Using a formulation based on Hamilton's ray equations, the variations of the path of a ray, and of the corresponding phase path, due to changes in the ray end points or the medium properties, are investigated. General expressions are obtained which represent the variations in terms of the solution of systems of ordinary differential equations. These may be integrated along the unvaried rays in order to evaluate the variations. The results, which may be applied to the analysis of a number of propagation problems, represent a simplification for anisotropic media and are also particularly well adapted to numerical applications.