  The recent measurements of weak lensing by large-scale structure present
significant new opportunities for studies of the matter distribution in the
universe. Here, we present a new cosmic shear survey carried out with the
Echelle Spectrograph and Imager on the Keck II telescope. This covers a total
of 0.6 square degrees in 173 fields probing independent lines of sight, hence
minimising the impact of sample variance. We also extend our measurements of
cosmic shear with the William Herschel Telescope (Bacon, Refregier & Ellis
2000) to a survey area of 1 square degree. The joint measurements with two
independent telescopes allow us to assess the impact of instrument-specific
systematics, one of the major difficulties in cosmic shear measurements. For
both surveys, we carefully account for effects such as smearing by the point
spread function and shearing due to telescope optics. We find negligible
residuals in both cases and recover mutually consistent cosmic shear signals,
significant at the 5.1 sigma level. We present a simple method to compute the
statistical error in the shear correlation function, including non-gaussian
sample variance and the covariance between different angular bins. We measure
shear correlation functions for all fields and use these to ascertain the
amplitude of the matter power spectrum, finding sigma_8 (Omega_m/0.3)^0.68 =
0.97 \pm 0.13 with 0.14<Omega_m<0.65 in a Lambda-CDM model with Gamma=0.21.
These 68% CL uncertainties include sample variance, statistical noise, redshift
uncertainty, and the error in the shear measurement method. The results from
our two independent surveys are both consistent with measurements of cosmic
shear from other groups. We discuss how our results compare with current
normalisation from cluster abundance.
