In the problem of the conservation of motion, we encountered the simplest form of the operational schemata relating to group structure, for the construction of this notion by the adolescent rests directly on formal reversibility by inversion. In the equilibrium problems, of which the problem of communicating vessels gives us a first example, we come to a more complex variety of schema resting on group structure. In every equilibrium the two possible forms of reversibility operate simultaneously: inversion, which corresponds to the additions or eliminations effected in the parts of the system which come into equilibrium, and reciprocity, which corresponds to the symmetries or compensations between these parts (thus to actions which are both equivalent as regards their respective products and oriented in opposite directions). But, inversions and reciprocities also form a group between themselves.