The correct answer is C) Checking the electrolyte specific gravity in the cells. The specific gravity of the electrolyte in a nickel-cadmium wet cell storage battery is the most reliable method to determine the state of charge during charging and discharging. As the battery charges and discharges, the specific gravity of the electrolyte changes, providing an accurate indication of the battery's state of charge. In contrast, options A, B, and D do not directly measure the state of charge and can provide less reliable information.