by H. S. Torrens
© Oxford University Press 2004 All rights reserved
Farey, John (1766-1826), geologist and surveyor, was born on 24 September 1766 at Woburn, Bedfordshire, on the fourth duke of Bedford's estate, at the farm tenanted by his parents, John Farey (1728-1798) and his second wife, Rachel, née Wright (1732-1804), a Wesleyan Methodist. From the village school Farey went in 1782 to the Halifax Academy where he studied drawing and surveying under Robert Pullman (d. 1789); this 'studious man and good mathematician' gave him 'gratuitous instruction in mathematics and [natural] philosophy' (Monthly Magazine) and recommended him to the engineer John Smeaton.
By 1785 Farey was in London, sketching a new steam engine being erected. His first interests were mathematical. Between 1787 and 1800 he contributed many propositions and answers to the Ladies' Diary, the Gentleman's Diary, Davison's Mathematical and Philosophical Repertory, and Leybourn's Mathematical Repository. On 10 May 1790 he married Sophia Hubert (1770-1830)--possibly from a French family--at St Pancras; their eldest son, John Farey (1791-1851), was born in Lambeth. Both Fareys were singers and musicians, John as tenor and Sophia as soprano, in the Choral Fund, Cecilian Society, Surrey Chapel Society, and in oratorios at Drury Lane. John was also the first secretary and librarian to the Choral Fund, founded in 1791 'for the relief of decayed musicians, their widows and orphans' (Laws ... of the Fund, 1807).
In 1792 Farey was appointed by Francis Russell, fifth duke of Bedford (1765-1802), as agent to his extensive Bedfordshire estates; he returned to his birthplace where he threw himself into the practice and study of agriculture and forestry, and writing reports for the board of agriculture. At the 1798 Woburn sheep-shearing Farey first met his later patron Sir Joseph Banks, president of the Royal Society, and showed him his improvements to the Woburn drainage, first planned by Joseph Elkington (1740-1806). Farey was encouraged by the duke to study drainage methods and in 1797 he visited Derbyshire and the northern counties, and in 1801 toured with drainer William Hart. The geologist William Smith (1769-1839) was also involved in Woburn drainage. Farey and Smith met in October 1801 and went on tour together late in 1801 and again, with engineer Benjamin Bevan (1773-1833), early in 1802 on a 50 mile round trip to investigate local strata. Farey had been actively studying geology before he met Smith but was so impressed by the novelty and importance of Smith's knowledge of stratification, and how fossils could be used to identify some rocks, that he wrote at length to Banks outlining Smith's discoveries in February 1802.
Lord Bedford died on 2 March 1802; his brother, John Russell (1766-1839), would not renew Farey's contract, and dismissed him in June after nearly ten years' service. Farey settled at 12 Crown Street, Westminster, to earn his living as land-surveyor and agent. In 1806 he was appointed paid secretary of the Smithfield Club, and in 1815-26 also held the post of treasurer. Farey was awarded a silver medal by the Society of Arts in 1805 for tree-planting work in Buckinghamshire and he found time to publish again on mathematics (1804-6). From 1805 he contributed to Abraham Rees's (1743-1825) important Cyclopaedia, on 'canals, geology, measures, music and trigonometrical survey' (Philosophical Magazine, 56, 1820, 219). In 1806 he started another long series of publications on music, becoming an enthusiastic advocate of equal temperament tuning, using instruments on which alternative temperaments could be demonstrated. In 1810-11, after a dispute with Rees about his geological contributions, he stopped writing for him (at the end of joint letter I/J); he was replaced on geology by the Wernerian Charles Koenig (1774-1851). Farey's musical work for Rees comprised all the more theoretical and mathematical articles dealing with temperaments, tuning, and harmonics. Farey was soon active, between 1810 and 1819, as contributor to the Edinburgh Encyclopaedia, again largely on music, his interests having arisen directly from his mathematical work.
In 1804 Farey, with Smith, attended the Woburn sheep-shearing at which Banks opened the subscription to support publication of Smith's Delineation of the Strata of England and Wales. By May 1806 Banks was pressing for its completion and Farey threw his energies into encouraging Smith and publicizing and demonstrating the importance of Smith's geological results, particularly in the Monthly and Philosophical magazines, and William Nicholson's Journal. Banks now offered to pay Farey to prepare a stratigraphic cross-section between London and Brighton. Farey's brother conveniently worked in Sussex and by early 1807 this enormous section was finished, and soon copied. It was the first such detailed cross-section to be prepared in England and correctly showed the denuded, anticlinal or 'strata-ridged' structure of the Weald. Farey prepared several other stratigraphic sections across many other parts of England, but all remained unpublished in his lifetime.
1807 brought Farey two new commissions, to Smith's great frustration, in Derbyshire. The first was the county survey for Sir John Sinclair's board of agriculture, which resulted in his best-known work, the remarkably detailed three-volume General View of the Agriculture and Minerals of Derbyshire (1811-17), with his pioneering analysis of the geometry of faulting and an early discussion of English stratigraphy. The other, privately for Banks, was a detailed geological survey of Banks's Overton estate, near Ashover. This was finished by 1812, but plans to publish it in the Transactions of the Geological Society of London were aborted in 1813 when some of its members found it too minute and detailed. Many in this society remained to be persuaded of the reliability and novelty of Smith's and Farey's methods. However, enough fragments of Farey's Ashover survey survive to demonstrate how extraordinarily advanced his geological field mapping then was. Up to 1813 Farey gave inadvertent, but vital, help to the society's work on producing a competitor (published in 1820) to Smith's Geological Map (1815). Farey was subsequently ostracized by the society (of which neither he nor Smith were ever members), despite W. H. Fitton's attempted mediation in 1817-18, and by 1822 Farey was referring to it as 'the Anti-Smithian Association' (Farey to James Sowerby, May 1822, Smithsonian Institution library, Washington, DC).
In September 1806 Farey visited explorations for coal being made at Bexhill, Sussex, by William James (1771-1837) and soon demonstrated their stupidity, and that of the many other searches then being made in impossible stratigraphic situations, pointing out the enormous sums of money which such trials wasted. From 1807 he advertised his services as 'mineralogical surveyor', for, as Banks wrote in 1811, 'we have now some Practical men well versd in stratification who undertake to examine the subterranean Geography of Gentlemens Estates in order to discover the Fossils likely to be useful for Manure, for Fuel etc' (G. De Beer, The Sciences were Never at War, 1960, 191). Farey became the leader in this field and was active all over the British Isles (and apparently France), preparing detailed reports on Yorkshire alum and coal, Edinburgh water, Borrowdale graphite, north Wales slates, and coal throughout Scotland and the Welsh borders. In 1814 he raised his charges from 2 to 3 guineas a day, plus expenses, but he was never able to interest a publisher in these private reports and they too remained in manuscript (and most are now lost).
The end of the Napoleonic Wars had a negative effect on such commissions and by 1824 Farey was reduced to offering himself as copyist to the Sowerbys (at a shilling an hour). Farey had been unjustly marginalized by the ruling élite of English geology from 1810, when his writing for Rees's Cyclopaedia was terminated. Many of his papers had now to be published under a cloak of anonymity as by A Constant Reader, but nevertheless he continued to publish to an extraordinary extent. More than 270 articles are now identified, over an amazing range of other subjects, including astronomy (long another interest), engineering, politics, and pacifism, and from supporting Thomas Malthus (1766-1834) in 1804 to urging that the English currency be decimalized, in 1817.
Farey achieved eponymous fame in mathematics with his 1816 publication on a curious property of vulgar fractions, shortly afterwards named 'Farey' numbers and series. Using the continued fractions methods he had worked out for his musical temperament work, Farey showed the properties of such fractions when arranged in order. The sixth Farey series was for example:
Farey's geological writings illuminate the highly political battles between the gentlemen geologists of the Geological Society and working practitioners such as himself. He felt strongly that the latter had made the more important contribution to unravelling the complexities of British strata; he was one of the first to claim that geological knowledge was of real economic importance in Britain's industrialization, and to demonstrate the truth of this claim. Following a paralytic stroke, Farey died on 6 January 1826 at his home, 37 Howland Street, Fitzroy Square, London, and was buried in St James's Chapel, St Pancras. His wife, who died in July 1830, tried in vain to sell his enormous geological collections to an uninterested British Museum in 1828, but these and his extensive manuscript collections have disappeared. Their eldest son built a reputation as one of the finest consulting engineers in England, while others of Farey's seven surviving children emigrated, to France and America.
H. S. TORRENS
Sources
H. Torrens, The practice of British geology, 1750-1850 (2002)
J. M. Eyles, 'William Smith, Sir Joseph Banks and the French geologists', From Linnaeus to Darwin, ed. A. Wheeler and J. H. Price (1985)
T. D. Ford, 'The first detailed geological sections across England by John Farey, 1806-8', Mercian Geologist, 2 (1967), 41-9
C. D. Waterston, 'John Farey's mineral survey of south-east Sutherland and the age of the Brora coalfield', Annals of Science, 39 (1982), 173-85
J. C. Kassler, The science of music in Britain, 1714-1830, 2 vols. (1979)
M. Bruckheimer and A. Arcavi, 'Farey series, etc.', Mathematical Intelligencer, 17 (1995), 64-7
parish register, Woburn, 12 Oct 1766 [baptism]
Monthly Magazine (April 1826), 430-31
M. Kassler, 'Farey, John', New Grove
J. M. Eyles, 'Farey, John', DSB
W. R. Dearman and S. Turner, 'Models illustrating John Farey's figures of stratified masses', Proceedings of the Geologists' Association, 94 (1983), 97-104
L. R. Cox, 'John Farey', Proceedings of the Yorkshire Geological Society, 25 (1942), 38-43
GM, 1st ser., 74 (1804), 182
Archives
BGS, geological sections
GS Lond., geological sections
Sheff. Arch., geological sections | Derbys. RO
Oxf. U. Mus. NH, corresp. with William Smith
Sutro Library, San Francisco, Joseph Banks MSS
UCL, G. B. Greenough MSS
University of Bristol, Sowerby MSS
Likenesses
W. Watson?, silhouette, 1807, repro. in R. E. R. Banks and others, eds., A global perspective (1994) [see illus.]
Wealth at death
'all his possessions' left to his wife, Sophia: will, PRO, PROB 11/1711
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