), N. Brouillet ( 
), A. Baudry ( ) ) IRAM, 300, rue de la Piscine, F-38406 St. Martin d'Hères ) Observatoire de Bordeaux, URA 352, CNRS/INSU, B.P. 89, F-33270 Floirac 
lines and thermal dust
continuum emission have been detected almost as far out. The
variation in the beam-independent CO( 
) line
intensity ratio is interpreted in terms of a variation in the CO
excitation temperature. Combining the temperature variation with the
galactic size-linewidth relation and the virial theorem enables us to
estimate how the 
factor varies as a
function of galactocentric radius. One then straightforwardly obtains
the distribution of the molecular gas. It should be noted that
because there is probably little or no star formation and neutral gas
in the nucleus of NGC 4414, we avoid problems associated with
conditions proper to galactic nuclei but thus make no predictions for
these regions.
In order to check the function obtained
above, we used our (1-0) and (2-1) data, in
conjunction with the 
and assuming the to be
optically thin, to derive absolute abundances as a function
of radius. The resulting abundances are in good agreement with
galactic observations. The millimeter-wave thermal emission from dust
is a second independent test. While grain cross-sections and, to a
lesser extent, dust temperatures are subject to debate, commonly used
values yield gas masses quite close to those we estimate from our
analysis. Unusually low cross-sections or temperatures and a peculiar
variation are required to fit the gas mass resulting from the use of a
constant ratio. All of our observations
support the variation and range of 
that we propose here for NGC 4414. It should however be borne in mind
that a number of assumptions about molecular clouds have been made and
that we have no means of verifying them for the clouds in NGC 4414.
As such an analysis is not yet available for other external spiral galaxies, we have applied our knowledge of the gas and stellar distributions to the question of what controls star formation on large scales. NGC 4414 is an ideal test case because of its inner and outer cutoffs in the HII region distribution and because it has probably not suffered tidal interactions with other galaxies recently. We find that both cutoff radii are well reproduced using the simple Q criterion for gravitational instability.