Bétancourt afterwards filled up the details in their "Essai sur la composition des machines" (1808). Monge had entitled the subject "Elements of Machines," which he intended to be equivalent to means for altering the direction of motion. He understood by these "means" mechanisms, and based on this idea the arrangement of mechanisms according to the possible combinations of four principal kinds of motion, viz.: continuous and reciprocating rectilinear, and continuous and reciprocating circular. Omitting repetitions, these give ten classes of mechanisms, corresponding to the changes of motion between
| Continuous rectilinear and | continuous | rectilinear |
| reciprocating | ' ' | |
| continuous | circular | |
| reciprocating | ' ' | |
| Continuous circular and | reciprocating | rectilinear |
| continuous | circular | |
| reciprocating | ' ' | |
| Reciprocating rectilinear and | reciprocating | rectilinear |
| ' ' | circular | |
| Reciprocating circular and | ' ' | ' ' |
This scheme,—or "system,"—was capable of extension,—and in the second edition (1819) it was extended by the addition of other fundamental motions,—continuous and reciprocating motions in curved lines,—increasing the number of classes from 10 to 21, but not altering the principle of classification. This indeed has remained with unimportant alterations in tolerably general use until the present time, and has thus acquired the sanction of very general recognition. Hâchette himself, who assisted in the production of Lanz' work,[1] adopted it unconditionally in his Traité élémentaire des machines, published in 1811. Borgnis, in his Traité complet de mécanique (1818) departed from it to a certain extent; he considered the problem more generally than his predecessors, and divided the parts of machines into six classes, which he called récepteurs, communicateurs, modificateurs, supports, régulateurs, and operateurs respectively.
- ↑ A third edition of this appeared in 1840: it is a repetition of the second, slightly enlarged and got up in a better form.
