A chromospheric H-alpha emission core is measured in 40 stars of types F8-G3 V on the basis of observations obtained with dispersion 1.6 nm/mm, resolution 74 pm, and S/N 200-350 using a coude spectrograph on the 2.05-m reflector and a single-array 1872-channel Reticon in the focal plane of the 1-m camera at Lick Observatory on six nights during December, 1982 - June, 1983. An emission spike of about 100 pm, corresponding to surface flux 1.4 Merg/sq cm sec, is detected in the most active stars by subtracting the spectrum of the reference star Beta CVn. The data are presented in tables and graphs along with corresponding Ca II H, K data from Mount Wilson and analyzed in detail. It is found that main-sequence H-alpha surface-flux decay can be described by either a power law with exponent -0.4 and rms scatter factor 1.5 or an exponential relation with e-folding time 3-5 Gyr. Although extrapolation of the power law to very young stars correctly predicts the H-alpha fluxes of the T Tau stars, important differences (suggesting a different emission mechanism) are shown to make such extrapolation invalid.