We present low-field magnetization and specific-heat data for ${\mathrm{Pd}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Fe}}_{\mathit{x}}$ alloys, with x ranging from 0.08 to 0.6 at. % Fe. Both types of measurements were done on the same samples. The samples are more homogeneous than those used in previous investigations. We find that in contrast to previous suggestions, all samples undergo sharp ferromagnetic transitions with ${\mathit{T}}_{\mathit{C}}$ ranging from 0.4 K for the 0.08-at. % Fe alloy to 18.0 K for the 0.6-at. % Fe alloy. The specific-heat anomalies associated with the transitions have the form of a cusp very close to ${\mathit{T}}_{\mathit{C}}$ as determined from the magnetization. However, because of large fluctuations, these anomalies are very broad, extending to a region of temperatures well above ${\mathit{T}}_{\mathit{C}}$. Combining our results with earlier data, we argue that the critical concentration for ferromagnetism in Pd-Fe alloys is near 0.01 at. % Fe, lower by a factor of 10 than previously assumed.

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