![image](clr_radtr_gra.eps){width="8.5cm"}

How can we distinguish the variation of $A_V$ from that of $\chi$? We expect that if the change of $A_V$ controls the colour variation there may be a correlation between dust content and FIR colours. Below we further discuss the observed FIR colours in BCDs in terms of the dust content.

Discussion {#sec:discussion}
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Dust content and FIR colours {#subsec:dust_content}
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The dust mass of the current BCD sample is estimated by the *WIDE-S* ($90~\mu$m) and *WIDE-L* ($140~\mu$m) fluxes, which are suitable to trace the total mass of large grains which have the dominant contribution to the total dust content [@galliano05].[^6] The dust mass $M_\mathrm{d}$ is related to the flux as (e.g. @hildebrand83; H08) $$\begin{aligned}
M_\mathrm{d}=
\frac{F_\nu (\lambda )D^2}{\kappa_\nu B_\nu (T_\mathrm{d})}
\, ,\label{eq:mdust}\end{aligned}$$ where $\kappa_\nu$ is the mass absorption coefficient of dust grains. The mass absorption coefficient is related with the absorption efficiency $Q_\nu$ as (e.g. H08) $$\begin{aligned}
\kappa_\nu =\frac{3Q_\nu}{4as}\, ,\end{aligned}$$ where $s$ is the grain material density. If the grain radius is much smaller than the wavelength, $Q_\nu /a$ is independent of $a$ [@hildebrand83]. The values adopted in Section \[subsec:properties\] indicate $Q_\nu /a=1.14\times 10^{-2}~\mu\mathrm{m}^{-1}$ for silicate and $1.23\times 10^{-2}~\mu\mathrm{m}^{-1}$ for graphite at $\lambda =125~\mu$m. By adopting typical densities 