When the reference of a unit is changed, the task remains of expressing the new definition in the terms of the previous one. In two centuries, for instance, the definition of the metre was changed six times. Around 1955, the definitions of the second as the SI unit of time were changed from astronomical ones, based on the rotation (or revolution) of the Earth, to a definition stemming from a quantum phenomenon. The expression of the new atomic second in terms of the previous definitions required a number of actions and measurements. The aim of this paper is to review these actions, some of which, fifty years later, are being forgotten for a lack of adequate documentation.