| Summary: | I analyse an x-ray selected sample of 128 late-type (F-M) stars. These stars were identified as optical counterparts to serendipitous x-ray detections made by the Einstein Observatory Extended Medium Sensitivity Survey. Once identified as x-ray sources, the stars were reobserved with an extensive program of optical observations consisting of high- and low-resolution spectroscopy and photometry. Spectral types, luminosity classes, absolute magnitudes, distances, x-ray luminosities, projected rotation rates (v sin i), radial velocities, and binary status have been determined for the sample. I find that Lₓ is correlated with v sin i for single stars. However, Lₓ does not correlate with Ω sin i, which leads me to believe that the correlation seen with v sin i is actually a correlation with radius. Indeed, Lₓ correlates strongly with radius (color, mass) for main sequence stars. This result provides a plausibility argument for rotational saturation in the coronae of late-type stars. Since this sample is flux limited, I use sky coverage and sensitivity information from the Einstein Observatory to calculate the bright end of the x-ray luminosity function for late-type stars. It appears that previously calculated luminosity functions from optically selected samples have underestimated the number of x-ray bright F and G dwarfs. I have also discovered 8 previously uncatalogued M dwarfs within 25 pc of the sun. My sample includes only M dwarfs of spectral type M5 and earlier, 93% of which are "emission" stars (i.e. type Me V), as well as two pre-main sequence M stars. Arguments involving kinematics and stellar rotational velocities are used to estimate the age of these x-ray "bright" M dwarfs; they appear to be quite young (≤ 1-3 x 10⁹ yrs). Since the local space density of x-ray "bright" M dwarfs increases with mass, I infer a longer activity timescale for lower masses. M dwarfs later than M5 lie below the sample's x-ray sensitivity limit. An upper limit of log Lₓ = 27.45 is put on their coronal emission. I also present H(α) and Ca II K line fluxes for most members of the M dwarf sample and show that the H(α) and Ca II K luminosities do indeed correlate with Lₓ. However, these chromospheric luminosities are weaker functions of rotation than Lₓ and may, in fact, represent saturated levels of activity. My results are consistent with the hypothesis that the chromosphere is heated by x-rays from the overlying corona. Finally, I discuss two unusual members of the sample which are attractive candidates for the recently proposed class of FK Comae stars.
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