Tidal Friction, Kant and Thomson-Tait on the Rotation of the Earth and Lunar Attraction¶
Core Argument¶
This chapter subjects the canonical theory of tidal friction, as formulated by Thomson and Tait and originating with Kant, to a rigorous internal critique grounded in the conservation of energy. The core argument is that Thomson and Tait, in attempting to provide a mathematical substantiation of Kant’s insight, inadvertently construct a theory that logically excludes the very phenomenon it purports to explain.
The chapter opens by reproducing Thomson and Tait’s own exposition at length. They argue that lunar attraction, acting on the Earth’s fluid surfaces, produces a tangential force that impedes the Earth’s rotation as long as the day is shorter than the month. This force, they claim, accelerates the Moon tangentially, causing it to spiral outward. Using the principle of moments of momentum, they calculate that the Earth-Moon system will ultimately reach a state of uniform rotation, with the Moon at 847,100 miles and a period of 48.36 days. They note, however, that solar tides would prevent this from being permanent, as fluid friction would continue to dissipate energy.
Engels then traces the theory’s lineage to Kant’s 1754 work, which correctly identified tidal friction as the sole cause of the Earth’s rotational retardation, but which lacked the scientific prerequisites for deeper analysis. The chapter’s decisive move is to demonstrate that Thomson and Tait’s generalisation, while presented as a refinement, in fact rests on a tacit assumption that the Earth is an entirely rigid body. Engels shows that friction, whether tidal or mechanical, converts kinetic energy into heat, which is then radiated into space and lost to the dynamic system. The kinetic energy expended in impeding the Earth’s rotation through the fluid masses cannot, therefore, reappear as potential energy in the Moon’s increased orbital distance. Only that portion acting on the solid mass of the Earth can be so compensated. Thomson and Tait’s error is to treat the system as fully conservative, ignoring the irreversible dissipation inherent in friction.
The polemic is directed squarely at Thomson and Tait’s mathematical formalism, which Engels argues has become detached from physical reality. By deriving a general law from the special case of tidal friction, they have produced a theory that excludes friction altogether. The chapter’s notes, added by later editors, acknowledge that Engels’s formulation was technically incorrect—the Earth is not rigid but elastic, producing solid tides—but affirm his fundamental point: the system cannot evolve without loss of energy. The critique thus anticipates later developments in geophysics while exposing a logical flaw at the heart of classical mechanical reasoning.