# Page:MichelsonMorley1886.djvu/3

379
Motion of the Medium on the Velocity of Light.

Fresnel's statement amounts then to saying that the ether within a moving body remains stationary with the exception of the portions which are condensed around the particles. If this condensed atmosphere be insisted upon, every particle with its atmosphere may be regarded as a single body, and then the statement is, simply, that the ether is entirely unaffected by the motion of the matter which it permeates.

It will be recalled that Fizeau[1] divided a pencil of light, issuing from a slit placed in the focus of a lens, into two parallel beams. These passed through two parallel tubes and then fell upon a second lens and were re-united at its focus where they fell upon a plane mirror. Here the rays crossed and were returned each through the other tube, and would again be brought to a focus by the first lens, on the slit, but for a plane parallel glass which reflected part of the light to a point where it could be examined by a lens.

At this point vertical interference fringes would be formed, the bright central fringe corresponding to equal paths. If now the medium is put in motion in opposite directions in the two tubes, and the velocity of light is affected by this motion, the two pencils will be affected in opposite ways, one being retarded and the other accelerated; hence the central fringe would be displaced and a simple calculation would show whether this displacement corresponds with the acceleration required by theory or not.

Notwithstanding the ingenuity displayed in this remarkable contrivance, which is apparently so admirably adopted for eliminating accidental displacement of the fringes by extraneous causes, there seems to be a general doubt concerning the results obtained, or at any rate the interpretation of these results given by Fizeau.

never be 1. The above expression, however gives this result when the particles are in contact - for then ${\displaystyle b=0}$ and ${\displaystyle x={\frac {n^{2}-1}{n^{2}}}+{\frac {1}{n^{2}}}=1}$.
Resuming equations (1) and putting ${\displaystyle a+b=l}$ we find ${\displaystyle (n-1)l=(\mu -1)a}$. But for the same substance ${\displaystyle \mu }$ and a are probably constant or nearly so; hence ${\displaystyle (n-1)l}$ is constant.
But Clausius has shown that ${\displaystyle l=\kappa {\frac {\sigma }{\rho }}a}$, where ${\displaystyle \kappa }$ is a constant, ${\displaystyle \sigma }$ the density of the molecule; ${\displaystyle \rho }$, that of the substance; and a, the diameter of the "sphere or action." ${\displaystyle \sigma }$ and a are probably nearly constant, hence we have finally ${\displaystyle {\frac {n-1}{\rho }}=constant}$.
Curiously enough, there seems to be a tendency towards constancy in the product ${\displaystyle (n-1)l}$ for different substances. In the case of 26 gases and vapors whose index of refraction and "free path" are both known, the average difference from the mean value of ${\displaystyle (n-1)l}$ was less than 20 per cent, though the factors varied in the proportion of one to thirteen; and if from this list the last nine vapors (about which there is some uncertainty) are excluded, the average difference is reduced to 10 per cent.

1. Ann. de Ch. et de Ph., III, lvii, p. 385, 1859.