### Translated for the Journal of the Franklin Institute

#### Physical Demonstration of the Rotation of the Earth by Means of the Pendulum

##### By M.L. Foucault

Such are the ideal conditions under which the motion of rotation of the globe would become evidently accessible to observation. But, in fact, we are obliged to take our fixed point upon a moving base; the parts to which the upper end of the pendulum thread is attached cannot be withdrawn from the diurnal movement, and it might be feared, at first sight, that this motion, communicated to the thread and to the mass of the pendulum, would alter the direction of the plane of oscillation. However, theory shews us here no serious difficulty, and on the other hand, experiment has shewn me that, provided the thread be round and homogeneous, it may be turned with considerable rapidity around its axis in either direction, without influencing sensibly the position of the plane of oscillation, so that the experiment such as I have described it, must succeed at the pole.*

 Foucault's Paper
But when we descend to our latitudes, the phenomenon becomes complicated by an element of considerable difficulty of appreciation, and to which I desire particularly to call attention of mathematicians.

In proportion as we approach the equator, the plane of the horizon assumes a position more and more oblique to the axis of the earth, and the vertical, in place of turning on itself, as at the pole, describes a cone of greater and greater angle; whence results a retardation in the apparent motion of the plane of oscillation, a motion which becomes nothing at the equator, and changes its sign in the other hemisphere. To determine the law according to which this motion varies in different latitudes, we must have recourse either to analysis or to mechanical and geometrical considerations, which do not suit the narrow limits of this note. I must, therefore, confine myself to announcing that the two methods accord (neglecting certain secondary phenomena) in shewing that the angular motion of the earth during the same time multiplied by the sine of the latitude. I then set to work with confidence, and in the following way I established the reality of the predicted phenomenon as to its direction and probable amount.