John James Waterston - Kinetic Theory

Kinetic Theory

While in India, he first developed his kinetic theory, independently of earlier and equally neglected partial accounts by Daniel Bernoulli and John Herapath. He published it, at his own expense, in his book Thoughts on the Mental Functions (1843). He correctly derived all the consequences of the premise that gas pressure is a function of the number of molecules per unit volume, N; molecular mass, M; and molecular mean-squared velocity, . He established the relationship:

.

He had been motivated to think of a wave theory of heat by analogy with the wave theory of light and some experiments by James Forbes and Macedonio Melloni on radiant heat. His statement that ... in mixed media the mean square molecular velocity is inversely proportional to the specific weight of the molecules has been seen as the first statement of the equipartition theorem for translational motion. Waterston grasped that, while the kinetic energy of an individual molecule with velocity v is ½mv², heat energy is proportional to temperature, T. That insight led him to derive the ideal gas law:

.

The publication made little impact, perhaps because of the title. He submitted his theory, under Beaufort's sponsorship, to the Royal Society in 1845 but was rejected. Referee Sir John William Lubbock wrote The paper is nothing but nonsense.

Unable to retrieve a copy of his paper (he had failed to make a copy for himself before submitting the paper to the Royal Society), he rewrote the work and sought to advertise it elsewhere, attracting little attention other than from William John Macquorn Rankine and Hermann von Helmholtz through whom it may have influenced August Krönig. The theory gained acceptance only when it was proposed by Rudolf Clausius and James Clerk Maxwell in the 1850s by which time Waterston's contribution had been forgotten.