Page:MichelsonMorley1886.djvu/9

 Observations of the double displacement A.

$\Delta$=double displacement; w=weight of observation.

2d Series. l=6.151, $\theta$=7.65.

3d Series. l=6.151, $\theta=5.67$.

If these results be reduced to what they would be if the tube were $$10^m$$ long and the velocity $$1^m$$ per second, they would be as follows:

The final weighted value of $$\Delta$$ for all observations is $$\Delta=.1840$$. From this, by substitution in the formula, we get

$x=.434$ with a possible error of $\pm.02$.

$\frac{n^{2}-1}{n^{2}}=.437$|undefined

The experiment was also tried with air moving with a velocity of 25 meters per second. The displacement was about $$\tfrac{1}{100}$$ of a fringe; a quantity smaller than the probable error of observation. The value calculated from $$\tfrac{n^{2}-1}{n^{2}}$$ would be .0036.

It is apparent that these results are the same for a long or short tube, or for great or moderate velocities. The result was also found to be unaffected by changing the azimuth of the fringes to 90°, 180° or 270°. It seems extremely improbable that this could be the case if there were any serious constant error due to distortions, etc.