Notes on the history of the Coriolis effect

A colleague recently shared with me some back issues of Physics Today. In one of them (August 2011, page 8 ), Christopher Graney wrote that the deflection of moving objects seen from within a rotating frame of reference was described by Giovanni Riccioli and Francesco Grimaldi in 1651, nearly two centuries before Gaspard-Gustave Coriolis obtained his celebrated theorem on relative motion. But it should be pointed out that Riccioli and Grimaldi were elaborating on an argument discussed by Galileo Galilei two decades earlier, in 1632: In the second day of his Dialogue Concerning the Two Chief World Systems, Galileo explains,

In shooting the cannon, it and the target are moving with equal speed, both being carried by the motion of the terrestrial globe. Although the cannon will sometimes be placed closer to the pole than the target and its motion will consequently be somewhat the slower, being made along a smaller circle, this difference is insensible because of the small distance from the cannon to the mark. ¹

Thus, whereas Galileo argued that the deflection produced by a rotating Earth was too small to be observed, Riccioli and Grimaldi argued that the lack of observation was proof of a steady Earth.

Continuing the discussion, Manuel López-Mariscal (Physics Today, November 2012, page 8 ) wrote that it is well known that Pierre Simon Laplace used the Coriolis force in his study of ocean tides in 1775. Earlier instances of the use of the Coriolis force are not so well known: Euler’s equations governing the motion of a liquid in a rotating tube and Clairaut’s equations governing the constrained motion of two masses in a plane. ² None of those antecedents should, however, undermine the fact that Coriolis’s theorem is one of the great achievements of classical mechanics. ³ Sometimes it is cursorily stated that Coriolis derived the force acting in a rotating system, but his theorem actually gives the complete transformation of the equations of motion for any moving frame. So, for example, Jean-Baptiste Bélanger used Coriolis’s theorem to study the motion relative to a translating system: ⁴ For uniform motion, he found that the equations are the same as in a system at rest (Galilean invariance), whereas for accelerated motion, he found that a uniform force field has to be added to the equations ⁵ (equivalence principle).