360 
LORD RAYLEIGH ON THE CONSTANT OF MAGNETIC 
made on light of the refrangibility of the thallium line. The corrected* * * § result for 
this light is in circular measure l'5238x 10~ 5 , or '05238 minute. To pass to sodium 
we may use a formula given by BecquerelI and Yerdet, according to which the 
rotation for different wave lengths (X) is proportional to /F(/x 3 —1)\ -2 , /x being the 
refractive index. At this rate the '05238 minute for thallium would be '04163 
minute for sodium. The temperature was not directly observed by Gordon, but was 
estimated to be about 13° C. Assuming this to be correct, the value for 18° would be 
'0413 minute, or about 2 per cent, less than according to my determinations. 
Appendix. 
Notes on Polarimetry in general. 
The problem of the polarimeter is how best to render evident the rotation through 
a small angle 0 of the jdane of polarisation of light of brightness h. The effect of the 
rotation is to introduce light of amplitude h) sin 0, or Jv0, polarised in the perpen¬ 
dicular plane, and it is this which must be made to produce a recognisable change. 
By the use of a Nicol, or double-image prism, adjusted to the original plane, the light 
of brightness h0 2 may be isolated, but, as will be proved presently, this is not the 
best method of rendering its existence evident. 
From the preceding mode of statement it is clear that the accuracy obtainable in 
determining the plane of polarisation increases indefinitely with the brightness of the 
light, and is in fact proportional to the square root of that brightness. J Again we see 
that little is to be expected from such devices as that of Fizeau, in which the rotation 
is magnified by causing the light to pass obliquely through a pile of glass plates. The 
brightness of the light polarised in the perpendicular plane (h0 2 ) can only be diminished 
by such treatment, and the increase of rotation, being due merely to weakening of the 
first component, is of no value. 
The arrangements to be adopted depend for their justification upon the physio¬ 
logical law of the perception of differences of brightness. If c?E denote the difference 
of sensations, corresponding to two degrees of brightness, FI and H+c?H, we have § 
clE—A 
dK 
H + H 0 
in which H 0 is a certain constant brightness, supposed to depend chiefly upon the 
proper or internal light of the eye, but to which may be added, the effect of light 
* Mr. Gordon’s result was originally given at double its proper value, 
t Ann. d. Cliim., t. xii., 1877, p. 78. 
X This point is insisted upon in an excellent paper by Lippich (Wien. Ber., 85, 9 Feb., 1882), which 
has lately come to my notice. 
§ Helmholtz : ‘ Physiologische Optik,’ § 27. 
