Superconducting transition temperatures between 0.7 K and 1.5
K are reported for the stage 1 potassium-mercury graphite
intercalation compound, C4KHg. A number of
experiments have been performed to investigate the
differences between the C4KHg samples at either
extreme in Tc. The only structural difference is
that the beta phase (Ic = 10.83 Å)
is consistently found in the lower-Tc samples,
while the higher-Tc samples always contain only
the alpha phase (Ic = 10.24 Å).
Adding a minute amount of hydrogen to the Tc = 0.8
K samples raises their transition temperature to 1.5 K.
Measurements of the angular dependence of the critical field
suggest that the higher-Tc samples have type I
character for a range of applied field orientations near 
. The temperature dependence of the upper
critical field of C4KHg shows extended linearity
for both types of samples. The critical field data of
C4KHg and other GIC's are discussed in light of
multiband and anisotropic Fermi surface models of
superconductivity. The thermodynamic parameters obtained from
the critical field experiments are compared to the specific
heat data of Alexander et al. The hydrogen-induced
enhancement of Tc is tentatively explained by a
charge-density wave hypothesis first proposed by DeLong and
Eklund.