  The surface-density profiles of dense filaments, in particular those traced
by dust emission, appear to be well fit with Plummer profiles, i.e.
Sigma(b)=Sigma_B+Sigma_O{1+[b/w_O]^2}^{[1-p]/2}. Here Sigma_B is the background
surface-density; Sigma_B+Sigma_O is the surface-density on the filament spine;
b is the impact parameter of the line-of-sight relative to the filament spine;
w_O is the Plummer scale-length (which for fixed p is exactly proportional to
the full-width at half-maximum, w_O=FWHM/2{2^{2/[p-1]}-1}^{1/2}); and p is the
Plummer exponent (which reflects the slope of the surface-density profile away
from the spine).} In order to improve signal-to-noise it is standard practice
to average the observed surface-densities along a section of the filament, or
even along its whole length, before fitting the profile. We show that, if
filaments do indeed have intrinsic Plummer profiles with exponent p_INTRINSIC,
but there is a range of w_O values along the length of the filament (and
secondarily a range of Sigma_B values), the value of the Plummer exponent,
p_FIT, estimated by fitting the averaged profile, may be significantly less
than p_INTRINSIC. The decrease, Delta p = p_INTRINSIC - p_FIT, increases
monotonically with increasing p_INTRINSIC; with increasing range of w_O values;
and -- if, but only if, there is a finite range of w_O values -- with
increasing range of Sigma_B values. For typical filament parameters the
decrease is insignificant if p_INTRINSIC = 2 (0.05 <~ Delta p <~ 0.10), but for
p_INTRINSIC =3 it is larger (0.18 <~ Delta p <~ 0.50), and for p_INTRINSIC =4
it is substantial (0.50 <~ Delta p <~ 1.15). On its own this effect is probably
insufficient to support a value of p_INTRINSIC much greater than p_FIT ~ 2, but
it could be important in combination with other effects.
