This paper takes up the calculation of the electromagnetic field scattered by a sphere composed of a material with any relative permittivity and permeability, according to the method of A.F. Stevenson (1953). Unlike Stevenson's original publication, the calculations are detailed and completed. This work completes that achieved for an ellipsoid (Gruy, hal-04655313). However, the result is not obtained by replacing (a,b,c) by (R,R,R) into the expressions of the electromagnetic field, revealing technical problems, but by directly applying Stevenson's method. The solution then uses the spherical harmonic functions in place of the ellipsoidal harmonic functions. The solution obtained by Stevenson's method has been successfully compared to that obtained by Mie's theory. The interest of this result, which has also been well known for a long time, lies in its use as a tool for partial validation of the solution obtained for the ellipsoid.