of it are devoted to Machine-Kinematics, or as Prof. Rankine calls it, the Geometry of Machinery,—and this subject is treated in a way which has some points in common with that now adopted by Reuleaux, although greatly differing from it.
Although neither Rankine's nomenclature nor his classification (given first partly in his Applied Mechanics) is now likely to be followed—it may be interesting to compare them with those of Reuleaux, the superiority of which I believe Rankine would have been the first to recognise had he lived to know them. Rankine considers a machine to be made up of a "frame" and "moving pieces" the latter being "primary" and "secondary." The frame is the fixed link of the mechanism (in the language of Reuleaux), the primary moving pieces are links the nature of whose motions are determined solely by their connection with the frame, the secondary moving pieces are all other links. He considers (erroneously) that the primary pieces can have no other motions than those he calls shifting, turning and helical, and that they must be connected to the frame by one of the lower pairs of elements. He then goes on to examine the simpler conditions of these three kinds of motion, which he does by the ordinary geometrical methods. The general nature of the motion of secondary moving pieces is treated by itself, principally by the method of instantaneous centres and axes, which Rankine afterwards uses freely and with great advantage throughout the work. In the next chapters, unfortunately, an entirely different set of ideas is introduced, and the comparative distinctness, as to system, of the earlier part of the work is lost. The idea of "elementary combinations" is brought in, and under this head are treated an immense number of kinematic chains of the most various descriptions, as well as the delineation of the profiles of several higher elements. The "mechanical powers" are placed as a subdivision under "elementary combinations." The lever and wheel and axle are taken together as cases of motion about a point, i.e. of turning,—and the inclined plane, wedge and screw as cases of sliding,—the "powers" are therefore not considered to be connected with the three simple motions of the first chapter. The place of the pulley among them is left unexplained. Some compound chains and some simple ones which in no way differ from "elementary combinations" are treated in two further chapters on "aggregate combinations" and "adjustments."
Notwithstanding the excellence of Prof. Rankine's book—and the value of some parts of it will be increased rather than diminished when read in the fresh light of Reuleaux's investigations,—it must be confessed that it contains neither a general theory of machines nor a systematic treatment of their motions. Most of its solutions are special rather than general, fresh methods being adopted for each new class of mechanisms.
