Degeneration of ALF D_n Metrics

Beginning with the Legendre transform construction of hyperk\"ahler metrics, we analyze the ALF version of the D_n metrics. We determine the constraint equation obtained from extremizing the $w$ coordinate of the generating function F(z,\bar{z},u,\bar{u},w) and study its behavior as we send two of the mass parameters of the $D_n$ metric to zero. We find that the constraint equation enforces the limit that the metric becomes that of multi-Taub-NUT.