The parameters *J*, , *J*/*M*, *M* and so forth depend to varying degrees upon
distance *D*, such that (for instance) , and . It follows that errors
in distance may give rise to correlations between rotational and physical
parameters over and above those attributable to intrinsic cloud properties. How
important are such effects for the sample investigated here?

To assess this, we have investigated a model containing 10^{3} clouds having
intrinsic values log *J*, log etc. distributed randomly within pre-set limits. These
limits are in turn defined such that the final "observed" ranges in these
parameters (including the effects of distance uncertainties) are comparable to
those noted in Table 1, and Figs. 2-7. In particular, if the intrinsic logarithmic
range in *J* is given by , and the range of values *J* which would be
determined through observation (and in the presence of distance errors) is
, then is tailored to make
; comparable to the range
noted in Figs. 6 and 7.

Errors in estimated distance are taken to be of a form:

where again is the "observed" or estimated value of distance, is the intrinsic value of
Under these circumstances, it is possible to investigate how important such
errors would be in creating spurious correlations, for a sample in which there is
no initial correlation between the various cloud parameters (i.e. in which
intrinsic values of , say, are uncorrelated with *M*, *J* or any other parameter). A
summary of the results is provided in Table 3, wherein we indicate correlation
coefficients for various values of , and relative parametric trends. The
simulated variation between *J* and *M* is also indicated in Fig. 14 for two values
of .

It is clear, from these, that appreciable correlations may indeed result, but only
where is large; and even for , which would correspond to a factor 5.6
uncertainty in distance, it is apparent that values for *r* are very much less than
observed here (Table 2). Similarly, the gradients *b* for these distributions depend
upon the intrinsic ranges in the parameters, and error factor . Even for the most
extreme case investigated here (the gradients *b* in Table 3
correspond to )
it is apparent that gradients are significantly different from what is observed
(Table 2).

Given that errors in *D* are almost certainly appreciably smaller, and
is no more
than ,
we conclude that the influence of such uncertainties upon
observed correlations is likely to be small.

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