Now the second term depends only on end points, and therefore has no
effect on path. The first term contains only the second power of
aberration magnitude; and hence it has much the same value as if
everything were stationary. A ray that was straight, will remain
straight in spite of motion. Whatever shape it had, that it will
retain.
Only cos ε, and variations in α², can produce any effect on path;
and effects so produced must be very small, since the value of cos ε
is
√ (1 - α²sin²θ).
A second-order effect on direction may therefore be produced by
irrotational motion, but not a first-order effect. A similar statement
applies to the time of journey round any closed periphery.
_Michelson's Experiment._
We conclude, therefore, that general etherial drift does not affect
either the path of a ray, or the time of its journey to and fro, or
round a complete contour, to any important extent. But that taking
second-order quantities into account, the time of going to and fro in
any direction inclined at angle θ to a constant drift is, from the
above expression,
T₁ + T₂ = 2T cos ε / (1-α²) = √(1 - α²sin²θ) / (1 - α²) × 2T,
where 2 T is the ordinary time of the double journey without any
drift.
Hence some slight modification of interference effects by reason of
drift would seem to be possible; since the time of a to-and-fro
light-journey depends subordinately on the inclination of ray to
drift.
The above expression applies to Michelson's remarkable experiment[10]
of sending a split beam to and fro, half along and half across the
line of the earth's motion; and is, in fact, a theory of it. There
ought to be an effect due to the difference between θ = 0 and θ = 90°.
But none can be detected. Hence, either something else happens, or the
ether near the earth is dragged with it so as not to stream through
our instruments.
_Alternative Explanation._
But if the ether is dragged along near moving matter, it behaves like
a viscous fluid, and all idea of a velocity-potential must be
abandoned. This would complicate the theory of aberration (pp. 45 and
61), and moreover is dead against the experimental evidence described
in Chapter V.
The negative result of Mr. Michelson's is, however, explicable in
another way,--namely, by the FitzGerald-Lorentz theory that the linear
dimensions of bodies are a function of their motion through the ether.
And such an effect it is reasonable to expect; since, if cohesion
forces are electrical, they must be affected by motion, to a known and
calculable amount, depending on the square of the ratio of the speed
to the velocity of light. (See end of Chap. IV.)
Public-domain text, read in full here on John Shaqi.
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