[1] An empirical relationship is supported by confirmatory data irrespective of theoretical basis such as first principles.
An example was the Rydberg formula to predict the wavelengths of hydrogen spectral lines.
Proposed in 1876, it perfectly predicted the wavelengths of the Lyman series, but lacked a theoretical basis until Niels Bohr produced his Bohr model of the atom in 1925.
[2] On occasion, what was thought to be an empirical factor is later deemed to be a fundamental physical constant.
[citation needed] Some empirical relationships are merely approximations, often equivalent to the first few terms of the Taylor series of an analytical solution describing a phenomenon.