William Wales, British astronomer and mathematician, married Mary Green on 5 September 1765. The next year the Astronomer Royal, Nevil Maskelyne, commissioned him to assist in the computations required for the first issue of the Nautical Almanac. By this time he was a competent mathematician. In 1768 he was chosen to lead one of the two expeditions organised by the Royal Society of London to observe the transit of Venus on 3 June 1769. He and Maskelyne's assistant, Joseph Dymond, sailed for Canada in June 1768 and set up their temporary observatory and a hut to live in at Fort Prince of Wales, on the western shore of Hudson Bay (now the town Churchill, Manitoba). There they overwintered, observed the transit successfully during the next summer, and returned to England in October 1769. An account of their observations was published in the Philosophical Transactions of the Royal Society.
In 1772 Wales and William Bayly* were engaged by the Board of Longitude to accompany Captain James Cook on his second voyage around the world and make astronomical observations for purposes of navigation and mapping. Wales, as the principal astronomer, travelled on the Resolution with Cook, while Bayly was stationed on the Adventure. The expedition circumnavigated the world and among others reached the ice along the shores of Antarctica. Wales made daily observations of the ship's latitude, observed lunar and solar eclipses, measured the extent of partial solar eclipses by a new method using a Hadlies quadrant, determined the longitudes of islands and other features by the method of lunar distances, made and used a tide guage in several places, made and used a simple clinometer to measure the disputed extent of the ship's rolling motion, and recorded some meteorological observations. He drew 22 charts, which are kept at the Royal Greenwich Observatory. On their way from England to New Zealand the expedition visited the Cape of Good Hope from 30 October to 23 November 1772. Wales and Bayly went ashore to test and calibrate their chronometers and check the longitude of the Cape. On the return journey they again visited the Cape from 21 March to 21 April 1775. They occupied the site in Concordia Gardens (behind the present Roman Catholic cathedral in Cape Town) where C. Mason* and J. Dixon* had observed the transit of Venus in 1761. A traverse was performed to link this site to the house in Strand Street where N. De la Caille* had established his temporary observatory in 1751.
Upon his return to England in 1775 Wales became master of the Royal Mathematical School within Christ's Hospital, London, where cadet ship's officers were taught navigation. He held this post to his death. In 1776 he was elected a Fellow of the Royal Society of London. He edited the observations made by himself and Bayly during the expedition and published them in 1777 as The original astronomical observations made in the course of a voyage towards the South Pole and round the world, in his Majesty's ships the Resolution and Adventure in the years 1772, 1773, 1774, and 1775, with Bayly as the second author. He also published Astronomical observations on a voyage with Captain Cook (1777) and Remarks on Mr Forster's account of Captain Cook's last voyage round the world, in the years 1772-1775 (1778). The latter was a pamphlet written in reply to the naturalist Johann G.A. Forster*, who had published an unauthorised account of the voyage a few weeks before Cook's own narrative appeared, in which he made some allegations against Cook and his officers which Wales wished to refute.
Both Wales and Bayly accompanied Captain Cook on his third expedition, from 1776 to 1780, during which Wales again sailed with Cook in the Resolution. The expedition visited the Cape from 8 October to 30 November 1776 and on the return journey anchored in Simon's Bay from 11 April to 9 May 1780.
In December 1795 Wales was appointed secretary to the Board of Longitude and held this position also to his death in 1798. In 1788 he published Astronomical observations made during the voyages of Byron, Wallis, Carteret, and Cook for making discoveries in the Southern Hemisphere. This work was based on the journals kept by the commanders during 1764-1771, but was mainly a critical analysis of the observations made by Cook and the astronomers Charles Green and Clerke during Cook's first voyage around the world. Charles Green was a brother of Wales's wife. Wales's other publications included The method of finding the longitude at sea, by time-keepers (1794, with subsequent editions to 1823); An inquiry into the present state of population in England and Wales... (1781); Tables requisite to be used with the Nautical Ephemeris (with Maskelyne, 1781, 1802); and a new edition of John Roberton's Elements of Navigation (1780, 1796).