A "baucher" is also a type of bit, named after the man.
François Baucher (1796–1873) was a French riding master whose methods are still debated by dressage enthusiasts today. His philosophy of training the horse changed dramatically over the course of his career and is often considered in two distinct phases or "manners."
Baucher published a number of works on equitation, including the Dictionnaire raisonné d'équitation, "Reasoned dictionary of equitation" in 1833; the Dialogues sur l'équitation, "Dialogues on equitation" (with Louis Charles Pellier) in 1835; and the Passe-temps équestres, "Equestrian pastimes" in 1840.
Baucher's most celebrated work is the Méthode d'équitation basée sur de nouveaux principes, "Method of riding based on new principles"; the earliest extant edition is the third, published in 1842. The numerous following editions up to 1863, when his contract with his publishers expired, are essentially reprints of the same book. The 12th edition, published in 1864 and called the deuxième manière or second manner, contained notable changes from his original method, and was continued in his 13th edition published in 1868.
Baucher's "first manner" is characterized by an attempt to "annul the instinctive forces" of the horse. To do so, he gradually applied both hands and heels at the halt, his theory being that they should cancel each other out and the horse should stand still. Applying both hands and heels to effect collection was termed the effet d'ensemble.
A prominent aspect of Baucher's method is "flexion" (and relaxation) of the horse's jaw in response to light pressure from either the snaffle or curb bit. Indirectly, this motion was intended to effect flexion at the poll. This part of Baucher's training taught the horse to relax to the bit pressure from the ground - applying gentle but consistent pressure to one side until the horse would "give", then releasing the pressure immediately. Once the horse relaxed to the right and left consistently, he would begin the jaw flexion (in effect, both sides at once, resulting in the horse giving to pressure from the bit to find the release, versus pushing against the bit, tossing his head, etc.).
Baucher also incorporated flexions of the haunches, including rotations of the croup around the shoulders. This intended to teach the horse to keep his haunches straight and to help move them backward in the rein back. The rein back was used to teach the horse to move his whole body mass away from the bit (to increase the power of the hand), and also to help close the angles of the hind legs, which would help increase impulsion.