  The lattice parameters of the tetragonal compounds Ce$M$In$_{5}$ and
Ce$_{2}M$In$_{8}$($M=$Rh, Ir and Co) have been studied as a function of
pressure up to 15 GPa using a diamond anvil cell under both hydrostatic and
quasihydrostatic conditions at room temperature. The addition of $M$In$_{2}$
layers to the parent CeIn$_{3}$ compound is found to stiffen the lattice as the
2-layer systems (average of bulk modulus values $B_{0}$ is 70.4 GPa) have a
larger $B_{0}$ than CeIn$_{3}$ (67 GPa), while the 1-layer systems with the are
even stiffer (average of $B_{0}$ is 81.4 GPa). Estimating the hybridization
using parameters from tight binding calculations shows that the dominant
hybridization is $fp$ in nature between the Ce and In atoms. The values of
$V_{pf}$ at the pressure where the superconducting transition temperature
$T_{c}$ reaches a maximum is the same for all Ce$M$In$_{5}$ compounds. By
plotting the maximum values of the superconducting transition temperature
$T_{c}$ versus $c/a$ for the studied compounds and Pu-based superconductors, we
find a universal $T_{c}$ versus $c/a$ behavior when these quantities are
normalized appropriately. These results are consistent with magnetically
mediated superconductivity.
