  We present the results of weak gravitational lensing statistics in four
different cosmological $N$-body simulations. The data has been generated using
an algorithm for the three-dimensional shear, which makes use of a variable
softening facility for the $N$-body particle masses, and enables a physical
interpretation for the large-scale structure to be made. Working in
three-dimensions also allows the correct use of the appropriate angular
diameter distances. Our results are presented on the basis of the filled beam
approximation in view of the variable particle softening scheme in our
algorithm. The importance of the smoothness of matter in the universe for the
weak lensing results is discussed in some detail. The low density cosmology
with a cosmological constant appears to give the broadest distributions for all
the statistics computed for sources at high redshifts. In particular, the range
in magnification values for this cosmology has implications for the
determination of the cosmological parameters from high-redshift Type Ia
Supernov\ae. The possibility of determining the density parameter from the
non-Gaussianity in the probability distribution for the convergence is
discussed.
