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Christiaan Huygens (1629–1695) connected mathematical mechanics with the design of a more accurate pendulum clock, and worked on astronomy, probability and the wave account of light. His optical account treats a wavefront as generating secondary wavelets, the geometric idea behind Huygens' principle.^[ref]

The clock provides a useful scientific motivation: a small-amplitude simple pendulum has period approximately $2\pi \sqrt{\ell /g}$, so a stable length supplies a repeatable time scale. Finite-amplitude corrections show why an approximate classroom formula does not by itself produce a perfect timekeeper. In wave propagation, the wavefront construction addresses a different problem: how a disturbance advances through space and changes direction under refraction.

A pendulum clock uses a periodically swinging simple pendulum as its timekeeping element. For small angular displacement, an ideal simple pendulum of length $\ell$ has period $T\simeq 2\pi \sqrt{\ell /g}$. This weak dependence on amplitude at small amplitude makes the simple pendulum useful for producing nearly equal time intervals.

Real friction would stop the swing. An escapement transfers small amounts of energy from a falling weight or wound spring while counting oscillations through a gear train. Changing the effective length changes the rate: increasing $\ell$ increases the period and makes the clock run slower. Temperature-dependent length and finite-amplitude corrections limit the ideal formula.