The bilinear method of cell averaging of the neutron cross sections developed by Nicholson from the variational principle has been explained and supported by a perturbation theory derivation. By introducing further approximations, a form of the method is derived which involves only the scalar fluxes and adjoints and the currents. The scalar form differs from that used previously by others. A physical explanation is given for the flux gradient term which leads to a pseudoabsorption effect.