  We explore the heating of the velocity distribution in the solar
neighbourhood by stochastic spiral waves. Our investigation is based on direct
numerical integration of initially circular test-particle orbits in the sheared
sheet. We confirm the conclusion of other investigators that heating by spiral
structure can explain the principal features of the age-velocity dispersion
relation and other parameters of the velocity distribution in the solar
neighbourhood. In addition, we find that heating by strong transient spirals
can naturally explain the presence of small-scale structure in the velocity
distribution (``moving groups''). Heating by spiral structure also explains why
the stars in a single velocity-space moving group have a wide range of ages, a
result which is difficult to understand in the traditional model that these
structures result from inhomogeneous star formation. Thus we suggest that old
moving groups arise from irregularities in the Galactic potential rather than
irregularities in the star-formation rate.
