the angle bab/ being equal to the aberration = α, is returned along ba/, (aba/=2α), and goes to the focus of the telescope, whose direction is unaltered. The transmitted ray goes along ac, is returned along ca/, and is reflected at a/ making ca/e equal 90 – α, and therefore still coinciding with the first
Fig. 2.
ray. It may be remarked that the rays ba/ and ca/ do not now meet exactly in the same point a/, though the difference is of the second order; this does not affect the validity of the reasoning. Let it now be required to find the difference in the two paths aba/ and aca/.
Let V=velocity of light.
v=velocity of the earth in its orbit.
D=distance ab or ac, fig. 1.
T=time light occupies to pass from a to c.
T/=time light occupies to return from c to a/ (fig. 2).
Then
The whole time of going and coming is
and the distance travelled in this time is
neglecting terms of the fourth order. The length of the other path is evidentlyor to the same degree
of accuracy, The difference is therefore
If now the whole apparatus be turned through 90°,
the difference will be in the opposite direction, hence the
displacement of the interference-fringes should be
Considering only the velocity of the earth in its orbit, this would be 2D × 10–8. If, as was the case in the first experiment, D = 2 × 106 waves of yellow light, the displacement to be expected would be 0. 04 of the distance between the interference-fringes.
In the first experiment, one of the principal difficulties encountered was that of revolving the apparatus without producing distortion; and another was its extreme sensitiveness to vibration. This was so great that it was impossible to see the interference-fringes except at brief intervals when working in the city, even at two o'clock in the morning. Finally, as before remarked, the quantity to be observed, namely, a displacement of something less than a twentieth of the distance between the interference-fringes, may have been too small to be detected when masked by experimental errors.
The first-named difficulties were entirely overcome by mounting the apparatus on a massive stone floating on mercury; and the second by increasing, by repeated reflexion, the path of the light to about ten times its former value.
The apparatus is represented in perspective in fig. 3, in plan in fig. 4, and in vertical section in fig. 5. The stone a (fig. 5) is about 1. 5 metre square and 0. 3 metre thick. It rests on an annular wooden float bb, 1. 5 metre outside diameter, 0. 7 metre inside diameter, and 0. 25 metre thick. The float rests on mercury contained in the cast-iron trough cc, 1. 5 centi-
