We investigate the effect of two important , but oft neglected , factors which can affect the detectability of H i 21-cm absorption in Mg ii absorption systems : The effect of line-of-sight geometry on the coverage of the background radio flux and any possible correlation between the 21-cm line strength and the rest frame equivalent width of the Mg ii 2796 Å line , as is seen in the case of damped Lyman- \alpha absorption systems ( DLAs ) .
Regarding the former , while the observed detection rate at small angular diameter distance ratios ( DA _ { abs } / DA _ { QSO } > 0.8 ) is a near certainty ( P > 0.9 ) , for an unbiased sample , where either a detection or a non-detection are equally likely , at DA _ { abs } / DA _ { QSO } \geq 0.8 the observed detection rate has only a probability of P \stackrel { < } { { } _ { \sim } } 10 ^ { -15 } of occuring by chance .
This \stackrel { > } { { } _ { \sim } } 8 \sigma significance suggests that the mix of DA _ { abs } / DA _ { QSO } values at z _ { abs } \stackrel { < } { { } _ { \sim } } 1 is correlated with the mix of detections and non-detections at low redshift , while the exclusively high values of the ratio ( DA _ { abs } / DA _ { QSO } \sim 1 ) at z _ { abs } \stackrel { > } { { } _ { \sim } } 1 contribute to the low detection rates at high redshift .

In DLAs , the correlation between the 21-cm line strength ( \int \tau dv / N _ { HI } ) and the Mg ii equivalent width ( { W } _ { r } ^ { \lambda 2796 } ) is dominated by the velocity spread of the 21-cm line .
This has recently been shown not to hold for Mg ii systems in general .
However , we do find the significance of the correlation to increase when the Mg ii absorbers with Mg i 2852 Å equivalent widths of { W } _ { r } ^ { \lambda 2852 } > 0.5 Å are added to the DLA sample .
This turns out to be a sub-set of the parameter space where Mg ii absorbers and DLAs overlap and the fraction of Mg ii absorbers known to be DLAs rises to 50 % ( 37 ) .
We therefore suggest that the width of the 21-cm line is correlated with W _ { r } ^ { \lambda 2796 } for all systems likely to be DLAs and note a correlation between W _ { r } ^ { \lambda 2852 } ( Mg i ) and N _ { HI } , which is not apparent for the singly ionised lines .
Furthermore , the 21-cm detection rate at DA _ { abs } / DA _ { QSO } < 0.8 rises to \stackrel { > } { { } _ { \sim } } 90 % for absorbers with { W } _ { r } ^ { \lambda 2852 } > 0.5 Å and large values of DA _ { abs } / DA _ { QSO } may explain why the absorbers which have similar values of { W } _ { r } ^ { \lambda 2796 } to the detections remain undetected .
We do , however , also find the neutral hydrogen column densities of the non-detections to be significantly lower than those of the detections , which could also contribute to their weak absorption .
Applying the \int \tau dv / N _ { HI } – { W } _ { r } ^ { \lambda 2796 } correlation to yield column densities for the Mg ii absorbers in which this is unmeasured , we find no evidence of a cosmological evolution in the neutral hydrogen column density in the absorbers searched for in 21-cm .