  Weak lensing by large-scale structure provides a direct measurement of matter
fluctuations in the universe. We report a measurement of this `cosmic shear'
based on 271 WFPC2 archival images from the Hubble Space Telescope Medium Deep
Survey (MDS). Our measurement method and treatment of systematic effects were
discussed in an earlier paper. We measure the shear variance on scales ranging
from 0.7' to 1.4', with a detection significance greater than 3.8. This allows
us to measure the normalization of the matter power spectrum to be sigma8 =
(0.94 +/- 0.10 +/- 0.14) (0.3/Omega_m)^0.44 (0.21/Gamma)^0.15, in a LCDM
universe. The first 1sigma error includes statistical errors only, while the
latter also includes (gaussian) cosmic variance and the uncertainty in the
galaxy redshift distribution. Our results are consistent with earlier cosmic
shear measurements from the ground and from space. We compare our cosmic shear
results and those from other groups to the normalization from cluster abundance
and galaxy surveys. We find that the combination of four recent cosmic shear
measurements are somewhat inconsistent with the recent normalization using
these methods, and discuss possible explanations for the discrepancy.
