, and dividing the former by the latter we get
. This value is very nearly equal to
; the deviation is, however, much greater than can be accounted for in any way by the errors of the experiments. It has been easy, however, to find a theoretical explanation of this point. In all the foregoing calculations we have assumed that the mass of the nucleus is infinitely great compared to that of the electron. This is of course not the case, even though it holds to a very close approximation; for a hydrogen atom the ratio of the mass of the nucleus to that of the electron will be about
and for a helium atom four times as great.
If we consider a system consisting of an electron revolving about a nucleus with a charge
and a mass