By measurement of the specific volume of solutions of poly- alpha -methylstyrene in alpha -methylstyrene monomer at 25C, the dilatometric constant was found to be K//D equals (0. 002007 plus or minus 0. 000030)%** minus **1. Estimation of the temperature dependence resulted in the equation (K//D)//t equals 1. 81 multiplied by 10** minus **3 plus 7. 82 plus 10** minus **6 t, where t denotes temperature in C. Applications of the dilatometric constant in the study of the rate at conversion in the polymerization of alpha -methylstyrene are demonstrated.