  We discuss the propagation of spectral line and continuum radiation in a
clumpy medium and give general expressions for the observed absorption or
emission from a cloud population. We show that the affect of the medium
clumpiness can usually be characterised by a single number multiplying the mean
column opacity. Our result provides a simpler proof and generalisation of the
result of Martin et al (1984). The formalism provides a simple way to
understand the effects of clumping on molecular line profiles and ratios, for
example how clumping effects the interpretation of 13CO(1-0) to 12CO(1-0) line
ratios. It can also be used as a propagation operator in physical models of
clumpy media where the incident radiation effects the spectral line emissivity.
We are working to extend the formalism to the propagation of masers in a clumpy
medium, but in this case there are special difficulties because formal
expectation values are not characteristic of observations because they are
biased by rare events.
