In the framework of a Kaluza-Klein-like scheme, based on a five-dimens
ional Riemannian space in which energy plays the role of the fifth dim
ension, we discuss a class of solutions of the five-dimensional Einste
in equations in vacuum, which allows us to recover the energy-dependen
t phenomenological metric for gravitation, recently derived from the a
nalysis of some experimental data concerning the slowing down of clock
rates in the gravitational field of Earth.