Herapath, John

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Herapath, John

(b. Bristol, England, 30 May 1790; d. Lewisham, England, 24 February 1868)

theoretical physics, journalism.

Although Herapath is best known as the first to work out extensive calculations and applications of the kinetic theory of gases, for most of his life he was regarded as an eccentric amateur who had unsuccessfully challenged the scientific establishment and then turned to a more profitable career as editor of a railway magazine. Occasionally given credit for his early work, Herapath did have a slight influence on later scientific developments. But because his theoretical ideas were so uncongenial to his generation, his scientific talents were mostly wasted.

Herapath was the son of a maltster, and a cousin of William Herapath, the chemist for whom the compound herapathite (used by Land in early forms of Polaroid) is named. He was largely self-educated; he learned French and was acquainted with some of the works of the great mathematical physicists of the late eighteenth and early nineteenth centuries. He seems to have absorbed their proclivity toward grand speculations in science which, on the one hand, may have led him to the kinetic theory and, on the other, been an obstacle to its acceptance by his more empirically minded countrymen.

By 1811 Herapath was engaged in researches on the theory of lunar motion. He came to the conclusion that the earth’s action on the moon is greater when the earth is nearer to the sun. Following Newton’s suggestion that gravitational forces might result from differences in density of the ether at various distances from massive bodies, Herapath added the notion that this variation might be connected with changes in temperature, as in the case of ordinary fluids. Thus the force of gravity would depend on temperature. But before working out a detailed application of this hypothesis to the lunar problem, Herapath was diverted by the question, what is temperature—or rather, what is heat?

He first tried to devise his theory on the accepted doctrine that heat is associated with repulsive forces between particles of a fluid, but he ran into difficulties and finally abandoned this position. Instead he concluded, in May 1814, that heat is the result or manifestation of “intestine motion.” He did not claim that this idea was an original discovery; but rather that he had succeeded in giving it a better and more consequential mathematical formulation than any he had previously seen. (Apparently he was not aware of Daniel Bernoulli’s brief excursion in kinetic theory in his Hydrodynamica [1738]. Had he known of this predecessor, his own theory would have been little different but, in advancing it, he might have benefited by Bernoulli’s authority.)

Herapath derived the basic equation relating the pressure (P) and volume (V) of a gas lo the mass (m) and speed (v) of its particles,

assuming that the N particles occupy altogether such a small part of the volume that each one can move freely through space most of the time, occasionally colliding with other particles or with the walls of the container. The gas pressure is thus attributed to impacts of the particles against the walls, rather than to continually acting interparticle repulsive forces, as in the Newtonian theory then generally accepted.

The main difference between Herapath’s theory and that found in modern textbooks is that Herapath stressed the conservation of average momentum (mv) in collisions of particles. He assumed that the quantity of heat contained in a gas is proportional to the total momentum of all its particles, but as in Descartes’s theory, this quantity is not added vectorially. He defined absolute or “true” temperature as the total momentum of a gas divided by the number of particles. Consequently he argued that when two gases or even two liquids at different temperatures are mixed, the temperature of the mixture must be calculated by averaging the “true” temperatures rather than those on the Fahrenheit or Celsius scale. He used this prediction to propose a crucial experiment to distinguish between his theory and the conventional one: If equal portions of water at 32 °F. and 212°F. are mixed, the temperature of the mixture, according to Herapath’s computation, should be 118.4°F., not

Although the existing experimental data were not accurate enough to resolve this point, Herapath claimed that they confirmed his theory.

Having published a preliminary notice of his theory in the Annals of Philosophy in 1816, Herapath submitted a detailed account to the Royal Society in 1820. Davy, who was elected to the presidency of the Society in November of that year, was primarily responsible for the fate of the paper. Although Davy was already known as an advocate of the qualitative idea that heat is molecular motion, he found Herapath’s quantitative development too speculative and complicated; he rejected the hypothesis of an absolute temperature implying an “absolute zero” of cold. Having been told that his paper would not be accepted for publication in the Philosophical Transactions, Herapath withdrew it and published it instead in the Annals of Philosophy in 1821. Five years later he launched an attack on Davy in the Times of London, accusing him of circulating unfounded criticisms of his experimental work, which prevented its publication. Although Davy ignored a series of letters and challenges published in the Times, Herapath later claimed Davy’s resignation from the presidency of the Royal Society (1827) as a victory for himself.

Herapath married in 1815 and gave up his association with his father’s business to start a private school of mathematics to prepare young men for the universities. Apparently this enterprise did not flourish because of his failure to establish a scientific reputation, although it is his only recorded source of income until 1832. His family responsibilities during this period were considerable since by 1837 he had eleven children, ranging in age from one to twenty-two.

In 1829 he took an interest in the promotion of Goldsworthy Gurney’s steam carriages, and while this particular project failed, it encouraged him to study the rapidly expanding railways. He began to write articles on engineering and commercial aspects of the new English railway lines in 1835, and in 1836 he became editor of the Railway Magazine and Annals of Science. This occupation provided financial security—the magazine, later known as Herapath’s Railway and Commercial Journal, was quite successful—and it gave him an opportunity to publish his own papers on scientific subjects. In addition to these advantages, it would appear from Herapath’s numerous writings that this new career provided ample personal satisfaction. As the scientist-turned-journalist, engineer, and operations-researcher, Herapath threw himself wholeheartedly into the excitement and controversies of England’s railway boom of the 1840’s.

One of the first scientific papers which Herapath published in his Railway Magazine was a calculation of the velocity of sound in air, which he had announced at a meeting of the British Association for the Advancement of Science in 1832. This is the first known calculation of the speed of a molecule from the kinetic theory of gases. Joule, usually credited with this accomplishment, undoubtedly based his own calculation on Herapath’s, who had published his computation in book III of his major work Mathematical Physics (London, 1847). Herapath’s application of the theory of molecular speeds to the wind resistance encountered by a fast railway locomotive (1836) is also an interesting example of the explicit use of scientific principles in engineering.

Maxwell, recognizing Herapath as a precursor of his own research in kinetic theory, gave the following assessment of Herapath’s work:

His theory of the collisions of perfectly hard bodies, such as he supposed the molecules to be, is faulty.... This author, however, has applied his theory to the numerical results of experiment in many cases, and his speculations are always ingenious, and often throw much real light on the questions treated. In particular, the theory of the temperature and pressure and gases and the theory of diffusion are clearly pointed out (“On the Dynamical Theory of Gases,” in The Scientific Papers of James Clerk Maxwell, II [Cambridge, 1890], 28).

While the refusal of the Royal Society to publish Herapath’s paper can hardly be defended, neither can it be argued that this refusal obstructed the progress of science to any significant extent. Herapath did manage to present his theory to a scientific community that no longer accepted the Royal Society as final arbiter. His theory simply did not provide an attractive explanation of the physical phenomena of gases and heat, which, like the phenomena of radiant heat, were then considered most important.


Herapath’s major work is reprinted in Mathematical Physics (Two Volumes in One) and Selected Papers by John Herapath (New York, in press), with intro. by the editor, Stephen G. Brush. This reprint includes the early paper, “A Mathematical Inquiry Into the Causes, Laws, and Principal Phaenomena of Heat, Gases, Gravitation, & c,” which was published in the Annals of Philosophy, 2nd ser., 1 (1821), 273–293, 340–351, 401–416; one of his articles on railways; and a bibliography of all known works by or about Herapath.

Stephen G. Brush