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In order to find the new wave-front, draw the arc fg with b as a centre and ad as radius; the tangent to this arc from d will be the new wave-front, and the normal to the tangent from b will be the new direction. This will differ from the direction ba by θ, which it is required to find. From the equality of the triangles adb and edb it follows that θ = 2φ, ab = ac,
or, neglecting terms of the order r3,
Now let the light fall on a parallel mirror facing the first, we should then have
and the total deviation would be
where p is the angle of aberration, if only the orbital motion of the earth is considered. The maximum displacement obtained by revolving the whole apparatus through 90° would be
With fifty such couples the displacement would be 0.2″. But astronomical observations in circumstances far less favourable than those in which these may be taken have been made to hundredths of a second ; so that this new method bids fair to be at least as sensitive as the former.
The arrangement of apparatus might be as in fig. 2; s, in the focus of the lens a, is a slit. bb/ cc/ are two glass mirrors optically plane, and so silvered as to allow say one twentieth of the light to pass through, and reflecting say ninety per cent. The intensity of the light falling on the observing telescope df would be about one millionth of the original intensity, so that if sunlight or the electric arc were used it could still be readily seen. The mirrors bb/ and cc/ would differ from parallelism sufficiently to separate the successive images. Finally, the apparatus need not be mounted so as to revolve, as the earth’s rotation would be sufficient.
If it were possible to measure with sufficient accuracy the
460 Messrs. Michelson and Morley on the Relative Motion