|Engraving of James Joule's 1843 paddle wheel experiment for measuring the mechanical equivalent of heat. |
On 24 Jun 1845, Joule had the following read before the Chemical Section of the British Association for the Advancement of Science in Cambridge: 
“The author gave the results of some experiments, in order to confirm the views he had already derived from experiments on the heat evolved by magneto-electricity, and from experiments on the changes of temperature produced by the condensation and rarefaction of elastic fluids. He exhibited to the section an apparatus consisting of a can of peculiar construction filled with water. A sort of paddle-wheel was placed in the can, to which motion could be communicated by means of weights thrown over two pulleys working in contrary directions. He stated that the force spent in revolving the paddle-wheel produced a certain increment in the temperature of the water; and hence he drew the conclusion that when the temperature of a pound of water is increased by one degree of Fahrenheit’s scale, an amount of vis viva is communicated to it equal to that acquired by a weight of 890 pounds after falling from the altitude of one foot.”
The following shows Joule’s original paddle wheel experimental devices, held at the Science Museum, London. 
|A screenshot of a 2013 video documentary (Ѻ) showing a re-construction of the original experiment and measurements.|
In 1989, historian Donald Cardwell summarizes the behind the scene details of this famous abstracted presentation as follows: 
“On Thursday 24 June, Joule read his paper on the new theory of heat. It was late in the day and, to save time, the Chairman asked him to confine himself to a brief summary of the principal points of his paper. He exhibited and explained his paddle-wheel apparatus. Experiments using water and sperm oil gave, he claimed, 781.5 and 782.1 foot-pounds respectively for the mechanical equivalent of heat. He had also made some experiments on the compression of steel springs. No heat, he found, was generated; all the living force used to compress the springs had been convened into attraction through space. It was, he believed, analogous to latent heat. These static experiments were not, Mendoza has pointed out, actually included in his brief summary and they were omitted from his subsequent paper in the Philosophical Magazine. They had to be published later.”
The results of this experiment were described in his famous 1845 paper "On the Mechanical Equivalent of Heat", in which Joule determined a value A for the amount of work W required to produce a unit of heat Q. The following, supposedly, is sketch of the 1847 model used by Joule to measure the mechanical equivalent of heat: (Ѻ)
The "Joule" as the unit if energy is now named in his honor.
1. Joule, James P. (1845). "On the Mechanical Equivalent of Heat", Brit. Assoc. Rep., trans. Chemical Sect, p.31, read before the British Association at Cambridge, June.
2. Author. (1869). “Article”, Harper's New Monthly Magazine (pg. #), No. 231, August.
3. Young, John. (2015). “Heat, Work, and Subtle Fluids: a Commentary on Joule (1850) ‘On the Mechanical Equivalent of Heat’” (Ѻ), Philosophical Transactions A, 373(2039), Apr.
4. (a) Joule, James. (1845). “On the Mechanical Equivalent of Heat”, Transactions of the Chemical Section (pg. 31), British Association for the Advancement of Science, Cambridge, Jun.
(b) Joule, James. (1884). The Scientific Papers of James Prescott Joule, Volume One (pg. 202). Publisher.
5. Cardwell, Donald S.L. (1989). James Joule: a Biography (pgs. 82-83). Manchester University Press.