Editing Pendulum (section)

=== Temperature compensation ===
[[Image:Observatório Astronômico da Universidade Federal do Rio Grande do Sul 04 clock closeup.jpg|thumb|upright=0.6|Mercury pendulum in  astronomical regulator clock by Adolf Opperman, late 1800s]]
The largest source of error in early pendulums was slight changes in length due to thermal expansion and contraction of the pendulum rod with changes in ambient temperature.<ref>[https://books.google.com/books?id=Lx0v2dhnZo8C&pg=PA3 Matthys 2004], p.3</ref>  This was discovered when people noticed that pendulum clocks ran slower in summer, by as much as a minute per week<ref name="Beckett1874" /><ref name="BritannicaCompensation">{{cite EB1911|wstitle= Clock |volume= 06 |last= Penderel-Brodhurst |first= James George Joseph |author-link= James George Joseph Penderel-Brodhurst | pages = 536&ndash;553; see pages 539 and 540 |quote= }}</ref> (one of the first was [[Godefroy Wendelin]], as reported by Huygens in 1658).<ref>{{cite book
  | last =Huygens
  | first = Christiaan
  | title = Horologium
  | publisher = Adrian Vlaqc
  | year = 1658
  | location = The Hague
  | url = http://www.antique-horology.org/_Editorial/Horologium/Horologium.pdf
  }}, translation by Ernest L. Edwardes (December 1970) ''Antiquarian Horology'', Vol.7, No.1</ref>  Thermal expansion of pendulum rods was first studied by [[Jean Picard]] in 1669.<ref name="Zupko">{{cite book
  | last = Zupko
  | first = Ronald Edward
  | author-link = Ronald Edward Zupko
  | title = Revolution in Measurement: Western European Weights and Measures since the Age of Science
  | publisher = Diane Publishing
  | year = 1990
  | page = 131
  | isbn = 978-0-87169-186-6}}</ref><ref>{{cite book |last= Picard |first= Jean |date= 1671 |title= La Mesure de la Terre |trans-title= The Measurement of the Earth |language= fr |location= Paris, France |publisher= Imprimerie Royale |page= 4 |url= https://gallica.bnf.fr/ark:/12148/btv1b7300361b/f14.item }} Picard described a pendulum consisting of a copper ball which was an inch (2.54&nbsp;mm) in diameter and was suspended by a strand of {{lang|fr|pite}}, a fiber from the aloe plant. Picard then mentions that temperature slightly effects the length of this pendulum: {{lang|fr|"Il est vray que cette longueur ne s'est pas toûjours trouvées si précise, & qu'il a semblé qu'elle devoit estre toûjours un peu accourcie en Hyver, & allongée en esté; mais c'est seulement de la dixieme partie d'une ligne&nbsp;..."}} ("It is true that this length [of the pendulum] is not always found [to be] so precise, and that it seemed that it should be always a bit shortened in winter, and lengthened in summer; but it is only by a tenth part of a line&nbsp;...") [1 {{lang|fr|[[ligne]]}} (line)&nbsp;= 2.2558&nbsp;mm].</ref> A pendulum with a steel rod will expand by about 11.3 [[parts per million]] (ppm) with each degree Celsius increase, causing it to lose about 0.27 seconds per day for every degree Celsius increase in temperature, or 9 seconds per day for a {{convert|33|C-change|abbr=on}} change. Wood rods expand less, losing only about 6 seconds per day for a {{convert|33|C-change|abbr=on}} change, which is why quality clocks often had wooden pendulum rods. The wood had to be varnished to prevent water vapor from getting in, because changes in humidity also affected the length.

==== Mercury pendulum ====
The first device to compensate for this error was the mercury pendulum, invented by [[George Graham (clockmaker)|George Graham]]<ref name="Graham1726" /> in 1721.<ref name="Milham1945" /><ref name="BritannicaCompensation" />  The liquid metal [[mercury (element)|mercury]] expands in volume with temperature. In a mercury pendulum, the pendulum's weight (bob) is a container of mercury. With a temperature rise, the pendulum rod gets longer, but the mercury also expands and its surface level rises slightly in the container, moving its [[centre of mass]] closer to the pendulum pivot. By using the correct height of mercury in the container these two effects will cancel, leaving the pendulum's centre of mass, and its period, unchanged with temperature. Its main disadvantage was that when the temperature changed, the rod would come to the new temperature quickly but the mass of mercury might take a day or two to reach the new temperature, causing the rate to deviate during that time.<ref name="MatthysCompensation">[https://books.google.com/books?id=Lx0v2dhnZo8C&pg=PA7 Matthys 2004], p.7-12</ref>  To improve thermal accommodation several thin containers were often used, made of metal. Mercury pendulums were the standard used in precision regulator clocks into the 20th century.<ref>Milham 1945, p.335</ref>

==== Gridiron pendulum ====
[[Image:BanjoPendulum.svg|thumb|Diagram of a gridiron pendulum{{ordered list
 | list_style=margin-left:0;
 | item_style=list-style-position:inside;
 | list-style-type=upper-alpha
 | exterior schematic
 | normal temperature
 | higher temperature
}}]]
{{Main|Gridiron pendulum}}
The most widely used compensated pendulum was the [[gridiron pendulum]], invented in 1726 by [[John Harrison]].<ref name="Milham1945" /><ref name="BritannicaCompensation" /><ref name="MatthysCompensation" />  This consists of alternating rods of two different metals, one with lower thermal expansion ([[Coefficient of thermal expansion|CTE]]), [[steel]], and one with higher thermal expansion, [[zinc]] or [[brass]]. The rods are connected by a frame, as shown in the drawing at the right, so that an increase in length of the zinc rods pushes the bob up, shortening the pendulum.  With a temperature increase, the low expansion steel rods make the pendulum longer, while the high expansion zinc rods make it shorter. By making the rods of the correct lengths, the greater expansion of the zinc cancels out the expansion of the steel rods which have a greater combined length, and the pendulum stays the same length with temperature.

Zinc-steel gridiron pendulums are made with 5 rods, but the thermal expansion of brass is closer to steel, so brass-steel gridirons usually require 9 rods. Gridiron pendulums adjust to temperature changes faster than mercury pendulums, but scientists found that friction of the rods sliding in their holes in the frame caused gridiron pendulums to adjust in a series of tiny jumps.<ref name="MatthysCompensation" /> In high precision clocks this caused the clock's rate to change suddenly with each jump. Later it was found that zinc is subject to [[Creep (deformation)|creep]]. For these reasons mercury pendulums were used in the highest precision clocks, but gridirons were used in quality regulator clocks.

Gridiron pendulums became so associated with good quality that, to this day, many ordinary clock pendulums have decorative 'fake' gridirons that don't actually have any temperature compensation function.

==== Invar and fused quartz ====
Around 1900, low thermal expansion materials were developed which could be used as pendulum rods in order to make elaborate temperature compensation unnecessary.<ref name="Milham1945" /><ref name="BritannicaCompensation" /> These were only used in a few of the highest precision clocks before the pendulum became obsolete as a time standard. In 1896 [[Charles Édouard Guillaume]] invented the [[nickel]] [[steel]] [[alloy]] [[Invar]]. This has a [[coefficient of thermal expansion|CTE]] of around {{val|0.9|ul=ppm|up=°C}} ({{val|0.5|u=ppm|up=°F}}), resulting in pendulum temperature errors over {{convert|71|°F|°C °F|order=out}} of only 1.3&nbsp;seconds per day, and this residual error could be compensated to zero with a few centimeters of aluminium under the pendulum bob<ref name="Marrison" /><ref name="MatthysCompensation" /> (this can be seen in the Riefler clock image above). Invar pendulums were first used in 1898 in the [[Riefler escapement|Riefler regulator clock]]<ref>Milham 1945, p.331-332</ref>  which achieved accuracy of 15&nbsp;milliseconds per day. Suspension springs of [[Elinvar]] were used to eliminate temperature variation of the spring's [[restoring force]] on the pendulum. Later [[fused quartz]] was used which had even lower CTE. These materials are the choice for modern high accuracy pendulums.<ref>[https://books.google.com/books?id=Lx0v2dhnZo8C&pg=PA153 Matthys 2004], Part 3, p.153-179</ref>