The same figure is obtained if the rectangular impulse be imparted when the pendulum is passing its position of rest, _d_. [Illustration: FIG. 176.] [Illustration: FIG. 177.] [Illustration: FIG. 178.] I have here supposed the time occupied by the pendulum in describing the line _a b_ to be one second. Let us suppose three-fourths of the second exhausted, and the pendulum at _d′_, Fig. 177, in its excursion toward _b_; let the rectangular impulse then be imparted to it, sufficient to carry it to _c_ in one-fourth of a second. Now the long pendulum requires that it should move from _d′_ to _b_ in one-fourth of a second; both impulses are therefore satisfied by the pendulum taking up the position _c′_ at the end of a quarter of a second. To reach this position it must describe the curve _d′ c′_. It will manifestly return along the same curve, and at the end of another quarter of a second find itself again at _d′_. From _d′_ to _d_ the long pendulum requires a quarter of a second. But at the end of this time the short pendulum must be at the lower limit of its swing: both requirements are satisfied by the pendulum being at _e_. We thus obtain one arm, _c′ e_, of a curve, which repeats itself to the left of _e_; so that the entire curve, due to the combination of the two vibrations, is that represented in Fig. 165. This figure is a parabola, whereas the figure of 8 before obtained is a lemniscata. We have here supposed that, at the moment when the rectangular impulse was applied, the motion of the pendulum was _toward_ _b_: if it were toward _a_ we should obtain the inverted parabola, as shown in Fig. 178. Supposing, finally, the impulse to be applied, not when the pendulum is passing through its position of equilibrium, nor when it is passing a point corresponding to three-fourths or one-fourth of the time of its excursion, but at some other point in the line, _a b_, between its end and centre. Under these circumstances we should have neither the parabola nor the perfectly symmetrical figure of 8, but a distorted 8.