Fearon Fallows, son of John Fallows and his wife Rebecca Fearon, was brought up in his father's trade of hand-loom weaving, but with his father's help and encouragement devoted much time to the study of mathematics, for which he showed considerable aptitude. At the age of nineteen he obtained a position as assistant to the headmaster of Plumbland Grammar School and the next year, with the financial support of several persons, entered St John's College, Cambridge, in June 1809. He graduated in January 1813, obtaining the third position in the Tripos (equivalent to the honours examination for the Bachelor of Arts degree in mathematics, but also including astronomy), the first position being achieved by John F.W. Herschel*. Fallows was one of the supporters of a movement to modernise mathematics teaching at Cambridge and bring it more in line with the continental approach. His mathematical prowess led to his appointment as lecturer in mathematics at Corpus Christy College, Cambridge, for the next two years, after which he taught at a school in Hertford, just north of London. Meanwhile he continued his divinity studies until December 1815. He was elected a fellow of St John's College in March 1815, awarded the degree Master of Arts in 1816, ordained as a priest in 1819, and elected a Fellow of the Royal Society of London in 1820. During these years he developed an interest in practical astronomy and built his own small reflecting telescope.
In October 1820 Fallows accepted an appointment as His Majesty's Astronomer at the Cape of Good Hope. Before his departure he spent some time at several observatories to study the use of astronomical instruments. He also compiled tables that would assist him in correcting observed star positions for precession, aberration and nutation. These tables were later published in Volume 1 of W. Pearson's An introduction to practical astronomy (London, 1824). On 1 January 1821 he married Mary Anne Hervey. They arrived at the Cape in August 1821 (on the same ship as Dr Andrew Smith*), accompanied by the astronomical assistant, James Fayrer*. Fallows' task was to select a suitable site and supervise the building of an observatory, equip it with instruments and carry out a programme of observations similar to that at the Royal Greenwich Observatory. Before completion of the observatory he was to catalogue the southern stars with portable instruments. However, he faced many administrative difficulties, delays and a shortage of funds.
Soon after his arrival Fallows erected a temporary observatory in Kloof Street, where he set up a transit instrument of 41 mm aperture, an altitude and azimuth circle to measure declinations, and an astronomical clock. A chance observation on 28 November 1821 led to his first paper submitted from the Cape, "Communication of a curious appearance (luminous spot) lately observed upon the moon" [in a dark region of the moon where similar lights had been observed before], published in the Philosophical Transactions of the Royal Society of London (1822). This was soon followed by "An account of some parhelia [mock suns] seen at the Cape of Good Hope", in the Quarterly Journal of Science, Literature and Arts (1823). Around January 1823 he moved his observatory to the corner of Wandel and Vrede Streets. The two observatory sites were linked by a survey carried out by Mynardus Ruysch*. At these sites Fallows observed and derived the positions of 273 southern stars. The results were published in "A catalogue of nearly all the principal fixed stars between the zenith of Cape Town, Cape of Good Hope, and the South Pole, reduced to the 1st of January 1824", in the Philosophical Transactions... (1824). The same year he published a paper on a method of comparing the times indicated by different chronometers, in the Quarterly Journal of Science. Meanwhile his assistant, James Fayrer, had been replaced in November 1822 by Rev. P.H. Scully*. After the latter's dismissal in October 1824 the post was filled by Captain W. Ronald*, who brought out the instruments for the observatory in 1826.
After thoroughly investigating the area around Cape Town Fallows chose a site for the Royal Observatory near the confluence of the Salt and Liesbeek rivers in March 1822. At the time the site was several kilometers outside Cape Town. After a delay of more than two years the plans for the observatory reached the Cape and building work was started in February 1825. Meanwhile he had made two lengthy journeys in search of suitable building stone. The building was completed in 1828, under the supervision of the clerk of works John Skirrow*, though Fallows himself was also involved in every phase of its construction. He also extended the grounds of the observatory by acquiring two adjacent properties.
The main instruments, a transit circle and a mural circle, supposed to be equal to the best in the world, were installed early in 1829 and the astronomical work of the observatory commenced. The transit circle worked fine, but unfortunately the mural circle turned out to be unreliable, causing Fallows much frustration and limiting the extent of his observations. Years later, on being examined in England, the steel collar of its pivot was found to be loose. A further problem arose when Captain Ronald became ill and left for England in October 1830. Fortunately Fallows was ably assisted by his wife, who furthermore discovered a comet in March 1830. His observations were eventually reduced and published under the superintendence of the Astronomer Royal, Sir George Airy, as "Results of the observations made by the Rev. Fearon Fallows at the Royal Observatory, Cape of Good Hope, in the years 1829-31" (Memoirs of the Royal Astronomical Society, 1849, Vol. 19). The work comprised a catalogue of 425 stars (including 12 double stars) and observations of the moon, planets, and the comet of 1830. Fallows also carried out pendulum observations from November 1828 to January 1829 (with Captain Ronald and Manuel J. Johnson*), and again from December 1829 to January 1830, to determine the acceleration due to gravity at the Cape, with a view to establishing the polar flattening of the earth. These observations were published in the most substantial of his papers, "Observations made with the invariable pendulum (No. 4 Jones) at the Royal Observatory, Cape of Good Hope, for the purpose of determining the compression of the earth" (Philosophical Transactions..., 1830, pp. 153-176). From these observations he derived an ellipticity of 1/288.5 for the earth.
Throughout his stay at the Cape Fallows corresponded regularly with his friend and former fellow student John F.W. Herschel. He was also on friendly terms with John Barrow*, secretary to the Board of Admiralty. In his spare time he read books on natural history and collected bulbs and seeds, which he sent to England in November 1824. He also collected minerals and presented 30 specimens to Dr Andrew Smith*, curator of the newly established South African Museum, in 1825. As an ordained priest he carried out some religious duties and in 1823 served as acting chaplain to the military. He was also a member of the committee set up in May 1824 to build an English church in Cape Town; served on the committee of the South African Public Library (now the Cape Town Campus of the National Library of South Africa) from 1825 to 1828 and thereafter as one of its trustees; and served on the committee of the South African Infirmary Fund. From 1826 to 1829 he was vice-president of the short-lived Cape of Good Hope Horticultural Society, and in June 1829 was elected joint vice-president of the newly founded South African Institution, the first South African society devoted entirely to the advancement of science.
Late in 1830 he suffered a severe attack of scarlet fever from which he never recovered. He was buried in the observatory grounds. His wife left the Cape for England in September 1831.