  From a heuristic calculation of the leading order essential singularity in
the distribution of Yang-Lee zeroes, we obtain new scaling relations near the
ferromagnetic-Griffiths transition, including the prediction of a discontinuity
on the analogue of the critical isotherm. We show that experimental data for
the magnetization and heat capacity of $\mathrm{La_{0.7}Ca_{0.3}MnO_3}$ are
consistent with these predictions, thus supporting its identification as a
Griffiths ferromagnet.
