Page:BraceRefraction1904.djvu/9

Rh increment in phase which represents the sensibility of the experiment in terms of the excess of the index above unity. This excess of index is $$\tfrac{1}{3}$$ while the index is $$\tfrac{4}{3}$$, hence our limit should be four times larger or $$3.1\times10^{-12}$$. The greatest change which could be expected is the difference between unity and $$\sqrt{1-\tfrac{v^{2}}{V^{2}}}$$ where $${v}$$ is orbital velocity and $${V}$$ light-velocity or

$\frac{1}{2}\frac{v^{2}}{V^{2}}=\frac{1}{2}(10^{-4})^{2}=5\times10^{-9}$,|undefined

or about 1600 times greater than the smallest effect which could be observed.

The effect of a change in the frequency of the order $$\tfrac{v^{2}}{2V^{2}}$$ on the index of the moving molecular vibrations relatively to the aether impulses in the direction of motion, is far too small to be observed. Thus the index of water for frequency $$5.1\times10^{14}$$ is 1.334 and for $$6.9\times10^{14}$$ is 1.341. This gives for a fractional increase in frequency of 4/3 a fractional increase in index of $$0.007\times\tfrac{4}{3}$$. Hence the fractional increase in index due to a change of frequency of order $$0.5\times10^{-8}$$ is

$\frac{0.5\times10^{-8}}{\frac{4}{3}\times10^{14}}\times9\times10^{-3}=3.5\times10^{-23}$,|undefined

while the smallest observable change was $$7.8\times10^{-13}$$.

Two different arrangements were tried with glass. In the first a large slab of "optical" glass (crown) was cut lengthwise and the edges of the two halves ground square. These were then cemented together side by side so as to give approximately square end-surfaces for grinding and polishing. Those end-surfaces were "built up" in the usual way so as to ensure a "flat" surface. These two prisms were then cemented end to end, giving a prism 42 cms. long with polished ends 10 cms. by 3.8 cms. These end-surfaces were silvered and a strip at the bottom and top of each removed. The system was then mounted on a support within the trough so that light from the polarizer could pass in and lie reflected backwards and forwards until it passed out through the unsilvered space at the other end, where it was again reflected back into the prism by a concave mirror 3 in. radius of curvature, approximately. After the same number of reflexions it passed out to one side of the entering ray and was received by the half-shade analysing system already