On the Structure of the Line-Spectra of the Chemical Elements by Johannes Rydberg (1890; doi:10.1080/14786449008619945)

Original paper: commons.princeton.edu/josephhenry/wp-content/uploads/sites/71/2021/01/Rydberg-1890.pdf

Philosophical Magazine 29, 331–337. The author explicitly works in wave numbers and organizes line-series regularities; pages 333–337 give the formula and comparisons. The argument precedes the later quantum energy-level interpretation.