Editing Gridiron pendulum (section)

==How it works==
[[File:BanjoPendulum.svg|thumb|A: exterior schematic<br>B: normal temperature<br> C: higher temperature]]
The gridiron pendulum is constructed so the high thermal expansion (zinc or brass) rods make the pendulum shorter when they expand, while the low expansion steel rods make the pendulum longer.  By using the correct ratio of lengths, the greater expansion of the zinc or brass rods exactly compensate for the greater length of the low expansion steel rods, and the pendulum stays the same length with temperature changes.<ref name="Baker2011" />  

The simplest form of gridiron pendulum, introduced as an improvement to Harrison's around 1750 by John Smeaton, consists of five rods, 3 of [[steel]] and two of [[zinc]].  A central [[steel]] rod runs up from the [[bob (physics)|bob]] to the suspension pivot.

At that point a cross-piece (middle bridge) extends from the central rod and connects to two [[zinc]] rods, one on each side of the central rod, which reach down to, and are fixed to, the bottom bridge just above the bob. The bottom bridge clears the central rod and connects to two further steel rods which run back up to the top bridge attached to the suspension. As the steel rods expand in heat, the bottom bridge drops relative to the suspension, and the bob drops relative to the middle bridge. However, the middle bridge rises relative to the bottom one because the greater expansion of the zinc rods pushes the middle bridge, and therefore the bob, upward to match the combined drop caused by the expanding steel.

In simple terms, the upward expansion of the zinc counteracts the combined downward expansion of the steel (which has a greater total length). The rod lengths are calculated so that the effective length of the zinc rods multiplied by zinc's [[thermal expansion]] coefficient equals the effective length of the steel rods multiplied by iron's expansion coefficient, thereby keeping the pendulum the same length.<ref name="Glasgow1" /><ref name="Britannica" /><ref name="Kater"/>{{rp|p.261}}

Harrison's original pendulum used [[brass]] rods (pure zinc not being available then); these required more rods because brass does not expand as much as zinc does.  Instead of one high expansion rod on each side, two are needed on each side, requiring a total of 9 rods, five steel and four brass.<ref name="Britannica" /><ref name="Matthys" /> The exact degree of compensation can be adjusted by having a section of the central rod which is partly brass and partly steel. These overlap (like a sandwich) and are joined by a pin which passes through both metals. A number of holes for the pin are made in both parts and moving the pin up or down the rod changes how much of the combined rod is brass and how much is steel. 

In the late 19th century the [[Dent (clocks and watches)|Dent company]] developed a tubular version of the zinc gridiron in which the four outer rods were replaced by two concentric tubes which were linked by a tubular nut which could be screwed up and down to alter the degree of compensation.

In the 1730s clockmaker [[John Ellicott (clockmaker)|John Ellicott]] designed a version that only required 3 rods, two brass and one steel (''see drawing''), in which the brass rods as they expanded with increasing temperature pressed against levers which lifted the bob.<ref name="Beckett">{{cite book
  |last=Beckett
  |first=Edmund (Lord Grimsthorpe)
  |year=1874
  |title=A Rudimentary Treatise on Clocks and Watches and Bells, 6th Ed.
  |publisher=Lockwood & Co.
  |location=London
  |url=https://archive.org/details/arudimentarytre01grimgoog/page/n69/mode/2up
  |page=59-60}}</ref><ref name="Turner"/> The Ellicott pendulum did not see much use.<ref name="Kater"/>{{rp|p.272-273}}