  The horizontal lateral density of a cosmic air shower with a non-zero zenith
angle is asymmetric. The asymmetry consist of a stretching of the iso-density
contours to ellipses and to a shift of the center of the elliptic contours with
respect to the core of the shower. The shift is caused by atmospheric
attenuation. The modeling of the attenuation results in an equation for the
shift as a function of zenith angle and the size of the iso-density contours. A
more accurate equation is obtained by investigating the shift in lateral
densities of simulated showers. It is shown how the shift can be incorporated
in an elliptic lateral density function. A linear approximation for the shift
allows for an analytical solution for the shifted elliptic density. Its
predictions for the polar variations of the density are compared with data of
simulated showers.
