  With the Wide Field Planetary Camera 2 (WFPC2) on the Hubble Space Telescope,
we have discovered in M4 (NGC 6121, C 1620-264) the first extensive sequence of
cooling white dwarfs seen in a globular cluster. Adopting a distance modulus of
(m-M)_V = 12.65 and a reddening of E(B-V) = 0.37, we show that the sequence,
which extends over 9 < M_U < 13, is comprised of white dwarfs of mass \sim 0.5
M_{\odot}. The total mass loss from the present turnoff to the white dwarf
sequence is 0.31 M_{\odot} and the intrinsic dispersion in the mean mass
appears to be < 0.05 M_{\odot}. Both the location of the white dwarf cooling
sequence in the cluster color-magnitude diagram and the cumulative luminosity
function attest to the basic correctness and completeness of the physics in
theoretical models for the upper three magnitudes of the observed white dwarf
cooling sequence. To test the theory in globular clusters at cooling ages
beyond \sim 3 \times 10^8 years will require deeper and more complete data.
