Illustration of the effect of beaming on the optical depth of the |$1_{10}{\!-\!}1_{11}$| and |$2_{11}{\!-\!}2_{12}$| transitions. The parameters for the calculation are shown in the upper panel. The red dashed vertical line indicates the specific column density where the |$4_{13}{\!-\!}4_{14}$| transition (48 GHz) switches from being inverted to non-inverted. The black dashed vertical line indicates the specific column density where the maser path-length equals |$7 \times 10^{16}$| cm.