The solid-solution SrRu$_{1-x}$Rh$_x$O$_3$ ($0le x le1$) is a variable-electron-configuration system forming in the nearly-cubic-perovskite basis, ranging from the ferromagnetic 4$d^4$ to the enhanced paramagnetic 4$d^5$. Polycrystalline single-phase samples were obtained over the whole composition range by a high-pressure-heating technique, followed by measurements of magnetic susceptibility, magnetization, specific heat, thermopower, and electrical resistivity. The ferromagnetic order in long range is gradually suppressed by the Rh substitution and vanishes at $x sim 0.6$. The electronic term of specific-heat shows unusual behavior near the critical Rh concentration; the feature does not match even qualitatively with what was reported for the related perovskites (Sr,Ca)RuO$_3$. Furthermore, another anomaly in the specific heat was observed at $x sim 0.9$.
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