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We present the results of a deep, serendipitous, long slit spectroscopy-based survey for Ly$\alpha$ emission at high redshifts, using the data obtained with the Double Spectrograph and the 4-Shooter instruments at the Palomar 200-inch telescope. A total of 421 independent spectroscopic frames, covering an area of 15 arcmin$^2$, was surveyed over a 2500\AA~span from 5000\AA~ to 7500\AA, with lesser areas surveyed across the entire optical passband. Out of 65 emission-line candidates, we were able to determine firm redshifts for two quasars and 30 galaxies. An additional 20 galaxies have only tentative redshifts assigned. The sample of galaxies with firm or probable redshifts has a median redshift $z = 0.52$, reaching out to $z \approx 1.2$. Properties of these galaxies are consistent with those of the field galaxy populations identified in complete, magnitude-limited deep spectroscopic surveys, showing at most a mild evolution out to $z \sim 1$. The remaining few objects are candidate Ly$\alpha$ galaxies at high redshifts, with isolated, unidentified emission lines and little or no continuum. They require further work to check on their nature. Assuming a cosmology with $H_0 = 75$ km/s/Mpc and $\Omega_0 = 0.2$, we have surveyed a restframe comoving volume of 20,400 Mpc$^3$ to a limit sufficient to detect unobscured star formation at a rate $SFR \sim 10 M_\odot$ yr$^{-1}$, and 102,600 Mpc$^3$ to a limit of 100 M\sun yr$^{-1}$. These limits are comparable to those achieved in narrow-band imaging surveys, while probing a different region of the relevant parameter space. Assuming a reasonable luminosity function, up to a few tens of young galaxies should have been detected in this volume. Their absence may be due to a dust obscuration of the Ly$\alpha$ line emission.
