Note 18 — § 3. Spectra emitted from systems containing more than one electron.

On this view we should expect the Rydberg constant in (13) to be not exactly the same for all elements, since the expression (5) depends to a certain extent on the mass of the nucleus. The correction is very small; the difference in passing from hydrogen to an element of high atomic weight being only 0.05 per cent. (see IV. p. 7). In a recent paper (Proc. Roy. Soc. A. xci. p. 255, 1915), Nicholson has concluded that this consequence of the theory is inconsistent with the measurements of the ordinary helium spectrum. It seems doubtful, however, if the measurements are accurate enough for such a conclusion. It must be remembered that it is only for high values of that the theory indicates values of very nearly unity; but for such values of , the terms in question are very small, and the relative accuracy in the experimental determination not very high. The only spectra for which a sufficiently accurate determination of seems possible at present are the ordinary hydrogen spectrum and the helium spectrum considered in the former section, and in these cases the measurements agree very closely with calculation.