or dividing by 20×12 to obtain the means in terms of the distance between the fringes,
| N. | N.E. | E. | S.E. | S. | S.W. | W. | N.W. |
| 0.131 | 0.131 | 0.108 | 20.102 | 0.096 | 0.086 | 0.075 | 0.046 |
If x is the number of the column counting from the right and y the corresponding footing, then the method of least squares gives as the equation of the straight line which passes nearest the points x, y —
If, now, we construct a curve with ordinates equal to the difference of the values of y found from the equation, and the actual value of y, it will represent the displacements observed, freed from the error in question.
These ordinates are:
| N. | N.E. | E. | S.E. | S. | S.W. | W. | N.W. |
| -.002 | -.011 | -.003 | -.001 | -.004 | -.003 | -.001 | +.018 |
| N. S. Mean= Excess= |
-.002 -.004 -.003 +.001 -.004 |
E. W. |
+.003 -.001 +.001 |
N.E. S.W. Mean= Excess= |
-.011 -.003 -.007 +.008 -.015 |
N.W. S.E. |
+.018 -.001 +.008 |
The small displacements -0.004 and -0.015 are simply errors of experiment.
The results obtained are, however, more strikingly shown by constructing the actual curve together with the curve that should have been found if the theory had been correct. This is shown in fig. 4.
The dotted curve is drawn on the supposition that the displacement to be expected is one-tenth of the distance between the fringes, but if this displacement were only , the broken line would still coincide more nearly with the straight line than with the curve.
The interpretation of these results is that there is no displacement of the interference bands. The result of the hypothesis of a stationary ether is thus shown to be incorrect, and the necessary conclusion follows that the hypothesis is erroneous.
This conclusion directly contradicts the explanation of the phenomenon of aberration which has been hitherto generally accepted, and which presupposes that the earth moves through the ether, the latter remaining at rest.
