Supposing the pendulum to be moving from _a_ to _b_, Fig. 168, and that at _d_ a shock is imparted to it sufficient of itself to carry it in half a second to _c_; it is here manifest that the resultant motion will be along the straight line _d g_ lying between _b d_ and _d c_. The pendulum will return along this line to _d_, and pass on to _h_. In this case, therefore, the pendulum will describe a straight line, _g h_, oblique to its original direction of oscillation. Supposing the direction of motion at the moment the push is applied to be from _b_ to _a_, instead of from _a_ to _b_, it is manifest that the resultant here will also be a straight line oblique to the primitive direction of oscillation; but its obliquity will be that shown in Fig. 169. [Illustration: FIG. 168.] [Illustration: FIG. 169.] When the impulse is imparted to the pendulum neither at the centre nor at the limit of its swing, but at some point between both, we obtain neither a circle nor a straight line, but something between both. We have, in fact, a more or less elongated ellipse with its axis oblique to _a b_, the original direction of vibration. If, for example, the impulse be imparted at _d′_, Fig. 170, while the pendulum is moving toward _b_, the position of the ellipse will be that shown in Fig. 170; but if the push at _d′_ be given when the motion is toward _a_, then the position of the ellipse will be that represented in Fig. 171. [Illustration: FIG. 170.] [Illustration: FIG. 171.] [Illustration: FIG. 172.] By the method of M. Lissajous we can combine the rectangular vibrations of two tuning-forks, a subject which I now wish to illustrate before you. In front of an electric lamp, L, Fig. 172, is placed a large tuning-fork, T′, fixed in a stand horizontally, and provided with a mirror, on which a narrow beam of light, L T′, is permitted to fall. The beam is thrown back, by reflection. In the path of the reflected beam is placed a second upright tuning-fork, T, also furnished with a mirror. By the horizontal fork, when it vibrates, the beam is tilted laterally; by the vertical fork, vertically. At the present moment both forks are motionless, the beam of light being reflected from the mirror of the horizontal to that of the vertical fork, and from the latter to the screen, on which it prints a brilliant disk. I now agitate the upright fork, leaving the other motionless. The disk is drawn out into a fine luminous band, 3 feet long. On sounding the second fork, the straight band is instantly transformed into a white ring _o p_, Fig. 172, 36 inches in diameter. What have we done here? Exactly what we did in our first experiment with the pendulum. We have caused a beam of light to vibrate simultaneously in two directions, and have accidentally hit upon the phase when one fork has just reached the limit of its swing and come momentarily to rest, while the beam is receiving the maximum impulse from the other fork.