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John Farey, Sr. (1766 – January 6, 1826) was an English geologist and writer. However, he is better known for a mathematical construct, the Farey series named after him.


He was born at Woburn in Bedfordshire and was educated at Halifax in Yorkshire, and showed such aptitude in mathematics, drawing and surveying, that he was brought under the notice of John Smeaton (1724-1792). After his education he moved to London, where he had relatives, and worked there for a number of years, during which time he met and married his wife, Sophia Hubert, (1770-1830). Whilst in London they had their first child John Farey, Jr. They later had eight more children, two of whom died in infancy.

Woburn and London

In 1792 he was appointed agent to Francis, 5th Duke of Bedford for his Woburn estates. After the decease of the duke, Farey in 1802 removed to London, and, after first contemplating emigrating or taking a farm in the country, he settled there as a consulting surveyor and geologist. That he was enabled to take this step was due largely to his acquaintance with William Smith (geologist), who in 1801 had been employed by the duke of Bedford in works of draining and irrigation. The duke, appreciating Smith's knowledge of the strata, commissioned him in 1802 to explore the margin of the chalk-hills south of Woburn in order to determine the true succession of the strata; and he instructed Farey to accompany him. Farey has remarked that Smith was his Master and Instructor in Mineral Surveying, and his subsequent publications show how well he had profited by the teachings he received.

In 1805, he succeeded Arthur Young as Secretary of the Smithfield Club. His surveying work took him all over the country and he was in much demand from landowners wishing to improve their estates, or exploit the minerals they held. His work on economic geology then was of importance in the burgeoning Industrial Revolution by locating new resources of coal and metal ores.


Farey was a prolific writer, and Professor Hugh Torrens (see references below) has traced around 270 papers by him, quadrupling the number given by the Royal Society's Catalogue of Scientific Papers. He wrote on all manner of subjects, ranging from horticulture, geology, meteorology, metrology, currency decimalisation, music and mathematics to pacifism.

He was an important contributor to Rees's Cyclopaedia with articles on canals, mineralogy, surveying and a number of the scientific and mathematical basis of sound. Various nineteenth century biographical sources, including the Dictionary of National Biography, claimed wrongly he wrote the Rees article on Steam. It was actually written by his son John Farey, Jr.

His most famous work is General View of the Agriculture and Minerals of Derbyshire (3 volumes 1811-17) for the Board of Agriculture. In the first of these volumes (1811) he gave an able account of the upper part of the British series of strata, and a masterly exposition of the Carboniferous and other strata of Derbyshire. In this classic work, and in a paper published in the Philosophical Magazine, vol. 51, 1818, p. 173, on 'Mr Smith's Geological Claims stated', he zealously called attention to the importance of the discoveries of William Smith.

Farey sequence

As well as being remembered by historians of geology, his name is more widely known by the Farey sequence which he noted as a result of his interest in the mathematics of sound (Philosophical Magazine, vol. 47, 1816, pp 385-6).

Farey died in London. Subsequently his widow offered his geological collection to the British Museum, which rejected it, and it was dispersed.


* John Farey, A General View of the Agriculture and Minerals of Derbyshire, Volume 1. With Introduction by Trevor D. Ford and Hugh S. Torrens. (Peak District Mines Historical Society, 1989. Reprint of 1811 Edition). The introduction contains a list of Farey's writings located to the date of the reprint.

* A.P. Woolrich, 'John Farey, Jr. (1791-1851): Engineer and Polymath' in History of Technology, 19, 1997, pp 111-142. (ISBN 0-7201-2365-8) (Includes a brief family history and a family tree)

* Trevor D. Ford; Hugh S. Torrens (2001). "A Farey Story: the pioneer geologist John Farey (1766-1826)". Geology Today 17 (2): 59–68. doi:10.1046/j.1365-2451.2001.00004.x.

* H. S. Torrens, 'Farey, John (1766-1826)', Oxford Dictionary of National Biography Oxford University Press, 2004 [accessed 26 Sept 2004:]

This article incorporates text from the Encyclopædia Britannica, Eleventh Edition, a publication now in the public domain.


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