  We present the results of proper-motion measurements of the dust shell
structure in the Egg Nebula (AFGL 2688, CRL 2688, V1610 Cyg), based on the
archived two-epoch imaging-polarimetry data in the 2 micron band taken with
NICMOS on-board the Hubble Space Telescope. We measured the amount of motions
of local structures in the nebula by determining their relative shifts over an
interval of 5.5 years. The dynamical age of the nebula is found to be roughly
350 years based on the overall motion of the nebula that exhibits a
Hubble-law-esque linear relation between the measured proper motion and the
projected radial distance from the origin of the expansion. By adopting the
de-projected velocity of 45 km/s at the tips of the bipolar lobes, our
proper-motion measurements indicate that the distance to the Egg Nebula is
about 420 pc and that the lobes are inclined at 7.7 degrees with respect to the
plane of the sky. The refined distance estimate yields the luminosity of the
central star of 3.3 x 10^3 L_sun, the total shell mass of 1.2 M_sun, and the
mass loss rate (the upper limit) of 3.6 x 10^(-3) M_sun/yr. Assuming 0.6 M_sun
central post-AGB stellar mass, the initial mass of the Egg is 1.8 M_sun. Upon
analysis, we also discovered that the central star of the Egg Nebula has proper
motion of its own at the rate of (14, -10) mas/yr.
