We have used the IRAM 30meter telescope with the MPlfR 7-channel bolom
eter to map the lambda1.3mm continuum emission from the central 4' x 3
' region of the edge-on spiral NGC 4631. About 6/7 of the flux is due
to thermal radiation from cool dust and its distribution has been comp
ared with recent HI and CO maps at similar angular resolution. The rem
aining 15% is due to the 12CO (2-1) line (approximately 11%), the 13CO
(2-1) line (approximately 1%), and synchrotron and free-free emission
. Both the CO and 1.3mm continuum are concentrated in the inner approx
imately 2kpc and have a similar morphology whereas the HI emission is
much more extended. To within observational uncertainties, however, th
e dust emission per gram of interstellar matter is similar in the atom
ic and molecular components after making the usual assumptions to conv
ert HI and CO line fluxes to HI and H2 column densities. The fact that
the gas mass calculated from the thermal dust emission is equal to or
slightly higher than the mass from the HI and CO lines suggests that
in NGC 4631 the N(H2)/I(CO)(1-0) ratio is not overestimated.