A general formula for the gR factor is derived in accordance with the spirit of Skyrme's variational method. Numerial values of gR for nine nuclei in the neighbourhood of Lu175 are obtained using Nilsson's wave functions. The calculated values of gR depend on the discrepancy of the spin-orbit coupling parameter x between the neutron and the proton. They are near to the observed values, smaller than Z/A and greater than those of the cranking model with pair-correlation interaction taken into account.