is Rydberg's universal constant and
is a constant which is different for the different functions. A particular spectral line will, according to this principle, correspond to each combination of
, as well as to the functions
. The establishment of this principle led therefore to the prediction of a great number of lines which were not included in the spectral formulae previously considered, and in a large number of cases the calculations were found to be in close agreement with the experimental observations. In the case of hydrogen Ritz assumed that formula (1) was a special case of the general formula
and therefore predicted among other things a series of lines in the infra-red given by the formula