“At the same time, as we may see by the uniting leg, the limb is either a little raised, that there may be no unnecessary friction, or it remains during the passive step also, with its means of locomotion in slight contact with the ground. “The curve of two steps, as inscribed by the end of the tibia of the left fore leg of a stag-beetle, affords an instructive summary of the conditions of which we have been speaking (Fig. 121, _B_). We see two curves. The thick one (_ab_), directed toward the axis of the body, corresponds to the effective act of a single walking function, which brings the body a bit forward; the thinner, on the other hand, or we might say the hair line (_bc_), which, however, is but rarely made quite clearly, is produced by the ineffectual backward movement, by which the insect again approaches its working posture (_c_). It is at first placed at some distance from the body, in order that (like _c_ also) it may draw near to the body again; but in such a way, naturally, that it coincides with the starting-point of the following active curve (_cd_). It is evident that even the passive curve is not the imprint of the movement accomplished exclusively by the leg, for this latter, while struggling to reach its resting-place, is really involuntarily carried forward with the rest of the body. “The scroll-like lines drawn by the swimming beetle (Dyticus), with the large, sharp points of its hind tibia, are also very instructive (Fig. 119, _A_). [Illustration: FIG. 119.—_A_, trail curves described by the tibial spines of the right and left hind limb of Dyticus. _B_, the same made by the right hind leg (_r_{3}_) alone. Natural size.—After Graber. ] [Illustration: FIG. 120.—The same by the two hind legs of Melolontha: _a_, the active and thickened section of the curve. Natural size. ] [Illustration: FIG. 121.—_A_, track curves of two of the tibial spines of the left, middle legs of a stag-beetle. Natural size. _B_, the same enlarged; _fg_, the longitudinal axis of the trunk; _cd_ and _ab_, the active curve passing inward,—_bc_ and _de_, the passive going outward. _C_, two curves described by the left hind legs; in this case, the curves are not inwards or backwards, but partly directly inward (_b_), and in part obliquely forwards (_a_). ]