Laying Down the Law
Foucault's First Law
Based on what we know about "degrees of freedom," as well as precession, we are equipped with the information necessary to gain a basic understanding of Foucault's Laws. His first law states that any gyroscope possessing three degrees of freedom, that is, free to move in all three planes and unaffected by the force of gravity, must indicate the rotation of the earth. Foucault proved this law when he performed the experiment with the optical sighting device. As we know from our previous discussion, the gyroscope seemed to move out of alignment with the sighting device, though in actuality this "movement" resulted because the sighting device rotated with the earth while the gyro maintained its orientation in space.
Foucault's Second Law
Foucault's second law considers a gyroscope possessing only two degrees of freedom, stating that any such gyroscope will, at any place on earth's surface, other than the two poles, tend to set itself with its axis of rotation in the plane of the axis of the earth itself by reason of the relative rotation of the two bodies. As the gyro rotates, it will tend to maintain its plane of rotation in space, while the earth's continued turning will cause it to rotate "out from under" the gyro. Eventually the force of gravity acting on the gyroscope will cause it to precess, and the plane of its rotation will become more nearly coincident with that of the earth, thus limiting the tendency of the earth to rotate "out from under" the gyroscope.
These laws point to the use of the gyroscope as a compass. A gyroscope possessing three degrees of freedom could be used to fix lines in space with which bearings could be compared, or by which courses already known could be maintained. The gyroscope having two degrees of freedom would place itself in the plane of the earth's rotation, thus indicating the north and south mechanically by the position of its axis.