  We calculate the ultrasonic absorption and the thermal conductivity in the
superconducting state of UPt$_{3}$ as functions of temperature and direction of
propagation and polarization. Two leading candidates for the superconducting
order parameter are considered: the $E_{1g}$ and $E_{2u}$ representations. Both
can fit the data except for the ultrasonic absorption in the $A$ phase. To do
that, it is necessary to suppose that the system has only a single domain, and
that must be chosen as the most favorable one. However, the $E_{2u}$ theory
requires fine-tuning of parameters to fit the low temperature thermal
conductivity. Thus, transport data favor the $E_{1g}$ theory. Measurements of
the thermal conductivity as a function of pressure at low temperature could
help to further distinguish the two theories.
