Using experimental data on the entropy S at intermediate temperatures, corrected for an electronic term to get the vibrational entropy, we obtain well-defined and accurate ``entropy Debye temperatures'' FTHETA=${\mathrm{FTHETA}}^{S}$. From ${\mathrm{FTHETA}}^{S}$ we define a quantity with the dimension of a force constant, ${k}^{S}$==M(${k}_{B}$FTHETA/\ensuremath{\Elzxh}${)}^{2}$, where M is the atomic mass. Similarly, data on the low-temperature vibrational heat capacity and the elastic coefficients yield Debye temperatures ${\mathrm{FTHETA}}^{C}$ and ${\mathrm{FTHETA}}^{\mathrm{elas}}$ and corresponding force constants ${k}^{C}$ and ${k}^{\mathrm{elas}}$. The ratios of ${k}^{S}$ for the 4d-5d pairs Zr,Hf, Nb,Ta, Mo,W, Tc,Re, Ru,Os, Rh,Ir, and Pd,Pt are remarkably constant, (${k}^{S}$${)}^{4d}$/(${k}^{S}$${)}^{5d}$ =0.76\ifmmode\pm\else\textpm\fi{}0.01, in spite of varying crystal structures. Further, (${k}^{C}$${)}^{4d}$/(${k}^{C}$${)}^{5d}$ =0.70\ifmmode\pm\else\textpm\fi{}0.07 and (${k}^{\mathrm{elas}{)}^{4d}/({k}^{\mathrm{elas}{)}^{5d}}}$ =0.69\ifmmode\pm\else\textpm\fi{}0.08. The corresponding force-constant ratios ${k}^{3d}$/${k}^{4d}$ vary more. This correlates with an approximately constant atomic-volume ratio ${\ensuremath{\Omega}}^{4d}$/${\ensuremath{\Omega}}^{5d}$=0.99\ifmmode\pm\else\textpm\fi{}0.02, while ${\ensuremath{\Omega}}^{3d}$/${\ensuremath{\Omega}}^{4d}$=0.81\ifmmode\pm\else\textpm\fi{}0.05 shows irregularities, mainly of magnetic origin. As a basis for our analysis, we review low-temperature Debye temperatures ${\mathrm{FTHETA}}^{\mathrm{elas}}$ and ${\mathrm{FTHETA}}^{C}$ and the bulk modulus B of the transition metals.