In the framr of r the rotational-vibrational pr to the pure rotational spectrum of the 9169162 nuclei of rare-earth metals, a new numericai value has been calculated for a previously estimated [4] adjusting factor. Precise calculations have shown that this factor is, unfortunatr by no means constant. Moreover, the deformation parameter has been computed for those nuelei. The graphical representation of both the adjusting factor, b, and the reciprocai of the deformation parameter,~-1, against the mass number, A, has been discussed. Ir has been found that b varir with A in a similar mannr as p-1.