A hydraulic machine, comprising: - a casing that extends longitudinally along an axis, and enclosing a cylindrical housing coaxial to the casing, - a differential piston having an upper ring and a lower base of a smaller cross-section, each suitable for sliding in reciprocating movement respectively in the casing and in the cylindrical housing, the piston and the cylindrical housing separating the interior of the casing according to a mixing chamber delimited by the cylindrical housing and the lower base of the piston, a chamber called "upper chamber" delimited by the upper ring and a cover of the casing, and a chamber called "lower chamber" delimited by the portion below the upper ring, the casing and the cylindrical housing, - hydraulic switching means for supplying and discharging the chambers separated by the piston, these switching means being controlled by the movements of the piston and including at least one rod acting on a distribution member able to adopt two stable positions, said distribution member including an upper valve cooperating with a first seat made in the upper ring of the piston so as to allow communication between the upper chamber and the lower chamber and at least one lower valve cooperating with a second seat made in the lower base of the piston so as to allow communication between the upper chamber and the mixing chamber, - triggering means comprising a push-piece suitable for causing, at the end of the stroke of the piston, a sudden change in the position of the switching means, under the action of an elastic means, to reverse the stroke, characterized in that the lower and upper valve seats respectively accept an upper frustoconical portion (25a; 26a) and a lower frustoconical portion (25c; 26c) tapering in opposite directions and each opening into one of the communicating chambers, such that the communication between the chambers is cut off when the associated valve closes off either one of the upper or lower frustoconical portions. - a casing that extends longitudinally along an axis, and enclosing a cylindrical housing coaxial to the casing, - a differential piston having an upper ring and a lower base of a smaller cross-section, each suitable for sliding in reciprocating movement respectively in the casing and in the cylindrical housing, the piston and the cylindrical housing separating the interior of the casing according to a mixing chamber delimited by the cylindrical housing and the lower base of the piston, a chamber called "upper chamber" delimited by the upper ring and a cover of the casing, and a chamber called "lower chamber" delimited by the portion below the upper ring, the casing and the cylindrical housing, - hydraulic switching means for supplying and discharging the chambers separated by the piston, these switching means being controlled by the movements of the piston and including at least one rod acting on a distribution member able to adopt two stable positions, said distribution member including an upper valve cooperating with a first seat made in the upper ring of the piston so as to allow communication between the upper chamber and the lower chamber and at least one lower valve cooperating with a second seat made in the lower base of the piston so as to allow communication between the upper chamber and the mixing chamber, - triggering means comprising a push-piece suitable for causing, at the end of the stroke of the piston, a sudden change in the position of the switching means, under the action of an elastic means, to reverse the stroke,