The period of the pendulum depends on its length, but the length of a metal pendulum rod changes with the temperature; as the temperature goes up, the length increases and the clock controlled by the pendulum runs slow. In 1715 the Englishman George Graham attached a mercury column to the lower end of the pendulum rod. When the temperature went up, the length of the mercury column increased, keeping the center of mass of the system the same distance from the pivot point.
REF: Thomas B. Greenslade, Jr., "Nineteenth Century Textbook Illustrations XIX: Clock Pendulums, Phys. Teach., 15, 546-7 (1977)
In 1725 the Englishman John Harrison invented the gridiron pendulum, another solution to the temperature compensation problem. Brass and iron rods, with different temperature coefficients of expansion, were fastened alternately top and bottom in a gridiron pattern to keep the center of mass at the same point.
The gridiron pendulum at the left is at Amherst College, and is post-1875.
This example is in the collection of the Smithsonian Institution.
At the right is a model of a compensated pendulum in the Garland Collection of Classical Physics Apparatus at Vanderbilt University. It was probably purchased about 1875, and was purchased from Deleuil of Paris. In the 1865 Deleuil catalogue the cost was 30 francs. The overall length was
| This multiple pendulum set at the Smithsonian is
from Colgate University in Hamilton, New York. When I discovered it in
the nineteen seventies, I was intrigued by the fact that the moment of
inertia and the location of the center of mass could be obtained by an
integration. With this information, the period of each physical pendulum
could be calculated. One of my students built a replica, and two decades
of Kenyon students have done the integrations and measured the periods of
each geometrical shape.
REF: Thomas B. Greenslade, Jr., "Reconstructed Nineteenth Century Experiment with Physical Pendula". American Journal of Physics, 48, 487-8 (1980)
Of course, the pendulum is not truly isochronous. To a first approximation, the increase in the period is proportional to the square of the amplitude. This is a nasty calculation, and undergraduate students have to be led carefully through the derivation.
About 1665 the Dutch physicist, Christiaan Huygens (1629-1695), showed that a pendulum hung from a flexible support would have a period independent of amplitude if the system were allowed to swing up against guides in the shape of a cycloid.
As far as I know, no modern apparatus manufacturer has a cycloidal pendulum in the catalogue. In the nineteenth century the situation was different. At the left below is a cycloidal pendulum in the Smithsonian collection. On the right is a cycloidal pendulum from Amherst College. It was made by E. Ducretet & Cie of Paris, and cost 50 francs in the 1879 catalogue. This is very close to the time when this apparatus was purchased by Amherst to replace that lost in the fire that destroyed the original apparatus in the early eighteen eighties.
| This cycloidal pendulum stand was made in 1836 by
John Millington (1779-1868) when he was teaching at William and Mary College
in Williamsburg, Virginia.
Millington, who was born in England and spent fifteen years as a lecturer at the Royal Institution, was the first Professor of Natural Sciences at the new University of Mississippi from 1848 to 1853. He brought a large collection of apparatus of his own manufacture with him to Mississippi, and it forms the basis for the collection of apparatus in the University Museum in Oxford. Other apparatus was ordered, mainly from France, by his successor, Frederick Barnard (1809-1889) who was the president of Columbia University after the War Between the States.
The Max Kohl catalogues of the second half of the 1920s had clock pendulumns of increasing degrees of sophistication. The basic device was the "seconds pendulum with audible beat, with dial and projecting pointer, on iron stand with levelling screws". A little more money got you a mercury contact at the bottom of the pendulum that provided an electrical signal every time the pendulum passed through dead center. The next step up was a compensating pendulum with five brass and four steel rods. All of the pendula had an effective length of about one meter, giving a two-second period.
This example is in the physics department of Hobart and William Smith Colleges in Geneva, New York.
At one time the Kenyon College physics department had a master clock with a pendulum that sent out electrical time signals to many of the rooms used by physics.
The 1928 catalogue of Max Kohl of Chemnitz, Germany identifies this apparatus as Overbeck's Cross Pendulum. It cost 23 DM.
The positions of the sliders can be adjusted to give various moments of inertia and centers of mass for experiments with the period of the pendulum.