290 
DE. T. M. LOWRY: NATURAL AND MAGNETIC ROTATORY DISPERSION 
The tabulation of the average errors gives a very fair idea of the degree of accuracy 
attained in the actual reading of the lines. As these errors average about 5 parts 
per million and do not exceed 13 parts per million, even in the case of the blue 
lines, it may be presumed that the first five decimals in the ratios can be relied on 
throughout the table, the prol^able error in nearly all the lines amounting only to a 
few units in the sixth decimal. These figures are multiplied by 25‘5371 to give the 
rotations in degrees per millimetre; but when tabulated to four places of decimals the 
errors in the last significant figure are reduced to a quarter of their previous values; 
the average error of reading is thus 0°’0001 per mm. or less in 12 of the 24 lines ; in 
the case of eight more lines it is 0°'0002 per mm. or less and in three lines only it 
reaches its highest value at 0°'0003 per mm. ; the fourth decimal is, therefore, subject 
on the average to an error of reading of oidy a little over one unit. 
The errors discussed in the preceding paragraph refer merely to the discrepancies 
introduced into the dispersion-ratios by changing from dextro- to Imvo-quartz or from 
a positive to a negative half-shadow angle. They do not take any account of errors 
due to imperfect purification of the light or to incorrect figures for the wave-length 
(or optical mass centre) of the lines, which may in some cases be appreciable, e.g., in 
the case of the two green copper lines, wliich are known to include satellites. Even 
the ordinary wave-length determinations may contribute appreciable errors, since an 
error of O'Ol Angstrom unit would introduce an error of three units in the sixth 
decimal of the dispersion-ratios. 
Some idea of the maximum amount of these irregular errors can be obtained from 
the values of the rotations calculated from a formula. Any attempt to discuss fully 
the equation to the dispersion-curve would be premature until work now in progress, 
on the rotatory dispersion in cj[uartz, in the ultra-violet and in the infra-red regions 
of the spectrum, has been carried to completion ; but a preliminary survey, for which 
I am greatly indebted to Mr. T. W. Dickson, of the City and Guilds College, 
South Kensington, has shown— 
(1) Tl lat tlie simple equati 
on 
_ k, k' 
«- + p ’ 
which Drude (‘Theory of Optics,’ p. 414) regarded as sufficient for calculating the 
rotatory dispersion of quartz to two places of decimals, is quite inadequate to 
represent the values now given to four places of decimals; 
(2) But the equation 
X'-Xj- X"-Xy X^ 
where X^^ = O'Ol0627, Xs^ = 78'22 gives values which, in the case of 22 out of 24 wave¬ 
lengths, differ on the average from the observed figures by only a single unit in the 
third decimal place, i.e., by 1 part in 25,000. This agreement is somewhat remarkable 
In an equation containing oidy three arbitraiy constants. 
