Spectra of quasars at high z often show absorption at the Lyman limit from intervening gas systems at intermediate z having N(H) approx. greater than 10(exp 7) cm(-2). In some circumstances, N(H) can be determined by measuring the strength of the Lyman limit absorption or the damping wings of Lyman - alpha. With a spectrum taken at low wavelength resolution, say, lambda/delta lambda approx. 10(exp 3), it is usually not possible to distinguish individual Lyman series lines near the limit, yet one can still discern how rapidly the average intensity drops off as the limit is approached from the long wavelength side. The purpose here is to point out the information which is available from measurements of this series convergence.