  Three-pion interferometry is investigated for new information on the
space-time structure of the pion source created in ultra-relativistic heavy-ion
collisions. The two- and three-pion correlations are numerically computed for
incoherent source functions based on the Bjorken hydrodynamical model, over a
wide range of the kinematic variables. New information provided by three-pion
interferometry, different from that provided by two-pion interferometry, should
appear in the phases of the Fourier transform of the source function. Variables
are identified that would be sensitive to the phases and suitable for
observation. For a positive, chaotic source function, however, a variation of
the three-pion phase is found to be difficult to extract from experiments.
Effects of asymmetry of the source function are also examined.
