# Page:MichelsonMorley1886.djvu/9

Observations of the double displacement A.
 1st Series. l=3.022 meters${\displaystyle \theta }$=8.72 meters per second
${\displaystyle \Delta }$=double displacement; w=weight of observation.
 ${\displaystyle \Delta }$. w. ${\displaystyle \Delta }$. w. ${\displaystyle \Delta }$. w. ${\displaystyle \Delta }$. w. .510.508.504.473.557.425.560.544.521.575 1.91.61.71.4.4.62.9.1.1.1 .521.515.575.528.577.464.515.460.510.504 0.9.9.62.1.61.71.2.4.5.5 .529.474.508.531.500.478.499.558.509.470 0.62.01.4.8.5.61.0.42.02.1 .515.525.480.493.348.399.482.472.490 2.52.7.810.62.85.72.12.0.8
2d Series. l=6.151, ${\displaystyle \theta }$=7.65.
 ${\displaystyle \Delta }$. w. ${\displaystyle \Delta }$. w. ${\displaystyle \Delta }$. w. ${\displaystyle \Delta }$. w. .789.760.840.633.876.956 4.93.54.61.17.33.6 .891.883.852.863.863.820 1.72.511.11.51.13.4 .909.899.832.857.848.877 1.01.74.32.11.94.7 .399.908.965.967 6.65.92.03.3
3d Series. l=6.151, ${\displaystyle \theta =5.67}$.
 ${\displaystyle \Delta }$. w. ${\displaystyle \Delta }$. w. ${\displaystyle \Delta }$. w. ${\displaystyle \Delta }$. w. .640 4.4 .026 11.9 .636 3.1 .619 6.5

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

 Series ${\displaystyle \Delta }$. 123 .1858.1838.1800

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

${\displaystyle x=.434}$ with a possible error of ${\displaystyle \pm .02}$.
${\displaystyle {\frac {n^{2}-1}{n^{2}}}=.437}$

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