  We derive the contributions of spin-orbit and spin-spin coupling to the
gravitational radiation from coalescing binary systems of spinning compact
objects. We calculate spin effects in the symmetric, trace-free radiative
multipoles that determine the gravitational waveform, and the rate of energy
loss. Assuming a balance between energy radiated and orbital energy lost, we
determine the spin effects in the evolution of the orbital frequency and
orbital radius. Assuming that a laser interferometric gravitational observatory
can track the gravitational-wave frequency (twice the orbital frequency) as it
sweeps through its sensitive bandwidth between about 10 Hz and one kHz, we
estimate the accuracy with which the spins of the component bodies can be
determined from the gravitational-wave signal.
