In a prior entry of this series, I explored the life of Christiaan Huygens (1629–1695) in a broad sense, as well as his specific contributions to the advancement of optics. In that discussion, I highlighted Huygens as a polymath who constructed some of the finest telescopes of the seventeenth century, made significant discoveries as an astronomer, and played an influential role as a mathematician and physicist. Today, I will examine his contributions to hydrostatics, with a particular focus on his notable input to mechanics.
Isaac Newton (1642–1728) is infamous for not publishing the majority of his research. When it comes to mathematics, for instance, only two works were released during his lifetime. The Arithmetica Universalis, essentially a textbook, was edited and published by William Whiston (1667–1752), his successor as Lucasian professor, contrary to Newton’s intentions and without crediting him. De analysi per aequationes numero terminorum infinitas (or On analysis by infinite series, On Analysis by Equations with an infinite number of terms) was authored in 1669, and although the manuscript circulated among scholars in both England and elsewhere, it was not published until 1711. Nonetheless, The Mathematical Papers of Isaac Newton, edited by D. T. Whiteside (1932–2008), comprise eight substantial volumes.
Although not as extreme as Newton and not as prolific, Huygens appeared to exhibit the same tendency of not publishing the scientific texts he devoted years to creating. In the field of optics, he spent a significant amount of time working on a comprehensive text only to abandon it and commence a new paper, of which he managed to publish just the first of three sections. This behavioral pattern recur with his hydrostatics work.
In his De iis quae liquido supernatant, composed around 1650 but never released, Huygens, mirroring others who delved into hydrostatics since Archimedes, paid considerable attention to the mathematical calculations of centers of gravity and cubatures, such as those of obliquely truncated paraboloids of revolution and of cones and cylinders. His views on hydrostatics rest upon a singular axiom: a mechanical system is in equilibrium if its center of gravity is at the lowest point relative to its constraints. He derived Archimedes’ law from this fundamental axiom and demonstrated that a floating object reaches equilibrium when the distance between the center of gravity of the entire body and that of its submerged section is minimized. The stable positioning of a floating sphere segment is thus established, along with the conditions that right truncated paraboloids and cones must meet to float vertically.
We noted in a previous post that Descartes formulated the laws governing impact bodies. These were, in fact, incorrect, and it is somewhat ironic that Huygens, a staunch Cartesian, was the one who revealed their flaws and provided the accurate laws governing the collisions of elastic bodies in his De motu corporum ex percussione during studies conducted between 1652 and 1656. Descartes’ analysis of collision laws presumed an absolute measurability of velocity. Huygens contested this, proposing that the forces exerted between colliding bodies only rely on their relative velocity. He included this perspective as hypothesis III in De motu corporum, asserting that all motion is gauged against a reference frame that is presumed to be at rest, meaning the outcomes of motion speculations shouldn’t depend on whether this frame holds an absolute state of rest. In 1661, Huygens performed collision experiments along with Christopher Wren (1632–1723). By 1668, The Royal Society initiated an inquiry into the subject, with Huygens, Wren, and John Wallis (1616–1703) all presenting similar and accurate solutions. The principle of momentum conservation was fundamental to their findings. Both Wren and Huygens limited their theories to perfectly elastic bodies (elastic collision), while Wallis extended his analysis to include imperfectly elastic bodies (inelastic collision). Huygens published his De motu corporum in the Journal des Sçavans (the earliest academic journal in Europe, founded in 1665) in 1669.
Huygens is also notably recognized for creating the first functional pendulum clock in 1657. His most significant revelation was that, contrary to Galileo, a simple pendulum does not exhibit true tautochronism. He addressed this challenge by determining the curve along which a mass would descend under gravity within the same duration, irrespective of its initial position; this is known as the tautochrone problem. Utilizing geometric methods that foreshadowed calculus, Huygens demonstrated