“The diversions and modifications in the course of the active step, as furnished by the moving factor of the remaining legs, are already clearly illustrated by the curves shown by the joints of the hind tibia of a May-beetle (Fig. 120) and a stag-beetle (Fig. 121, _c_). The actual faint line in this case does not run from the front toward the back, as would correspond to the active leg-motion, but either directly inward (Fig. 121, _cb_), or even somewhat to the front. In the May-beetles, and even more in the running garden-beetle, the curves of the hind legs present themselves as screw-like lines (Fig. 122, _l_{3}_), while the scrawling of the remaining members (_l_{1}_, _l_{2}_) is much simpler. “Inasmuch as we now have a cursory knowledge of the movements made by each individual leg for itself,—movements, however, which plainly occur very differently according to the structure of these appendages,—the question now is of the combined play, the total effect of all the legs taken together, and therefore of the walk and measure of the united work of the foot. “In opposition to the caterpillars and many other crawling animals which extend their legs in pairs and really swing them by the worm-like mode of contraction of the dermo-muscular tube, the legs of fully grown insects are moved in the contrary direction and in no sense in pairs, but alternately—or, more strictly speaking, in a diagonal direction. “For an examination of the gait of insects, we choose, for obvious reasons, those which have very long legs and which at the same time are slow walkers. “Insects may be called ‘double-three-footed,’ from the manner in which they alternately place their legs. There are always three legs set in motion at the same time, or nearly so, while in the meantime the remaining legs support the body, after which they change places. [Illustration: FIG. 122.—The same by the left fore (_l_{1}_), middle (_l_{2}_), and hind, leg (_l_{3}_) of a Carabus. Natural size. ] [Illustration: FIG. 123.-Tracks of a _Blaps mortisaga_ marked by the differently painted tibial points: ●, tracks of fore, —○, middle, —/, hind leg. Natural size. ] [Illustration: FIG. 124.—Tracks of _Necrophorus vespilio_. Natural size. ] “To be more exact, it is usually thus: At first (Fig. 118) the left fore leg (_L_{1}_) steps out, then follows the right middle leg (_R_{2}_), and the left hind leg (_L_{3}_). Then while the left fore leg begins to retract and thus make the backward movement, the right fore leg is extended, whereupon the left middle leg and the right hind leg are raised in the same order as the first three feet.” Graber[23] painted the feet of beetles and let them run over paper, and goes on to say: