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Doppler measurements with precision {\bf20 m s}$^{-1}$ of 80 main--sequence stars of spectral types, F - M, have been obtained repeatedly for 4 years. The Lick Observatory 3-m telescope and echelle spectrograph gathers 5000 to 6200 \AA$~$ with dispersion of 2500 $m~s^{-1}$ per pixel. An iodine absorption cell in the telescope beam superimposes lines of known laboratory wavelengths, accurate to 8 digits. The iodine line shapes reveal the precise instrumental profile (IP) at each location of the echelle image. The IP is extracted by inversion of the convolution integral, using the intrinsic (FTS) iodine spectrum and non-linear least squares, on a grid of sub-pixels. This in-situ determination of the local IP and the wavelength calibration eliminates the two historical sources of systematic errors in Doppler measurements.
The Doppler precision and time baseline permit detection of ``planets'' having masses above 4 $M_{Jup}$ with orbital radii up to 5 AU. We will present the Doppler results for the brightest stars in the survey, which are also monitored by Campbell, Walker,Yang (ApJ,{\bf331},902), Cochran,Hatzes (Proc.SPIE,{\bf1318},148) and McMillan et al. (SPIE,{\bf1235},601). For example, the G8V dwarf, tau Ceti, shows no Doppler variation above the errors of 20 $m~s^{-1}$ during five years, in agreement with the above groups. We will discuss the prospects for planet detection around the 20 M dwarfs in the survey whose lower masses yield more interesting thresholds for planetary detection.
