Observations were made upon bisulphide of carbon in a tube 76 cms. long, and upon water in a tube 73½ cms. long. In neither case could the slightest shift of the band be seen on rotation of the board from the north-south position to the east-west position, whether at noon or at 6 p.m. The time required to pass from one observation to the other did not exceed 15 seconds, and the alternate observations were repeated until it was quite certain that nothing could be detected.
Of course the significance of this result depends entirely upon the delicacy of the apparatus, and it is worth little without an estimate of the smallest double refraction that would have been detected. It may even be objected that the investigation stands self-condemned. In consequence of the earth's magnetism there must be a rotation of the plane of polarization when the light traverses the bisulphide of carbon in the north and south position; and this effect, it may be argued, ought to manifest itself upon rotation of the board.
To take the objection first, it is easy to calculate the rotation of the plane of polarization. For one C.G.S. unit of magnetic potential the rotation in CS2 at 18° is .042 minute of angle.[1] In the present case the length is 76 cms. and the earth's horizontal force is .18; so that the whole rotation to be expected[2] is
- 76 x .18 x .042 = .58'.
So small a rotation of the plane, which would show itself, if at all, by a fading and not by a displacement of the band, is below the limit of observation.
The delicacy of the apparatus for its purpose may, indeed, be inferred indirectly from the rotation of the nicol found necessary to engender a marked revival of light at the darkest part of the band. If θ be this angle, the revived light is sin²θ, expressed as a fraction of the maximum obtainable with parallel nicols. In the actual observation the nicols remain accurately crossed, and the question is as to the effect of a double refraction causing e. g. a retardation of vertical vibrations relatively to horizontal ones. If this retardation amounted to ½λ, λ being the wave-length, the effect would be the same as of a rotation of the nicol through 90°. In general, a retardation of phase ε, in place of π, gives a revival of light measured by sin²(½ε). If the revivals of light in the two cases be the same, we may equate
