  Recent discoveries by the Rossi X-Ray Timing Explorer indicate that most of
the rapidly accreting and weakly magnetic neutron stars in the Galaxy are
rotating at spin frequencies greater than 250 Hz. Remarkably, they all rotate
in a narrow range of frequencies. I suggest that these stars rotate fast enough
so that, on average, the angular momentum added by accretion is lost to
gravitational radiation. The strong spin frequency dependence of the angular
momentum loss rate from gravitational radiation then provides a natural reason
for similar spin frequencies. Provided that the interior temperature has a
large scale asymmetry misaligned from the spin axis, then the temperature
sensitive electron captures in the deep crust can provide the quadrupole needed
to reach this limiting situation at 300 Hz. This quadrupole is only present
during accretion and makes it difficult to form radio pulsars spinning more
rapidly than 600-800 Hz via rapid accretion. The gravity wave strength is
<10^{-26} from most neutron stars and >2 X 10^{-26} for Sco X-1. Prior
knowledge of the position, spin frequency and orbital periods will allow for
deep searches for these periodic signals with gravitational wave
interferometers (LIGO, VIRGO and the dual-recycled GEO 600 detector) and
experimenters need to take such sources into account. Sco X-1 will most likely
be detected first.
