
A 1900 version of Willem Gravesande's circa 1730 ball and ring experiment and modern version (video). [1]

In experiments, the ball and ring experiment is a volume expansion demonstration experiment in which: (a) a cold (room temperature) brass ball is shown to be able to pass through tightly-fitted brass ring, (b) the ball is then heated with a flame, and (c) the experimenter then shows that the hot steel ball is unable to fit through the ring, as it previous was able to before, in the cold state, thus providing experimental proof that bodies do measurably expand when heated.

A circa 1900 version of the ring and ball experiment, is shown adjacent, wherein, a brass ball with a diameter of 29 mm, at height 260 mm, when heated will not pass through the brass ring, but when cold or ambient temperature will. [1]

History
In circa 1725, Dutch physicist Willem Gravesande, at Leiden University, supposedly, performed the first ball and ring experiment; shown approximately as follows, wherein a brass ball is first shown to go through a metal ring, then is heated, after which it is shown not to be able to go through the ring:

The general picture, however, can be gleamed by the intermediate interactions of French philosopher-physicist Voltaire and Dutch physician and chemist Herman Boerhaave.

In 1726, Voltaire, after being released from the Bastille (jail), on the condition that he go to England, went to London, where he occupied himself mainly with mathematics and made himself familiar with the philosophy of Isaac Newton, of which he made a more special study afterwards at Leyden University. He remained in London for three years, then returned to Paris, made several journeys, and then in 1736 settled in Leyden under the name of “Revol”, which he dropped when he found the pseudonym was useless. In a letter to the crown prince of Prussia (afterwards Frederick the Great), with whom he had entered into an active corresponds with, Voltaire says:

“I am the town of two simple citizens, Boerhaave and Gravesande attract from four to five hundred strangers.”

During this period, Voltaire was very busy writing a work on the philosophy of Newton, and received great assistance from the learned Gravesande and also consulted with Boerhaave. [2]

The generality of this volume expansion experiment, as what seems to have been worked on by both Boerhaave and Gravesande, latter came to be termed, by French chemist Antoine Lavoisier, "Boerhaave's law", being that Boerhaave chemistry lectures, at the University of Leyden, introduced the idea of volume expansion by heat as a general law of nature; the finalized version of which included in his chemistry textbook Elements of Chemistry, and later forming the opening sentence of Lavoisier's 1787 Elements of Chemistry, and the basis of his quest to outline the caloric theory of volume expansion by heat.

References
1. Turner, Gerard L. (1983). Nineteenth-century Scientific Instruments (§Expansion, pgs. 112-). University of California Press.
2. Van Sypesteyn, J.H.R. C.A. (1877). “Voltaire in the Netherlands”, The Living Age (pg. 100), 134: 97-105.