**3.2 Using a R-Dependent Mean Curve**

If the value of *R* has been measured along a sightline of interest, or
if some general information is available about the dust grain
environment (e.g., dense region or diffuse region?), then the
uncertainties in dereddening can be reduced somewhat by adopting an
*R*-dependent extinction curve computed at the appropriate value of
*R*. For the original 29 sightlines used by CCM, the standard
deviation of the individual observed extinction curves minus the
computed *R*-dependent curves is about a factor of 2 smaller than when
the individual curves are compared to the average Galactic (*R* = 3.1)
curve. Thus the uncertainties in a dereddened energy distribution can
be estimated using eq. 1 and adopting 0.5 times the
_{k(-V)} values from
Table 1. If *R* is poorly
measured or only estimated from environmental factors, then allowance must be
made for this in the error analysis.

Using an appropriate *R*-dependent curve can slightly improve the
accuracy of results from ironing out the 2175 Å bump. The values
of ^{2}_{m(-V)} can be estimated as above in
Section 3.1, using
the same value of _{E
(B-V)} 20% and 0.5 x
_{k(-V)} from
Table 1. The resultant values of
^{2}_{m(-V)} are about 85% as large as those listed in
the last column of Table 1. The gain
from using the *R*-dependent
curves is only marginal because the normalized bump heights are highly
variable and not correlated with *R*.

It is important to note that, even when *R* and *E (B - V)* are
well-determined, the use of an *R*-dependent extinction curve only
reduces - but does not eliminate - the wavelength dependent
dereddening error. The standard deviation of the observed vs.
*R*-dependent curves does not go to zero, even for the sample of 29
sightlines used by CCM to define the *R*-dependence, because the
UV/optical curves are not really a one-parameter family dependent only on
*R*. Curves derived for different sightlines with the same values of
*R* show a wide range of properties, including differences in the
strengths of the bump and the far-UV rise. Thus, as noted by CCM, the
CCM formula reproduces a general trend, but does not provide
particularly good fits to individual extinction curves, even when the
value of *R* is well-determined.

Apart from this intrinsic scatter around the mean *R* relation, the
accuracy of the CCM results is limited in the IR/optical region due to
bandpass effects with the broadband Johnson filters used to measure the
extinction. As a result, CCM tends to overestimate the level of
extinction in the near-IR and blue-visible. In the Appendix, a new
derivation of the *R*-dependence of IR-through-UV extinction is
presented. This corrects for the systematic bandpass effects in CCM,
but is still plagued by the same uncertainties caused by the ``cosmic''
scatter of extinction properties around the mean *R* relation.