  The lifetime of the structure in grand design spiral galaxies is
observationally ill-determined, but is essentially set by how accurately the
pattern's rotation can be characterized by a single angular pattern speed. This
paper derives a generalized version of the Tremaine-Weinberg method for
observationally determining pattern speeds, in which the pattern speed is
allowed to vary arbitrarily with radius. The departures of the derived pattern
speed from a constant then provides a simple metric of the lifetime of the
spiral structure. Application of this method to CO observations of NGC 1068
reveal that the pattern speed of the spiral structure in this galaxy varies
rapidly with radius, and that the lifetime of the spiral structure is
correspondingly very short. If this result turns out to be common in
grand-design spiral galaxies, then these features will have to be viewed as
highly transient phenomena.
