John Farey, Sr.

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John Farey in Derby Museum. The silhouette is by his friend White Watson whilst the QR Code takes you to this article

John Farey, Sr. (1766 – January 6, 1826) was an English geologist and writer. However, he is better known for a mathematical construct, the Farey sequence 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[edit]

In 1792 he was appointed agent to Francis Russell, 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, 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 Cyclopædia 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. In 1809 Farey met William Martin who had published work on Derbyshire fossils, to investigate whether they could create a joint geological map of Derbyshire. Martin however was too ill to meet a second time and he died the following year.[1]

Farey's 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[edit]

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.


  1. ^ Torrens, H. S. (2004). "Martin, William (1767–1810)". The Oxford Dictionary of National Biography (Oxford University Press). doi:10.1093/ref:odnb/18216. 101018216.  edit

Wikisource This article incorporates text from a publication now in the public domainChisholm, Hugh, ed. (1911). "Farey, John". Encyclopædia Britannica (11th ed.). Cambridge University Press.