The solution of polarization field strength in ellipsoid and a homogeneous dielectric in condition of a constant external field is obtained with strict derivation and ellipsoidal coordinate. The conclusion that some textbooks given: the direction of polarization field strength with the direction of external field holds strict anti-parallel must be supplemented with additive certain conditions, otherwise it will not be correct. By means of the latticework and the step change calculation, the angle value of polarization vector with the external field is calculated and the changing situation about the angle value with the change of three half axes of ellipsoid is analysied.