Details

The period of a pendulum is , where is the pendulum length and is the acceleration due to gravity. The thermal expansion of a pendulum made of all iron or brass can lead to minutes of inaccuracy per day. The gridiron pendulum consists of a framework of nine alternating iron and brass rods. These metals have different coefficients of thermal expansion, where and .

The total expansion of the gridiron pendulum is , where is the length of the gridiron portion. The variable can be selected so that the total expansion is always zero.

Reference

[1] The Engineering ToolBox. "Coefficients of Linear Thermal Expansion." www.engineeringtoolbox.com/linear-expansion-coefficients-d_ 95.html.