

As a result of the experiment, we conclude that the velocity of