  We describe a program to identify optical counterparts to radio sources from
the VLA FIRST survey using the Cambridge APM scans of the POSS-I plates. We use
radio observations covering 4150 square degrees of the north Galactic cap to a
20 cm flux density threshold of 1.0 mJy; the 382,892 sources detected all have
positional uncertainties of <1" (radius of 90% confidence). Our description of
the APM catalog, derived from the 148 POSS-I O and E plates covering this
region, includes an assessment of its astrometric and photometric accuracy, a
photometric recalibration using the Minnesota APS catalog, a discussion of the
classification algorithm, and quantitative tests of the catalog's reliability
and completeness. We go on to show how the use of FIRST sources as astrometric
standards allows us to improve the absolute astrometry of the POSS plates by
nearly an order of magnitude to ~0.15" rms. Matching the radio and optical
catalogs yields counterparts for over 70,000 radio sources; we include detailed
discussions of the reliability and completeness of these identifications as a
function of optical and radio morphology, optical magnitude and color, and
radio flux density. An analysis of the problem of radio sources with complex
morphologies (e.g., double-lobed radio galaxies) is included. We conclude with
a brief discussion of the source classes represented among the radio sources
with identified counterparts.
