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A great difficulty was posed by an interference experiment, executed by Michelson^[1] in order to decide between the two theories.

It was noted by Maxwell, that if the aether remains at rest, then the motion of earth must have an influence on the time required by light to travel forth and back between two points regarded as fixed to earth. If $l$ is the distance of the points, $V$ the velocity of light, and $p$ that of earth, then the relevant time is given by (if the line of points is parallel to the direction of motion):

$2{\frac {l}{V}}\left(1+{\frac {p^{2}}{V^{2}}}\right)$

(1)

and if it is perpendicular to it

$2{\frac {l}{V}}\left(1+{\frac {p^{2}}{2V^{2}}}\right)$

(2)

making a difference of

${\frac {lp^{2}}{V^{3}}}$

(3)

Michelson used a device with two equally long-standing horizontal arms perpendicular to each other, with mirrors at the ends and perpendicular to their direction. An interference phenomenon occurred, when (from the radius of the intersection) a ray traveled forth and back along one arm, and another along the other arm. The entire device - including the light source and the observation telescope - could be rotated around a vertical axis, and the observation time was chosen, so that one can bring, as good as possible, one arm or the other arm into the direction of motion of earth. Let us assume for convenience that this is really the case, then - if Fresnel's theory is correct - due to the earth's motion the rays that travel forth and back into the earth's direction, must suffer a certain delay determined by (3) in respect to the other ray. When rotated by 90°, all phase shifts must be altered by an amount, which, expressed in unit time, can be given by the double of magnitude (3). But a displacement of the interference fringes could not be observed.

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1. American Journal of Science, 3d Ser. Vol. XXII, p. 120.