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The Relative Motion of the Earth and the Luminiferous Ether

by Albert A. Michelson. Master, U. S. Navy.

The undulatory theory of light assumes the existence of a medium called the ether, whose vibrations produce the phenomena of heat and light, and which is supposed to fill all space. According to Fresnel, the ether, which is enclosed in optical media, partakes of the motion of these media, to an extent depending on their indices of refraction. For air, this motion would be but a small fraction of that of the air itself and will be neglected.

Assuming then that the ether is at rest, the earth moving through it, the time required for light to pass from one point to another on the earth’s surface, would depend on the direction in which it travels.

Let ${\textrm {V}}$ be the velocity of light.

$v$ = the speed of the earth with respect to the ether.

${\textrm {D}}$ = the distance between the two points.

$d$ = the distance through which the earth moves, while light travels from one point to the other.

$d_{1}$ = the distance earth moves, while light passes in the opposite direction.

Suppose the direction of the line joining the two points to coincide with the direction of earth’s motion, and let ${\textrm {T}}$ = time required for light to pass from the one point to the other, and ${\textrm {T}}_{1}$ = time required for it to pass in the opposite direction. Further, let ${\textrm {T}}_{0}$ = time required to perform the journey if the earth were at rest. Then

${\textrm {T}}={\frac {{\textrm {D}}+d}{\textrm {V}}}={\frac {d}{v}}$; and ${\textrm {T}}_{1}={\frac {{\textrm {D}}-d}{\textrm {V}}}={\frac {d_{1}}{v}}$

From these relations we find $d={\textrm {D}}{\tfrac {v}{{\textrm {V}}-v}}$ and $d_{1}={\textrm {D}}{\tfrac {v}{{\textrm {V}}+v}}$, whence ${\textrm {T}}={\tfrac {\textrm {D}}{{\textrm {V}}-v}}$ and ${\textrm {T}}_{1}={\tfrac {\textrm {D}}{{\textrm {V}}+v}}$; ${\textrm {T}}-{\textrm {T}}_{1}=2{\textrm {T}}_{0}{\tfrac {v}{\textrm {V}}}$ nearly, and $v={\textrm {V}}{\tfrac {{\textrm {T}}-{\textrm {T}}_{1}}{2{\textrm {T}}_{0}}}$.

If now it were possible to measure ${\textrm {T}}-{\textrm {T}}_{1}$, since ${\textrm {V}}$ and ${\textrm {T}}_{0}$ are known, we could find $v$ the velocity of the earth’s motion through the ether.

In a letter, published in “Nature” shortly after his death, Clerk Maxwell pointed out that ${\textrm {T}}-{\textrm {T}}_{1}$, could be calculated by measuring the velocity of light by means of the eclipses of Jupiter’s satellites at periods when that planet lay in different directions from earth; but that for this purpose the observations of these eclipses must greatly exceed in accuracy those