We have made extensive spectroscopic and photometric observations of PG
1224+309, a close binary containing a DA white dwarf primary and an M4+
secondary. The H alpha line is in emission due to irradiation of the M-star by
the hot white dwarf and is seen to vary around the orbit. From the radial
velocities of the H alpha line we derive a period of P = 0.258689 +/- 0.000004
days and a semi-amplitude of K_Halpha = 160 +/- 8 km/s. We estimate a
correction Delta_K = 21 +/- 2 km/s, where K_M = K_Halpha + Delta_K. Radial
velocity variations of the white dwarf reveal a semi-amplitude of K_WD = 112
+/- 14 km/s. The blue spectrum of the white dwarf is well fit by a synthetic
spectrum having T_eff = 29,300 K and log(g) = 7.38. The white dwarf contributes
97% of the light at 4500 Angstroms and virtually all of the light blueward of
3800 Angstroms. No eclipses are observed. The mass inferred for the white dwarf
depends on the assumed mass of the thin residual hydrogen envelope: 0.40 < M_WD
< 0.45 solar masses for hydrogen envelope masses of 0 < M_H < 4.0E-4 solar
masses. We argue that the mass of the white dwarf is closer to 0.45 solar
masses, hence it appears that the white dwarf has a relatively large residual
hydrogen envelope. The mass of the M-star is then M_M = 0.28 +/- 0.05 solar
masses, and the inclination is i = 77 +/- 7 degrees. We discuss briefly how PG
1224+309 may be used to constrain theories of close binary star evolution, and
the past and future histories of PG 1224+309 itself. The star is both a
``post-common envelope'' star and a ``pre-cataclysmic binary'' star. Mass
transfer by Roche-lobe overflow should commence in about 10 Gyr.Comment: 17 pages, 8 figures, AAS LaTeX, to appear in AJ, March 199