The gain of a photomultiplier is given by the equation G = k.σ^n, where k is the efficiency of collection of photoelectrons on the first dynode, σ is the secondary emission ratio, i.e. the number of secondary electrons emitted for each electron incident on the dynode and n is the number of dynodes.
Source:
PAC, 1995, 67, 1745. 'Nomenclature, symbols, units and their usage in spectrochemical analysis-XI. Detection of radiation (IUPAC Recommendations 1995)' on page 1753 (https://doi.org/10.1351/pac199567101745)