The deepest optical image of the sky, the Hubble Deep Field, obtained with
the Hubble Space Telescope in 1995 December, has been compared to a similar
image taken in 1997 December. Two very faint, blue, isolated, and unresolv
ed objects are found to display a substantial apparent proper motion, 23 +/
- 5 and 26 +/- 5 mas yr(-1); a further three objects at the detection limit
of the second-epoch observations may also be moving. Galactic structure mo
dels predict a general absence of stars in the color-magnitude range in whi
ch these objects are found. However, these observations are consistent with
recently developed models of old white dwarfs with hydrogen atmospheres, w
hose color, contrary to previous expectations, has been shown to be blue. I
f these apparently moving objects are indeed old white dwarfs with hydrogen
atmospheres and masses near 0.5 M-., they have ages of approximately 12 Gy
r and a local mass density that is sufficient, within the large uncertainti
es arising from the small size of the sample, to account for the entire mis
sing Galactic dynamical mass.