The conventional treatment of a vibrating membrane with a small mass load, originated by Rayleigh, leads to perturbed eigenfrequencies slightly lower than the unperturbed values and independent of the area of the load so long as it is small compared to the area of the membrane. It is shown that this result is incorrect because of an invalid initial assumption about the amplitude of vibration of the load. Actually the perturbed frequencies are slightly higher than the unperturbed values, depend upon the area of the load, and approach the unperturbed values as the load approaches point mass. In addition a very low frequency mode exists whose frequency approaches zero as the load becomes smaller in area; this mode represents a perturbation of the trivial zero-frequency solution in the unperturbed case. The special case of a circular membrane loaded at the center is discussed in some detail.