The Royal Society was founded in 1660, and in April 1661 the society debated a short tract on the rising of water in slender glass pipes, in which Hooke reported that the height water rose was related to the bore of the pipe (due to what is now termed capillary action). His explanation of this phenomenon was subsequently published in Micrography Observ. issue 6, in which he also explored the nature of "the fluidity of gravity". On 5 November 1661, Sir Robert Moray proposed that a Curator be appointed to furnish the society with Experiments, and this was unanimously passed with Hooke being named. His appointment was made on 12 November, with thanks recorded to Dr. Boyle for releasing him to the Society's employment.
In 1664, Sir John Cutler settled an annual gratuity of fifty pounds on the Society for the founding of a Mechanick Lecture, and the Fellows appointed Hooke to this task. On 27 June 1664 he was confirmed to the office, and on 11 January 1665 was named Curator by Office for life with an additional salary of £30 to Cutler's annuity.
Hooke's role at the Royal Society was to demonstrate experiments from his own methods or at the suggestion of members. Among his earliest demonstrations were discussions of the nature of air, the implosion of glass bubbles which had been sealed with comprehensive hot air, and demonstrating that the Pabulum vitae and flammae were one and the same. He also demonstrated that a dog could be kept alive with its thorax opened, provided air was pumped in and out of its lungs, and noting the difference between venous and arterial blood. There were also experiments on the subject of gravity, the falling of objects, the weighing of bodies and measuring of barometric pressure at different heights, and pendulums up to 200 ft long (61 m).
Instruments were devised to measure a second of arc in the movement of the sun or other stars, to measure the strength of gunpowder, and in particular an engine to cut teeth for watches, much finer than could be managed by hand, an invention which was, by Hooke's death, in constant use.
In 1663 and 1664, Hooke produced his microscopical observations, subsequently collated in Micrographia in 1665.
On 20 March 1664, Hooke succeeded Arthur Dacres as Gresham Professor of Geometry. Hooke received the degree of "Doctor of Physic" in December 1691.
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