Polhode - History

History

The concept of polhode motion dates back to the 17th century, and Corollary 21 to Proposition 66 in Section 11, Book 1, of Isaac Newton's Principia. Later Leonhard Euler derived a set of equations that described the dynamics of rigid bodies in torque-free motion. In particular, Euler and his contemporaries Jean d’Alembert, Louis Lagrange, and others noticed small variations in latitude due to wobbling of the Earth around its polar spin axis. A portion of this wobble (later to be called the Earth’s polhode motion) was due to the natural, torque-free behavior of the rotating Earth. Incorrectly assuming that the Earth was a completely rigid body, they calculated the period of Earth’s polhode wobble to be about 9–10 months.

During the mid 19th century, Louis Poinsot developed a geometric interpretation of the physics of rotating bodies that provided a visual counterpart to Euler’s algebraic equations. Poinsot was a contemporary of Leon Foucault, who invented the gyroscope and whose pendulum experiments provided incontrovertible evidence the Earth rotates. In the fashion of the day, Poinsot coined the terms polhode and its counterpart, herpolhode, to describe this wobble in the motion of rotating rigid bodies. Poinsot derived these terms from the ancient Greek πόλος (pivot or end of an axis) + ὁδός (path or way)—thus, polhode is the path of the pole.

Poinsot’s geometric interpretation of Earth’s polhode motion was still based on the incorrect assumption that the Earth was a completely rigid rotating body. It was not until 1891 that the American astronomer, Seth Carlo Chandler, made measurements showing that there was a periodic motion of 14 months in the Earth’s wobble and suggesting that this was the polhode motion. Initially, Chandler’s measurement, now referred to as the “Chandler wobble,” was dismissed because it was significantly greater than the long-accepted 9–10 month period calculated by Euler, Poinsot, et al. and because Chandler was unable convincingly to explain this discrepancy. However, within months, another American astronomer, Simon Newcomb, realized that Chandler was correct and provided a plausible reason for Chandler’s measurements. Newcomb realized that the Earth’s mass is partly rigid and partly elastic, and that the elastic component has no effect on the Earth’s polhode period, because the elastic part of the Earth’s mass stretches so that it is always symmetrical about the Earth’s spin axis. The rigid part of the Earth’s mass is not symmetrically distributed, and this is what causes the Chandler Wobble, or more precisely, the Earth’s polhode path.