I say “almost,” because it is practically impossible to suspend a pendulum without some little departure from perfect symmetry around its point of attachment. In consequence of this, the weight deviates sooner or later from a straight line, and describes an oval more or less elongated. Some years ago this circumstance presented a serious difficulty to those who wished to repeat M. Foucault’s celebrated experiment, demonstrating the rotation of the earth. Nevertheless, in the case now before us, the pendulum is so carefully suspended that its deviation from a straight line is not at first perceptible. Let us suppose the amplitude of its oscillation to be represented by the dotted line _a b_, Fig. 166. The point _d_, midway between _a_ and _b_, is the pendulum’s point of rest. When drawn aside from this point to _b_, and let go, it will return to _d_, and in virtue of its momentum will pass on to _a_. There it comes momentarily to rest, and returns through _d_ to _b_. And thus it will continue to oscillate until its motion is expended. The pendulum having first reached the limit of its swing at _b_, let us suppose a push in a direction perpendicular to _a b_ imparted to it; that is to say, in the direction _b c_. Supposing the time required by the pendulum to swing from _b_ to _a_ to be one second,[78] then the time required to swing from _b_ to _d_ will be half a second. Suppose, further, the force applied at _b_ to be such as would carry the bob, if free to move in that direction alone, to _c_ in half a second, and that the distance _b c_ is equal to _b d_, the question then occurs, where will the bob really find itself at the end of half a second? It is perfectly manifest that both forces are satisfied by the pendulum reaching the point _e_, exactly opposite the centre _d_, in half a second. To reach this point, it can be shown that it must describe the circular arc _b e_, and it will pursue its way along the continuation of the same arc, to _a_, and then pass round to _b_. Thus, by the rectangular impulse the rectilinear oscillation is converted into a rotation, the pendulum describing a circle, as shown in Fig. 167. [Illustration: FIG. 166.] [Illustration: FIG. 167.] If the force applied at _b_ be sufficient to urge the weight in half a second through a greater distance than _b c_, the pendulum will describe an ellipse, with the lines _a b_ for its smaller axis; if, on the contrary, the force applied at _b_ urge the pendulum in half a second through a distance less than _b c_, the weight will describe an ellipse, with the line _a b_ for its greater axis. [Illustration: Fig. 167.] Let us now inquire what occurs when the rectangular impulse is applied at the moment the ball is passing through its position of rest at _d_.