θ to ½ε. Hence if we find that rotation θ produces a sensible effect in lessening the darkness at the darkest place, we may infer that there is delicacy sufficient to detect a relative retardation of 2θ due to double refraction. This comparison would apply if the test for double refraction were made by simple observation of the revival of light. As actually carried out by location of the band, the test must be many times more delicate.
It was found that a marked fading of the band attended a rotation of the nicol through 4'. According to this ε would be 1/450; or since a retardation of ½λ corresponds to ε = π, a retardation amounting to 1/1400 x ½λ should be perceptible many times over, regard being paid to the superior delicacy of the method in which a band is displaced relatively to fixed marks.
Another and perhaps more satisfactory method of determining the sensitiveness was by introducing a thin upright strip of glass which could be compressed in the direction of its length by small loads. These loads were applied symmetrically in such a manner as to cause no flexure. The double refraction due to the loads is of exactly the character to be tested for, and accordingly this method affords a very direct check. If the load be given, the effect is independent of the length of the strip and of its thickness along the line of vision, but is inversely as the width. The strip actually employed had a width of 15 mm.; and the application (or removal) of a total of 50 gms. caused a marked shifting of the band, while 25 gms. was just perceptible with certainty.
To interpret this we may employ some results of Wertheim (Mascart's Traité d'Optique, t. ii. p. 232), who found that it requires a load of 10 kilograms per millimetre of width to give a relative retardation of ½λ, so that with the actual strip the load would need to be 150 kilograms. The retardation just perceptible is accordingly ½λ6000. This may be considered to agree well with what was expected from the effect of rotating the nicol.
We have now only to compare the relative retardation which would be detected with the whole retardation incurred in traversing the 76 cm. of bisulphide of carbon. In this length there are contained 1,200,000 wave-lengths of yellow light, or 2,400,000 half wave-lengths. The retardation due to the refraction may be reckoned at .6 of this, or 1,440,000 half wave-lengths. Thus the double refraction that might be detected, estimated as a fraction of the whole refraction,
