Page:MichelsonMorley1886.djvu/9

Observations of the double displacement A.

1st Series. l=3.022 meters
$\theta$=8.72 meters per second

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

$\Delta$.	w.	$\Delta$.	w.	$\Delta$.	w.	$\Delta$.	w.
.510 .508 .504 .473 .557 .425 .560 .544 .521 .575	1.9 1.6 1.7 1.4 .4 .6 2.9 .1 .1 .1	.521 .515 .575 .528 .577 .464 .515 .460 .510 .504	0.9 .9 .6 2.1 .6 1.7 1.2 .4 .5 .5	.529 .474 .508 .531 .500 .478 .499 .558 .509 .470	0.6 2.0 1.4 .8 .5 .6 1.0 .4 2.0 2.1	.515 .525 .480 .493 .348 .399 .482 .472 .490	2.5 2.7 .8 10.6 2.8 5.7 2.1 2.0 .8

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

$\Delta$.	w.	$\Delta$.	w.	$\Delta$.	w.	$\Delta$.	w.
.789 .760 .840 .633 .876 .956	4.9 3.5 4.6 1.1 7.3 3.6	.891 .883 .852 .863 .863 .820	1.7 2.5 11.1 1.5 1.1 3.4	.909 .899 .832 .857 .848 .877	1.0 1.7 4.3 2.1 1.9 4.7	.399 .908 .965 .967	6.6 5.9 2.0 3.3

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

$\Delta$.	w.	$\Delta$.	w.	$\Delta$.	w.	$\Delta$.	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 $10^{m}$ long and the velocity $1^{m}$ per second, they would be as follows:

Series	$\Delta$.
1 2 3	.1858 .1838 .1800

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 $\pm .02$.
${\frac {n^{2}-1}{n^{2}}}=.437$

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.