  We directly measure the evolution of the intergalactic Lyman-alpha effective
optical depth, tau_eff, over the redshift range 2<z<4.2 from a sample of 86
high-resolution, high-signal-to-noise quasar spectra obtained with Keck/ESI,
Keck/HIRES, and Magellan/MIKE. We find that our estimates of the quasar
continuum levels in the Ly-alpha forest obtained by spline fitting are
systematically biased low, but that this bias can be accounted for using mock
spectra. The mean fractional error <Delta C/C_true> is <1% at z=2, 4% at z=3,
and 12% at z=4. We provide estimates of the level of absorption arising from
metals in the Ly-alpha forest based on both direct and statistical metal
removal results in the literature, finding that this contribution is ~6-9% at
z=3 and decreases monotonically with redshift. The high precision of our
measurement indicates significant departures from the best-fit power-law
redshift evolution, particularly near z=3.2.
