The theory of the figure of the Earth on the hydrostatic hypothesis, developed by Darwin and de Sitter, is applied to models for Jupiter and Saturn proposed by W. H. Ramsey and B. Miles. It is found that the integral equation for the coefficient of the fourth harmonic is more easily solved directly than by conversion into a differential equation. The results show that the ratio D/J 2 , which is equal to 35 l /12 k2 in the treatment of H. and G. Struve, is substantially larger than for a homogeneous body in a hydrostatic state, and in satisfactory agreement with observation for Saturn. Comparison with a model given by Darwin indicates that an inequality stated by de Sitter for the coefficient of the fourth harmonic is not general.