The empirical form for the dependence, T-g(n) approximate to T-g(infinity).(1 + alpha/n), of the glass transition temperature T-g on the average number n of repeat units between crosslinks, is generalized for randomly crosslinked high polymers. The new form, T-g(n) approximate to T-g(infinity).[1 + c/(n . N-rot)], is based on a correlation study of data for 77 samples of 10 different sets of resins. The fitting parameter a is resolved into composition-dependent N-rot and composition-independent c terms. N-rot summarizes the average number of rotational degrees of freedom per repeat unit, and is estimated in a straightforward manner from the structure and mol fraction of each repeat unit. The value of c is found from data analysis to be 5 +/- 2. The results of this work are consistent with expectations based on the entropy theory of glasses, and provide improved understanding and predictive ability for the properties of crosslinked polymers.