  We have measured v sin i with high precision for a sample of dM3 stars (86
targets). We detected rotation in 82 stars (73 dM3 stars, and 9 dM3e stars). We
compare our measurements of v sin i for all the stars in our dM0, dM2, dM3 and
dM4 samples to those from other authors. We find a good agreement down to v sin
i values of less than 1 km/s. The mean of the differences between measurements
is only 0.42 km/s.
  We find that the distribution of P/sini for our dM3 stars is different from
the distribution of P/sini among our samples of dM2 and dM4 stars. The mean
rotation rate for the dM3 stars (excluding dM3e and sdM3 stars) is
significantly slower (25.8 days) than for dM2 (14.4 days) and dM4 stars (11.4
days). Analogous behavior also emerges among the faster rotators (dMe stars):
we find that a longer rotation period also occurs at spectral sub-type dM3e.
Our data suggest that, as regards the rotational properties of lower main
sequence stars, spectral sub-type dM3 stands out as exhibiting unusual slow
rotation compared to that of adjoining sub-types. Our data lead us to suggest
that the unusual rotational properties of M3 dwarfs may represent a signature
of the transition to complete convection (TTCC).
