Abstract
The rate of convergence of the transfer matrix finite-size scaling (or phenomenological renormalisation) method is studied. It is shown both heuristically and numerically that the convergence of estimates for exponents, etc. is governed asymptotically by the leading irrelevant-variable scaling exponent. The more rapid apparent convergence rates observed in many practical calculations for two-dimensional lattices of widths up to ten lattice spacings are attributed to cancellation between various correction terms.