“Though it might be supposed that the feet would remain stationary during the extension or retraction of the limbs, this never occurs in actual walking. Not merely the upper, but also the lower, thigh is either drawn in or stretched out, as the case may be. The latter then describes a straight line with its point during this scraping or scratching motion (Fig. 115, _no_), which is obviously the chord to that quadrant which would be drawn by the tibia or foot in a yielding medium, as water, for instance. But even this motion results extremely rarely, and never in actual walking. If we fix our eye anew upon the fore leg at the very moment when it is again retracted, after the resultant ‘fixing,’ we shall then observe that the hip also is simultaneously turned backward in a definite angle. The tibia would describe the arc _nq_ (Fig. 115) by means of the latter alone. “This plane, in conjunction with the rectilinear ‘movement’ (_no_) obtained by the retraction of the tibia, produces a path (_nr_), and this is what is actually described by a painted foot upon a properly prepared surface, as a sheet of paper;[22] supposing, however, that the body in the meantime is not moved forward by other forces. In the last case, and this indeed always takes place in running, the trunk is moved a bit forward, together with the leg which is just describing its curve with a rapidity corresponding to the momentum obtained; the result of this is that the curve of the foot from its beginning (_n_) to its end (_a_) bends round close to itself, just as a man who, when on board a ship in motion, walks across it diagonally, and yet on the whole moves forward, because his line of march, uniting with that of the ship, results in a change of position in space. “The case is the same in the middle and hind legs, which must make a double course also, yet in such a way that the straight line is drawn, not during the retraction, but during the extension; during which, however, quite as in the fore leg, the members mentioned (_R_{3}_) gradually approach the body. “When the legs have reached the maximum of their retraction, or of their extension, as the case may be, and therefore the end of their active course for that time, then begins the opposite or backward movement; that is, the fore legs are again extended, while their levers draw the remaining legs together again. [Illustration: FIG. 118.—A Carabus beetle in the act of walking or running: three legs (_L_{1}_, _R_{2}_, _L_{3}_) are directed forward, while the others (_R_{1}_, _L_{2}_, _R_{3}_), which are directed backward toward the tail, have ended their activity; _ab_, _cd_, and _ef_ are curves described by the end of the tibiæ, and passing back to the end of the body; _bh_, _di_, and _fg_ are curves described by the same legs during their passive change of position.—After Graber. ]