  The model for the cuprates based on the modified electron-phonon pairing
mechanism has been tested. For this purpose, the superconductors with high
value of the critical temperature have been taken into consideration. In
particular: ${\rm YBa_{2}Cu_{3}O_{7-y}}$, ${\rm HgBa_{2}CuO_{4+y}}$, ${\rm
HgBa_{2}Cu_{1-x}Zn_{x}O_{4+y}}$, and ${\rm HgBa_{2}Ca_{2}Cu_{3}O_{8+y}}$. It
has been shown that the dependence of the ratio $R_{1}\equiv
2\Delta_{tot}^{(0)}/k_{B}T_{C}$ on the doping ($p$) can be properly predicted
in the framework of the presented theory; the symbol $\Delta_{tot}^{(0)}$
denotes the energy gap amplitude at the temperature of zero Kelvin, and $T_{C}$
is the critical temperature. The numerical results have been supplemented by
the formula which describes the function $R_{1}(p)$.
