  Existing studies of the atomic hydrogen gas content in distant galaxies,
through the absorption of the 21-cm line, often infer that the total column
density is anti-correlated with the linear extent of the background radio
source. We investigate this interpretation, by dissecting the various
parameters from which the column density is derived, and find that the
relationship is driven primarily by the observed optical depth, which, for a
given absorber size, is anti-correlated with the linear size. Therefore, the
inferred anti-correlation is merely the consequence of geometry, in conjunction
with the assumption of a common spin temperature/covering factor ratio for each
member of the sample, an assumption for which there is scant observational
justification. While geometry can explain the observed correlation, many radio
sources comprise two radio lobes and so we model the projected area of a two
component emitter intercepted by a foreground absorber. From this, the observed
optical depth/linear size relationship is best reproduced through models which
approximate either of the two Fanaroff & Riley classifications, although the
observed scatter in the sample cannot be duplicated using a single deprojected
radio source size. Furthermore, the trend is best reproduced using an absorber
of diameter ~100 - 1000 pc, which is also the range of values of linear sizes
at which the 21-cm detection rate peaks. This may indicate that this is the
characteristic linear size of the absorbing gas structure.
