Resonance Transitions in Molecular Beams Experiments. II. Averages Over the Velocity Distribution

General expressions are given for the average, over a $v^3$ velocity distribution, of the transition probability in a resonance line of an atomic or molecular beams experiment. Explicit expressions are given for multiple quantum transitions which are similar to those of Torrey for "allowed" transitions. The case when the complete velocity distribution is cut off on either the high- or low-velocity side or both is discussed.