The gridiron pendulum was an improved clock pendulum invented by British clockmaker John Harrison around 1726. It didn't change its effective length with temperature, so its period of swing stayed constant with changes in ambient temperature. It consisted of alternating brass and iron rods arranged so that their different thermal expansions (or contractions) counteracted each other.
Its simplest and later form consists of five rods. A central iron rod runs up from the bob to just below the suspension. 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 iron rods which run back up to the top bridge attached to the suspension. As the iron 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, upwards to match the combined drop caused by the expanding iron.
In simple terms, the upwards expansion of the zinc counteracts the combined downwards expansion of the iron (which has a greater total length). The rod lengths are calculated so that the effective length of the zinc rods multiplied by zinc's expansion coefficient equals the effective length of the iron rods multiplied by iron's expansion coefficient thereby keeping the pendulum the same length.
Harrison's original construction using brass (pure zinc not being available then) is more complex since brass does not expand as much as zinc does. A further set of rods and bridges is needed giving nine rods in all, five iron and four brass. The exact degree of compensation can be adjusted by having a section of the central rod which is partly brass and partly iron. 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 iron. In the late 19th century the Dent company marketed a further development 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.
Scientists in the 1800s found that the gridiron pendulum had disadvantages that made it unsuitable for the highest precision clocks. The friction of the rods sliding in the holes in the frame caused the rods to adjust to temperature changes in a series of tiny jumps, rather than with a smooth motion. This caused the rate of the pendulum, and therefore the clock, to change suddenly with each jump. Later it was found that zinc is not very stable dimensionally; it is subject to creep. Therefore another type of temperature-compensated pendulum, the mercury pendulum, was used in the highest precision clocks. Both types were superseded by pendulums using low-expansion materials such as Invar and fused silica.