The liquid-liquid coexistence of dimethyl carbonate + n-decane and dimethyl carbonate + n-tetradecane has been determined within 10 K from the critical temperature by measurements of refractive index n. The critical amplitude B and the critical exponent beta have been deduced from the coexistence curves. Experimental values of beta are consistent with theoretical prediction. The results have also been analyzed to determine Wegner-correction terms when beta and Delta are fixed at the theoretical values and to examine the asymmetric behavior of the diameters of the coexistence curves.