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law of inverse squares in his ‘Cometa’ (1678), and a letter from him in 1679, containing a sagacious conjecture relative to the paths of projectiles, induced Newton ‘to resume his former thoughts concerning the moon’ (Brewster, Life, i. 287). Hooke's protests, on the presentation of the ‘Principia’ to the Royal Society, that ‘he gave Newton the first hint of this invention,’ evoked the scholium to the fourth proposition of the first book, admitting his anticipation of the law of inverse squares; but Newton's irritation led him to suppress his ‘Optics’ until after Hooke's death. His other inventions included an odometer, an ‘otocousticon’ as an aid to hearing, a sounding-machine, and a reflecting quadrant (Sprat, History of the Royal Society, p. 246). He first asserted the true principle of the arch, and described in 1684 a practicable system of telegraphy. The ‘wheel barometer’ and ‘double barometer,’ the universal joint, the anchor escapement of clocks, originated with him. He constructed an arithmetical machine, and in 1674 the first Gregorian telescope; propounded on 19 March 1675 a remarkable theory of the variation of the compass; recommended for helioscopes the principle of diagonal reflections; anticipated Chladni's method of showing the nodal lines in vibrating surfaces; explained in 1667 the scintillation of the stars by irregular atmospheric refractions; inferred the action of a solar repellent force in producing the tails of comets (Posthumous Works, p. 168); suggested the motion of the sun among the stars (ib. p. 506); and propounded correct notions as to the nature of fossils and the succession of living things upon the globe (ib. pp. 291, 333). Halley described his last invention, a ‘marine barometer,’ to the Royal Society in February 1700 (Phil. Trans. xxii. 791).

Hooke's mind was so prolific that there was scarcely a discovery made in his time which he did not conceive himself entitled to claim. To guard against infringements of his supposed rights, he adopted from 1682 a policy of reserve, designing thenceforward to perfect before suggesting his inventions. In June 1696 an order was granted to him for renewing his experiments at the expense of the Royal Society, but his strength was no longer equal to the task. The death, in 1687, of his niece and housekeeper, Mrs. Grace Hooke, the daughter of his elder brother, a grocer at Newport, permanently affected his spirits, and he suffered from headaches, giddiness, and faintings. A chancery suit with Sir John Cutler about his salary, decided in his favour in 1696, aggravated his ill-health. He was created a doctor of physic at Doctors' Commons by a warrant from Archbishop Tillotson in December 1691; read a ‘curious discourse’ on the tower of Babel before the Royal Society in 1692, and expounded Ovid's ‘Metamorphoses’ in 1693. But his health was broken, and during the last year of his life he was rendered helpless by blindness and swelling of the legs. He died at Gresham College on 3 March 1703, at the age of sixty-seven, and was buried in the church of St. Helen, Bishopsgate Street. Among his many unfulfilled projects was that of a testamentary disposition of his estate for the benefit of natural science.

His biographer, Waller, describes him as ‘in person but despicable, being crooked and low of stature, and as he grew older more and more deformed. He was always very pale and lean, and latterly nothing but skin and bone, with a meagre aspect, his eyes grey and full, with a sharp, ingenious look whilst younger. He wore his own hair of a dark brown colour, very long, and hanging neglected over his face uncut and lank, which about three years before his death he cut off, and wore a periwig. He went stooping and very fast, having but a light body to carry, and a great deal of spirits and activity, especially in his youth. He was of an active, restless, indefatigable genius, even almost to the last, and always slept little to his death, oftenest continuing his studies all night, and taking a short nap in the day. His temper was melancholy, mistrustful, and jealous, which more increased upon him with his years.’ He led ‘a collegiate, almost monastic life,’ latterly rendered sordid by penury, and was in his way religious, though his mind was warped by congenital infirmities of body and temper.

His ‘wonderful sagacity in diving into the most hidden secrets of nature’ was in great measure neutralised by the desultoriness of his inquiries. But his power of forecasting discovery was extraordinary, and he was the greatest mechanic of his age. He professed to have made a ‘century of inventions.’

Hooke's papers were, after his death, placed in the hands of Richard Waller, F.R.S., who edited from them in 1705 a folio volume of ‘Posthumous Works,’ prefixing a life of the author, to a small extent autobiographical. The volume includes: 1. A discourse ‘On the Present Deficiency of Natural Philosophy,’ expounding a ‘Philosophical Algebra’ upon Baconian principles, for the purpose of reducing discovery to a teachable art. 2. A ‘Treatise on Light, including Observations and Speculations on the Comets of 1680 and 1682.’ 3. ‘An Hypothetical Explanation of Memory.’ 4. ‘An Hypothesis of the Cause of Gravity,’ found in a ‘propagated pulse’ of the