The field equations in the neighbourhood of a particle for a spherically symmetric metric in the conformal theory of gravitation put forward by Hoyle & Narlikar are examined in detail. This metric is assumed to be of the usual form $ds^2 = e^vdt^2-e^\lambdadr^2-r^2(d\theta^2+sin^2\theta d\psi^2)$ where $\lambda$ and v are functions of r only. Hoyle & Narlikar obtained a solution of the field equations under the assumption $\lambda$ + v = 0. In this paper the case $\lambda$ + v $\neq$ 0 is investigated, and it is shown that the only solution that satisfies all the boundary conditions is the special solution obtained by setting $\lambda$ + v = 0. The significance of this result is discussed.