In this paper a tester is described which can be used to determine the linearity and fatigue in photomultipliers. Using this device, we have shown how to find the optimum arrangement of voltages to be applied to the dynodes of the photomultipliers to give linearity over the greatest possible range. When perfect linearity cannot be achieved, we have described a method which may be used to correct measured results for the lack of linearity. Detailed results are given for the 1P28 photomultiplier, but most of the ideas can similarly be applied to the other types.