John Farey Sr.

After the death of the duke, Farey in 1802 moved to London, and, after first contemplating emigrating or taking a farm in the country, he settled there as a consulting surveyor and geologist.

[2] That he was enabled to take this step was due largely to his acquaintance with the geologist William Smith, who in 1801 had been employed by the duke of Bedford in works of draining and irrigation.

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.

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.

He devised a notation which allowed a sound to be expressed by the sum of three small values Σ + f + m.[7] He made great use of the researches of Marmaduke Overend (music theorist and organist) (c1730-1790), whose manuscripts were then in the library of the Royal Institution.

[9] 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.