Based on observations with ISO, an ESA project with instruments funded by ESA Member States (especially the PI countries: France, Germany, the Netherlands and the UK) and with the participation of ISAS and NASA.

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Using the grain radius, a, as a variable the size distribution reads d ${\cal N}\sim a^\alpha\,$ da. We thus have the relationship $\beta=(\alpha-d+1)/d$ , where d is the dimension of the grain: d=2 for planar grains and d=3 for spherical grains. For instance, assuming PAHs are planar ( $a=0.9\sqrt{N_{\rm C}}$ ) a value of -3.5 for $\alpha$ corresponds to $\beta = -2.25$ .

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... objects

This result is not sensitive to the amount of cooling occurring in the far-IR ( $\lambda \leq 20$ $\mu$ m): multiplying or dividing our far-IR cross-section by 10 did not alter much our match of the 16.4 $\mu$ m-band.

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