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COLLINS, JOHN (1625–1683), mathematician, was the son of a nonconformist divine, and was born at Wood Eaton in Oxfordshire, 5 March 1625. Apprenticed at the age of sixteen to Thomas Allam, a bookseller, living outside the Turl Gate of Oxford, he was driven to quit the trade by the troubles of the time, and accepted a clerkship in the employment of John Marr, clerk of the kitchen to the Prince of Wales. From him he derived some instruction in mathematics, but the outbreak of civil war drove him to sea for seven years, 1642-9, most of which time he spent on board an English merchantman, engaged by the Venetians as a ship of war in their defence of Candia against the Turks. He devoted his leisure to the study of mathematics and merchants' accounts, and on leaving the service set up in London as a teacher. In 1652 he published 'An Introduction to Merchants' Accounts,' originally drawn up for the use of his scholars. Reprinted in 1665, the major part of the impression perished in the great fire of London, but was replaced in 1674 by a new and amplified folio edition. He next wrote 'The Sector on a Quadrant, or a Treatise containing the Description and Use of three several Quadrants.' Also an appendix touching 'Reflected Dyalling, from a Glass however posited' (London, 1658); and 'The Description and Uses of a general Quadrant, with the Horizontal Projection upon it Inverted ' (1658). In 1659 appeared his 'Geometricall Dyalling, or Dyalling performed by a Line of Chords only,' and 'The Mariner's Plain Scale new Plained,' a useful treatise on navigation, dedicated to 'the governor, deputy, and committee of merchant-adventurers trading to the East India,' and designed especially for use in their navy. It was well received, and became a class-book with the students of navigation at Christ Church Hospital.

After the Restoration, Collins was appointed successively accountant to the excise office, accountant in chancery, and secretary to the council of plantations, exchanging the last post in 1672 for that of manager of the farthing office. With this employment went a 'fair dwelling-house' in Fenchurch Street, where he had thoughts of setting up a stationer's shop, and hoped 'to fall into the printing of books,' including some he himself designed to write, 'particularly one of the modern advancement of mathematical sciences, and an account of the best authors of that kind' (Rigaud, Correspondence of Scientific Men, i. 201). He did not, however, succeed in carrying the plan into effect. With the failure of his arguments against the issue of tin farthings his office ceased, and he was glad subsequently to accept a small post as accountant to the Royal Fishery Company.

He had refused in March 1669 a lucrative situation offered to him in Ireland by the surveyor-general, Sir James Shaen, and about the same time married one of two daughters of William Austen, head cook to Charles II. As his family increased his means of subsistence became more and more precarious. He had a pension of 50l. a year from the excise office, which rapidly fell into arrear; his official salary, and that of his wife as laundress to the queen's table linen, were scantily, if at all, forthcoming, and in order to support his seven children he was obliged to undertake any remunerative tasks that offered, especially in the disentangling of intricate accounts, neglecting the learned correspondence which was his especial delight.

Several of his writings testify to his acquaintance with the course of trade and interest in public matters. He published in 1680 'A Plea for the bringing in of Irish Cattel, and keeping out Fish caught by Foreigners, together with an humble Address to the Honourable Members of Parliament of the counties of Cornwall and Devon, about the Advancement of Tin, Fishery, and divers Manufactures;' and in 1682 a little treatise entitled 'Salt and Fishery,' in which he dwelt upon the several modes of preparing salt in England and abroad, the catching of fish, the salting and cooking of fish and meat, besides offering proposals for the relief of the salt-workers.

Collins died, 10 Nov. 1683, at his lodging on Garlick Hill, London, of asthma and consumption, contracted in July of the previous year during a ride from Oxford to Malmesbury, and was buried in the parish church of St. James. An enlarged edition of his 'Doctrine of Decimal Arithmetick,' the preparation of which had engaged his attention during about a year before his death, appeared in 1685. It had originally been printed in 1664 on a quarter of a sheet for portability in a letter-case. His 'Arithmetic in whole Numbers and Fractions, both Vulgar and Decimal, with Tables for the Forbearance and Rebate of Money,' &c., was published by Thomas Plant in 1688.

Collins was elected a fellow of the Royal Society 24 Oct. 1667, and on 11 Nov. following communicated a useful exposition of a theorem by the learned Jesuit De Billi, entitled 'A Method for finding the Number of the Julian Period for any Year assigned, the Number of the Cycle of the Sun, the Cycle of the Moon, and of the Indictions for the same Year being given, together with the Demonstration of that Method' (Phil. Trans. ii. 568). He contributed further 'An Account concerning the Resolution of Equations in Numbers' (ib. iv. 929), being a narrative of recent algebraical improvements made in England, and 'A Solution of a Chorographical Problem' (ib. vi. 2093); while a letter written to Dr. Wallis, 3 Oct. 1682, 'giving his thoughts about some defects in algebra' (ib. xiv. 575), was imparted to the society 20 May 1684. This was designed as preliminary to a formal treatise on the same subject, the composition of which was anticipated by his death.

For his zeal in collecting and diffusing scientific information, and in urging the accomplishment of appropriate and useful tasks, Collins was not undeservedly styled the 'English Mersennus.' 'He was considered as a kind of register of all new improvements in the mathematics, and was constantly stimulating others to useful inquiries and pointing out the defects in different branches of science, and the methods by which those defects might be supplied' (Biog. Brit.iv.22). His correspondence with eminent mathematicians, both British and foreign, was an important factor in the progress of his time; he spared no expense in procuring new and rare books, and helped forward many important publications. To him was due the printing of Dr. Barrow's 'Optical and Geometrical Lectures,' as well as of his editions of Apollonius and Archimedes; of Kersey's 'Algebra,' Brancker's translation of Rhonius's 'Algebra,' and Wallis's 'History of Algebra.' He took besides an active part in seeing Horrocks's 'Astronomical Remains' through the press.

About twenty-five years after Collins's death his books and papers came into the possession of W. Jones, F.R.S. They included a voluminous correspondence with Newton, Leibnitz, Gregory, Barrow, Flamsteed, Wallis, Slusius, and others, providing a repertory of the utmost value to the history of science. From it was selected and published in 1712, by order of the Royal Society, the 'Commercium Epistolicum,' by which Newton's priority over Leibnitz in the discovery of the infinitesimal calculus was established; the first specimens of results from the use of the fluxional method, transmitted 20 July 1669 through Barrow to Collins, and by him made widely known, affording positive proof of Newton's early possession of it. Collins is described by Wood as 'a person of extraordinary worth, considering his education.' He never learned Greek, nor more of Latin than an ordinary schoolboy; he himself designates his attainments as 'mean,' and his works as 'toys done in ignorance and haste' (Rigaud, Correspondence, ii. 178). Yet his influence was widely felt, and willingly recognised. The exceptional position thus accorded to him was due in part to his disinterested love of science, in part to the sterling qualities and genuine modesty of his character. 'A man' (as Sir Philip Warwick styled him) 'of good arts, and yet greater simplicity; able, but no ways forward,' he found in unobtrusive zeal the secret of effectiveness without pretension, yet even beyond the proportion of his abilities.

[Biog. Brit, ed. Kippis, iv. 20; Wood's Fasti Oxon. (Bliss), ii. 202; Gen. Diet. Hist, and Critical, iv. 405 (1736); Watt's Bibl. Brit.; Rigaud's Correspondence of Scientific Men of the Seventeenth Century; Sherburne's Sphere of M. Manilius, p. 116; Boase and Courtney's Bibl. Cornub. i. 82.]

A. M. C.