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Publications and inventions

In 1676, Flamsteed helped Halley publish his first paper, titled "A Direct and Geometrical Method of Finding the Aphelia, Eccentricities, and Proportions of the Primary Planets, Without Supposing Equality in Angular Motion", about planetary orbits, in Philosophical Transactions of the Royal Society. Influenced by Flamsteed's project to compile a catalogue of stars of the northern celestial hemisphere, Halley proposed to do the same for the southern sky, dropping out of school to do so. He chose the south Atlantic island of Saint Helena (west of Africa), from which he would be able to observe not only the southern stars, but also some of the northern stars with which to cross-reference them. King Charles II supported his endeavour. Halley sailed to the island in late 1676, then set up an observatory with a large sextant with telescopic sights. Over a year, he made observations with which he would produce the first telescopic catalogue of the southern sky, and observed a transit of Mercury across the Sun. Focusing on this latter observation, Halley realised that observing the solar parallax of a planet—more ideally using the transit of Venus, which would not occur within his lifetime—could be used to trigonometrically determine the distances between Earth, Venus, and the Sun.

Halley returned to England in May 1678, and used his data to produce a map of the southern stars. Oxford would not allow Halley to return because he had violated his residency requirements when he left for Saint Helena. He appealed to Charles II, who signed a letter requesting that Halley be unconditionally awarded his Master of Arts degree, which the college granted on 3 December 1678. Just a few days before, Halley had been elected as a fellow of the Royal Society, at the age of 22. In 1679, he published Catalogus Stellarum Australium ('A catalogue of the stars of the South'), which includes his map and descriptions of 341 stars. Robert Hooke presented the catalogue to the Royal Society. In mid-1679, Halley went to Danzig (Gdańsk) on behalf of the Society to help resolve a dispute: because astronomer Johannes Hevelius ' observing instruments were not equipped with telescopic sights, Flamsteed and Hooke had questioned the accuracy of his observations; Halley stayed with Hevelius and checked his observations, finding that they were quite precise.

By 1681, Giovanni Domenico Cassini had told Halley of his theory that comets were objects in orbit. In September 1682, Halley carried out a series of observations of what became known as Halley's Comet; his name became associated with it because of his work on its orbit and predicting its return in 1758 (which he did not live to see). In early 1686, Halley was elected to the Royal Society's new position of secretary, requiring him to give up his fellowship and manage correspondence and meetings, as well as edit the Philosophical Transactions. Also in 1686, Halley published the second part of the results from his Helenian expedition, being a paper and chart on trade winds and monsoons. The symbols he used to represent trailing winds still exist in most modern day weather chart representations. In this article he identified solar heating as the cause of atmospheric motions. He also established the relationship between barometric pressure and height above sea level. His charts were an important contribution to the emerging field of information visualisation.

Halley spent most of his time on lunar observations, but was also interested in the problems of gravity. One problem that attracted his attention was the proof of Kepler's laws of planetary motion. In August 1684, he went to Cambridge to discuss this with Isaac Newton, much as John Flamsteed had done four years earlier, only to find that Newton had solved the problem, at the instigation of Flamsteed with regard to the orbit of comet Kirch, without publishing the solution. Halley asked to see the calculations and was told by Newton that he could not find them, but promised to redo them and send them on later, which he eventually did, in a short treatise titled On the motion of bodies in an orbit. Halley recognised the importance of the work and returned to Cambridge to arrange its publication with Newton, who instead went on to expand it into his Philosophiæ Naturalis Principia Mathematica published at Halley's expense in 1687. Halley's first calculations with comets were thereby for the orbit of comet Kirch, based on Flamsteed's observations in 1680–1681. Although he was to accurately calculate the orbit of the comet of 1682, he was inaccurate in his calculations of the orbit of comet Kirch. They indicated a periodicity of 575 years, thus appearing in the years 531 and 1106, and presumably heralding the death of Julius Caesar in a like fashion in 45 BC. It is now known to have an orbital period of circa 10,000 years.

In 1691, Halley built a diving bell, a device in which the atmosphere was replenished by way of weighted barrels of air sent down from the surface. In a demonstration, Halley and five companions dived to 60 feet (18 m) in the River Thames, and remained there for over an hour and a half. Halley's bell was of little use for practical salvage work, as it was very heavy, but he made improvements to it over time, later extending his underwater exposure time to over 4 hours. Halley suffered one of the earliest recorded cases of middle ear barotrauma. That same year, at a meeting of the Royal Society, Halley introduced a rudimentary working model of a magnetic compass using a liquid-filled housing to damp the swing and wobble of the magnetised needle.

In 1691, Halley sought the post of Savilian Professor of Astronomy at Oxford. While a candidate for the position, Halley faced the animosity of the Astronomer Royal, John Flamsteed, and the Anglican Church questioned his religious views, largely on the grounds that he had doubted the Earth's age as given in the Bible. After Flamsteed wrote to Newton to rally support against Halley, Newton wrote back in hopes of reconciliation, but was unsuccessful. Halley's candidacy was opposed by both the Archbishop of Canterbury, John Tillotson, and Bishop Stillingfleet, and the post went instead to David Gregory, who had Newton's support.

In 1692, Halley put forth the idea of a hollow Earth consisting of a shell about 500 miles (800 km) thick, two inner concentric shells and an innermost core. He suggested that atmospheres separated these shells, and that each shell had its own magnetic poles, with each sphere rotating at a different speed. Halley proposed this scheme to explain anomalous compass readings. He envisaged each inner region as having an atmosphere and being luminous (and possibly inhabited), and speculated that escaping gas caused the aurora borealis. He suggested, "Auroral rays are due to particles, which are affected by the magnetic field, the rays parallel to Earth's magnetic field."

In 1693 Halley published an article on life annuities, which featured an analysis of age-at-death on the basis of the Breslau statistics Caspar Neumann had been able to provide. This article allowed the British government to sell life annuities at an appropriate price based on the age of the purchaser. Halley's work strongly influenced the development of actuarial science. The construction of the life-table for Breslau, which followed more primitive work by John Graunt, is now seen as a major event in the history of demography.

The Royal Society censured Halley for suggesting in 1694 that the story of Noah's flood might be an account of a cometary impact. A similar theory was independently suggested three centuries later, but is generally rejected by geologists.

In 1696, Newton was appointed as warden of the Royal Mint and nominated Halley as deputy comptroller of the Chester mint. Halley spent two years supervising coin production. While there, he caught two clerks pilfering precious metals. He and the local warden spoke out about the scheme, unaware that the local master of the mint was profiting from it.

In 1698, the Czar of Russia (later known as Peter the Great) was on a visit to England, and hoped Newton would be available to entertain him. Newton sent Halley in his place. He and the Czar bonded over science and brandy. According to one disputed account, when both of them were drunk one night, Halley jovially pushed the Czar around Deptford in a wheelbarrow.