  We present a method for detection of weak continuous signals from sources in
binary systems via the incoherent combination of many "short"
coherently-analyzed segments. The main focus of the work is on the construction
of a metric on the parameter space for such signals for use in matched-filter
based searches. The metric is defined using a maximum likelihood detection
statistic applied to a binary orbit phase model including eccentricity. We find
that this metric can be accurately approximated by its diagonal form in the
regime where the segment length is << the orbital period. Hence correlations
between parameters are effectively removed by the combination of many
independent observation. We find that the ability to distinguish signal
parameters is independent of the total semi-coherent observation span (for the
semi-coherent span >> the segment length) for all but the orbital angular
frequency. Increased template density for this parameter scales linearly with
the observation span. We also present two example search schemes. The first
uses a re parameterized phase model upon which we compute the metric on
individual short coherently analyzed segments. The second assumes long >> the
orbital period segment lengths from which we again compute the coherent metric
and find it to be approximately diagonal. In this latter case we also show that
the semi-coherent metric is equal to the coherent metric.
