Page:Philosophical Transactions of the Royal Society A - Volume 184.djvu/845

straight, will remain straight in spite of motion; whatever shape it had, that it will retain. Only $\cos \epsilon$, and variations in $\alpha ^{2}$, can produce any effect on path, and effects so produced must be very small, since the value of $\cos \epsilon$ is ${\sqrt {\left(1-\alpha ^{2}\sin ^{2}\theta \right)}}$. 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.

25. We conclude, therefore, that general ethereal drift does not affect either the path of a ray or the time of its journey 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 $\theta$ to a constant drift is, from the above expression, § 24,

${\frac {2\mathrm {T} \cos \epsilon }{1-\alpha ^{2}}}={\frac {\sqrt {\left(1-\alpha ^{2}\sin ^{2}\theta \right)}}{1-\alpha ^{2}}}\times 2\mathrm {T}$,

where $2\mathrm {T}$ is the ordinary time of the double journey.

Hence, by this means, interference effects due to drift would seem to be possible, since the time depends subordinately on the inclination of ray to drift (cf. §§ 59–62)

The above expression applies to Michelson’s^[1] remarkable experiment of sending a split beam to and fro, half along and half across the line of earth motion; and is, in fact, the theory of it. There ought to be an effect due to the difference between $\theta =0$ and $\theta =90$°, but he does not observe any. Hence, either something else happens, or the ether near the earth is dragged with it, so as not to stream through our instruments. When $\alpha$ is constant I see no way out of this conclusion, except hypothetical disturbance at reflexion of some minute kind, one of the mirrors being normal and the other tangential to the drift; but I perceive no adequate reason for this suggestion (see § 60). It is true that if the earth is carrying the ether with it, $\alpha$ will not be constant, at different distances from its surface; but, then, the plane of Michelson’s experiment was horizontal.

If the ether is dragged along near moving matter it behaves like a viscous fluid, and a velocity-potential must (save by some exceptional theory, § 31) be abandoned; but, as this would involve the curvature of rays striking the earth and much complication, it seems a pity to abandon it until compelled by direct experimental evidence to recognize ethereal viscosity.

The experiment of Michelson’s raises a strong presumption in favour of such viscosity, nevertheless his negative result is conceivably explicable in other ways: one of which has been ingeniously suggested by Professor Fitzgerald, viz., that the cohesion force between molecules, and, therefore, the size of bodies, may be a

1. ‘Phil. Mag.,’ Dec., 1887.