  RX J1914.4+2456 is a candidate double-degenerate binary (AM CVn) with a
putative 569 s orbital period. If this identification is correct, then it has
one of the shortest binary orbital periods known, and gravitational radiation
should drive the orbital evolution and mass transfer if the binary is
semi-detached. Here we report the results of a coherent timing study of the
archival ROSAT and ASCA data for RX J1914.4+2456. We performed a phase coherent
timing analysis using all five ROSAT observations spanning a 4.6 year period.
We demonstrate that all the data can be phase connected, and we show evidence
that the 1.756 mHz orbital frequency is increasing at a rate of 8 +- 3 e-18
Hz/s, consistent with the expected loss of angular momentum from the binary
system via gravitational radiation. In addition to providing evidence for the
emission of gravitational waves, our measurement of the orbital decay
constrains models for the X-ray emission and the nature of the secondary. If
stable mass accretion drives the X-ray flux, then orbital decay is inconsistent
with a degenerate donor. A helium burning dwarf is compatible if indeed such
systems can have periods as short as that of RX J1914.4+2456, an open
theoretical question. Our measurement is consistent with the unipolar induction
model of Wu et al. which does not require accretion to drive the X-ray flux. We
discuss how future timing measurements of RX J1914.4+2456 (and systems like it)
with for example, Chandra and XMM-Newton, can provide a unique probe of the
interaction between mass loss and gravitational radiation. We also discuss the
importance of such measurements in the context of gravitational wave detection
from space, such as is expected in the future with the LISA mission.
