## Abstract

The correct expression for the velocity of sound in general relativity is not obvious, because of ambiguity in defining the density of matter. The velocity is investigated in part I of this paper, and it is found that it never becomes greater than the velocity of light, having the value 3$^{-\frac{1}{2}}$ for incompressible matter. In part II this result is used in discussing the Schwarzchild solution for the interior of a fluid sphere. Eddington has already pointed out that this does not correspond to incompressible matter, and a solution for a sphere in which the velocity of sound is constant is sought, particular attention being paid to the special case of an incompressible fluid. No solution in closed form is found, but the equations are discussed in sufficient detail to enable the form of the solutions to be described. The limiting solution when the central pressure becomes infinite is tabulated in the incompressible case, and a number of numerical results are obtained.