Page:MichelsonEmission.djvu/3

The corresponding displacement of the interference fringes is

$\Delta ={\frac {V\left(T_{1}-T_{2}\right)}{\lambda }}=4{\frac {D}{\lambda }}(2-r){\frac {v}{V}}$

For	$r=0$	$\Delta =8{\frac {D}{\lambda }}{\frac {v}{V}}$
"	$r=1$	$\Delta =4{\frac {D}{\lambda }}{\frac {v}{V}}$
"	$r=2$	$\Delta =0$

The experiment was tried under the following conditions.

The revolving mirrors were mounted on the shaft of an electric motor the speed of which (measured by a speed counter) could be varied from zero to 1800 revolutions per minute. The distance between centers of the mirrors was l = 26.5 cm;^[1] the distance OE was 608 cm. The light of the carbon arc (in one experiment, sunlight) was filtered through a gelatine film transmitting light of mean wave-length λ = 0^μ.60.

The formula for the displacement,

$\Delta =8\pi n{\frac {l}{\lambda }}{\frac {D}{V}}$ if n is turns per sec.

or

$\Delta ={\frac {8}{60}}\pi N{\frac {l}{\lambda }}{\frac {D}{V}}$ if N is turns per min.

gives with these data and r = 0 a displacement of 3.76 fringes for 1000 revolutions per minute.

Following is a table of results of observations reduced to this speed.

It appears therefore that within the limit of error of experiment (say 2 per cent) the velocity of a moving mirror is without influence on the velocity of light reflected from its surface.

Assuming that the effect is actually nil, this interference method may be used to measure the velocity of light with an order of accuracy equal to that of the improved Foucault method or of the "combination" method proposed in an article in the Phil. Mag.,

1. This agrees within less than 1 per cent with the distance calculated from the measured distance AB of the interferometer mirrors.