  We investigate the effects of weak gravitational lensing in the standard Cold
Dark Matter cosmology, using an algorithm which evaluates the shear in three
dimensions. The algorithm has the advantage of variable softening for the
particles, and our method allows the appropriate angular diameter distances to
be applied to every evaluation location within each three-dimensional
simulation box. We investigate the importance of shear in the distance-redshift
relation, and find it to be very small. We also establish clearly defined
values for the smoothness parameter in the relation, finding its value to be at
least 0.88 at all redshifts in our simulations. From our results, obtained by
linking the simulation boxes back to source redshifts of 4, we are able to
observe the formation of structure in terms of the computed shear, and also
note that the major contributions to the shear come from a very broad range of
redshifts. We show the probability distributions for the magnification, source
ellipticity and convergence, and also describe the relationships amongst these
quantities for a range of source redshifts. We find a broad range of
magnifications and ellipticities; for sources at a redshift of 4, 97{1/2}% of
all lines of sight show magnifications up to 1.3 and ellipticities up to 0.195.
There is clear evidence that the magnification is not linear in the
convergence, as might be expected for weak lensing, but contains contributions
from higher order terms in both the convergence and the shear.
