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 and finally left it in May 1662. His self-training now began, and it was directed towards astronomy by the opportune loan of Sacrobosco's ‘De Sphærâ’ In the intervals of prostrating illness he also read Fale's ‘Art of Dialling,’ Stirrup's ‘Complete Diallist,’ Gunter's ‘Sector’ and ‘Canon,’ and Oughtred's ‘Canones Sinuum.’ He observed the partial solar eclipse of 12 Sept. 1662, constructed a rude quadrant, and calculated a table of the sun's altitudes, pursuing his studies, as he said himself, ‘under the discouragement of friends, the want of health, and all other instructors except his better genius.’ Medical treatment, meantime, as varied as it was fruitless, was procured for him by his father. In the spring of 1664 he was sent to one Cromwell, ‘cried up for cures by the nonconformist party;’ in 1665 he travelled to Ireland to be ‘stroked’ by Valentine Greatrakes [q. v.] A detailed account of the journey was found among his papers. He left Derby 16 Aug., borrowed a horse in Dublin, which carried him by easy stages to Cappoquin, and was operated upon 11 Sept., ‘but found not his disease to stir.’ His faith in the supernatural gifts of the ‘ stroker,’ however, survived the disappointment, and he tried again at Worcester in the February following, with the same negative result, ‘though several there were cured.’

His talents gradually brought him into notice. Among his patrons was Imanuel Halton of Wingfield Manor, who lent him the ‘ Rudolphine Tables,’ Riccioli's ‘Almagest,’ and other mathematical books. For his friend, William Litchford, Flamsteed wrote, in August 1666, a paper on the construction and use of the quadrant, and in 1667 explained the causes of, and gave the first rules for, the equation of time in a tract, the publication of which in 1673, with Horrocks's ‘Posthumous Works,’ closed controversy on the subject. His first printed observation was of the solar eclipse of 25 Oct. 1668, which afforded him the discovery ‘that the tables differed very much from the heavens.’ Their rectification formed thenceforth the chief object of his labours.

Some calculations of appulses of the moon to fixed stars, which he forwarded to the Royal Society late in 1669 under the signature ‘In Mathesi a sole fundes’ (an anagram of ‘Johannes Flamsteedius’), were inserted in the ‘Philosophical Transactions’ (iv. 1099), and procured him a letter of thanks from Oldenburg and a correspondence during five years with John Collins (1625–1683) [q. v.]

About Easter 1670 he ‘made a voyage to see London; visited Mr. Oldenburg and Mr. Collins, and was by the last carried to see the Tower and Sir Jonas Moore’ (master of the ordnance), ‘who presented me with Mr. Townley's micrometer and undertook to procure me glasses for a telescope to fit it.’

On his return from London he made acquaintance with Newton and Barrow at Cambridge, and entered his name at Jesus College. His systematic observations commenced in October 1671, and ‘by the assistance of Mr. Townley's curious mensurator’ they ‘attained to the preciseness of 5″.’ ‘I had no pendulum movement,’ he adds, ‘to measure time with, they being not common in the country at that time. But I took the heights of the stars for finding the true time of my observations by a wood quadrant about eighteen inches radius fixed to the side of my seven-foot telescope, which I found performed well enough for my purpose.’ This was by necessity limited to such determinations as needed no great accuracy in time, such as of the lunar and planetary diameters, and of the elongations of Jupiter's satellites. He soon discovered that the varying dimensions of the moon contradicted all theories of her motion save that of Horrocks, lately communicated to him by Townley, and its superiority was confirmed by an occultation of the Pleiades on 6 Nov. 1671. He accordingly undertook to render it practically available, fitting it for publication in 1673, at the joint request of Newton and Oldenburg, by the addition of numerical elements and a more detailed explanation (HORROCCII Op. Posth. p. 467). An improved edition of these tables was appended to Flamsteed's ‘Doctrine of the Sphere,’ included in Sir Jonas Moore's ‘New System of the Mathematicks’ (vol. i. 1680).

A ‘monitum’ of a favourable opposition of Mars in September 1672 was presented by him both to the Paris Academy of Sciences and to the Royal Society, and he deduced from his own observations of it at Townley in Lancashire a solar parallax ‘not above 10″, corresponding to a distance of, at most, 21,000 terrestrial radii’ (Phil. Trans. viii. 6100). His tract on the real and apparent diameters of the planets, written in 1673, furnished Newton with the data on the subject, employed in the third book of the ‘Principia;’ yet the oblateness of Jupiter's figure was, strange to say, first pointed out to Flamsteed by Cassini.

At Cambridge on 5 June 1674, he took a degree of M.A. per literas regias, designing to take orders and settle in a small living near Derby, which was in the gift of a friend of his father's. He was in London as a guest of Sir Jonas Moore's at the Tower 13 July to 17 Aug., and by his advice compiled a table of the tides for the king's use; and the