The rates and degrees of polymerization of styrene by perhcloric acid have been measured dilatometrically at 25, 0 and -30 $^\circ$C in solution in 1,2-dichloroethane (DCE), carbon tetrachloride and mixtures of these and other solvents. The rates, throughout the conversion are found proportional to the first power of the monomer concentration, and to the initial concentration of perchloric acid. They are unaffected by traces of water, but show a strong solvent effect. In DCE + CCl$_4$ mixtures the rates correlate simply with the dielectric constant of the mixture; other solvents show specific solvent effects especially nitro compounds which inhibit. The molecular weights are very low (1000 to 6000) and give evidence of two rapid transfer processes, spontaneous and to monomer. The polymer contains both saturated and unsaturated chains, the fraction of the former correlating with the fraction stopped by the monomer transfer process. The catalyst is not consumed. Further doses of monomer are polymerized at virtually the original rate, but are not added to the first formed chains. The polymerization is interpreted as a 'transfer-dominated' living polymerization, with a fast initiation and no termination. The overall rate is therefore taken to be that of the propagation step. Rate constants and activation energies for this and for the transfer processes are derived.