The temperature dependence of the Mossbauer spectrum centroid S of Zn-67(2+) impurity atoms at the copper and yttrium sites of YBa2Cu3O6.9, YBa2Cu3O6.6, YBa2Cu4O8, Nd1.85Ce0.15CuO4, La1.85Sr0.15CuO4, HgBa2CuO4, HgBa2CaCu2O6, Bi2Sr2CaCu2O8, and Tl2Ba2CaCu2O8 compounds at temperatures T > T-c (T-c is the superconducting transition temperature) is controlled by a second-order Doppler shift. The value of S in the temperature range T < T-c is affected by the energy-band mechanism associated with the formation of Cooper pairs and their Bose condensation. A relationship between the electron density at the metal site of the crystal and its superconducting transition temperature is found. In the case of compounds containing two structurally nonequivalent sites for copper atoms, a change in the electron density caused by the Bose condensate of Cooper pairs is shown to be different for these sites. The experimental temperature dependence of the superconducting electron fraction conforms to a similar dependence following from the Bardeen-Cooper-Schrieffer theory for all the sites under study. (C) 2003 MAIK "Nauka/Interperiodica".