Recent interest in bimesogenic liquid crystals showing two nematic phases has led us to investigate the nematic mean-field interactions in these nematic phases by using rigid solutes as probes. The nematic potential that is modelled by two independent Maier-Saupe terms is successful in fitting the observed dipolar couplings (order parameters) of para-, meta- and ortho-dichlorobenzene solutes in both the nematic phases of 39wt% of 4-n-pentyl-4 '-cyanobiphenyl (5CB) in alpha,omega-bis(4-4 '-cyanobiphenyl)nonane (CB_C9_CB) to better than the 5% level. The derived liquid-crystal potential parameters G(1) and G(2) for each solute in the N and N-tb phases will be discussed. The most interesting observation is that G(1) (associated with size and shape interactions) is almost constant in the N-tb phase, whereas G(2) (associated with longer-range electrostatic interactions) has large variation, even changing sign.