  For three anyons confined in a harmonic oscillator, only the class of states
that interpolate nonlinearly with the statistical parameter contributes to the
third virial coefficient of a free anyon gas. Rather than evaluating the full
three-body partition function as was done in an earlier publication (Phys. Rev.
{\bf A46}, 4693 (1992)), here only the nonlinear contribution is calculated,
thus avoiding delicate cancellations between the irrelevant linear part and the
two-body partition function. Our numerical results are consistent with the
simple analytical form suggested recently by Myrheim and Olaussen.
