Atomic clocks are crucial in understanding the connections between electrodynamics and gravitation. To this purpose a revisitation of a well-known derivation of Schiff, about variation of period of atomic clocks, is performed. The Weak Equivalence Principle and Special Relativity are found not sufficient to derive, from Schiff’s proposal, gravitational time dilation, even to a first order approximation. Schiff’s derivation of time dilation in absence of gravitation, can match, to all orders of approximation, relying on conservation of energy, the one derived in static gravitation. Energy conservation and WEP bridge the two interactions, such that, variations of periods of oscillators on Earth depend on their kinetic energy and potential energy, referred to the Earth-Centered Inertial frame.