Page:BraceRefraction1904.djvu/8

From the above data we may calculate the least change in the index which could be observed if the water had become doubly refracting. If θ is the angle which the plane of polarization makes with one of the principal axes of the mica then the component vibrations or the principal axes of the resultant ellipse in the quarter-wave plate are in the ratio of tan θ to 1. For small angles then the ratio of the change of phase to the total or ${\tfrac {\lambda }{4}}$ is proportional to the angle θ. Thus 1° rotation of the mica gives

${\frac {1}{45}}\times {\frac {\lambda }{4}}={\frac {\lambda }{180}}$,

but 16' of the quarterwave plate was equivalent to 5° of the compensator, and as 0°.2 rotation of the latter could be detected, this reduces to

${\frac {16}{60}}\div 5\times 0.2\times {\frac {\lambda }{180}}={\frac {\lambda }{17,000}}=6\times 10^{-5}\lambda$

approx. for green. The total path of the light in the water was 2856 cms. Taking its index as 1.33, the number of waves is

${\frac {2856\times 1{\frac {1}{3}}}{.00005}}=7.6\times 10^{7}$.

As $6\times 10^{-5}$ of a single wave could be detected, the fraction of the total would be

$6\times 10^{-5}\times {\frac {1}{7.6}}\times 10^{-7}=7.8\times 10^{-13}$.

This represents the greatest difference in velocity or in index between the two components which could exist referred to that of water^[1] for green light, λ = .00005 cm.

Mascart^[2] has shown that in the case of water under compression the increment in the excess of the index above unity is nearly proportional to the increment of its density. If in the movement of matter through æther an increase in density in this direction took place, producing a change in the natural frequency of the molecular systems similar to that which occurs in glass, say, then, to determine how great it might be from these results, it is necessary to measure the

1. For carbon bisulphide Rayleigh obtained the corresponding limit of $4\times 10^{-11}$ for yellow light. His retardation was calculated from Wertheim's results. This checks with the data obtained above as 200 gms. gave 2°.5, hence 25 gms. would give 0°.31 or ${\tfrac {\lambda _{D}}{13000}}$ instead of ${\tfrac {\lambda _{D}}{12000}}$ which he gives.
2. Optique, t. iii. p. 613.