  We have measured the field-dependent heat capacity in the tetragonal
antiferromagnets CeRhIn$_{5}$ and Ce$_{2}$RhIn$_{8}$, both of which have an
enhanced value of the electronic specific heat coefficient $\gamma \sim 400$
mJ/mol-Ce K$^{2}$ above $T_{N}$. For $T<T_{N},$ the specific heat data at zero
applied magnetic field are consistent with the existence of an anisotropic
spin-density wave opening a gap in the Fermi surface for CeRhIn$_{5},$ while
Ce$_{2}$RhIn$_{8}$ shows behavior consistent with a simple antiferromagnetic
magnon. From these results, the magnetic structure, in a manner similar to the
crystal structure, appears more two-dimensional in CeRhIn$_{5}$ than in
Ce$_{2}$RhIn$_{8}$ where only about 12% of the Fermi surface remains ungapped
relative to 92% for Ce$_{2}$RhIn$_{8}$. When $B||c,$ both compounds behave in a
manner expected for heavy fermion systems as both $T_{N}$ and the electronic
heat capacity decrease as field is applied. When the field is applied in the
tetragonal basal plane ($B||a$), CeRhIn$_{5}$ and Ce$_{2}$RhIn$_{8}$ have very
similar phase diagrams which contain both first- and second-order field-induced
magnetic transitions .
