  Weak lensing by large scale structure induces correlated ellipticities in the
images of distant galaxies. The two-point correlation is determined by the
matter power spectrum along the line of sight. We use the fully nonlinear
evolution of the power spectrum to compute the predicted ellipticity
correlation. We present results for different measures of the second moment for
angular scales \theta \simeq 1'-3 degrees and for alternative normalizations of
the power spectrum, in order to explore the best strategy for constraining the
cosmological parameters. Normalizing to observed cluster abundance the rms
amplitude of ellipticity within a 15' radius is \simeq 0.01 z_s^{0.6}, almost
independent of the cosmological model, with z_s being the median redshift of
background galaxies.
  Nonlinear effects in the evolution of the power spectrum significantly
enhance the ellipticity for \theta < 10' -- on 1' the rms ellipticity is \simeq
0.05, which is nearly twice the linear prediction. This enhancement means that
the signal to noise for the ellipticity is only weakly increasing with angle
for 2'< \theta < 2 degrees, unlike the expectation from linear theory that it
is strongly peaked on degree scales. The scaling with cosmological parameters
also changes due to nonlinear effects. By measuring the correlations on small
(nonlinear) and large (linear) angular scales, different cosmological
parameters can be independently constrained to obtain a model independent
estimate of both power spectrum amplitude and matter density \Omega_m.
Nonlinear effects also modify the probability distribution of the ellipticity.
Using second order perturbation theory we find that over most of the range of
interest there are significant deviations from a normal distribution.
