BENJAMIN, an ingenious mathematician, was born at Bath in 1707. His parents were Quakers of low condition; and consequently were unable to have him much instructed in human learning; but his own propensity to science having procured him a recommendation to Dr Pemberton at London, by his assistance, while he attained the sublimer parts of mathematical knowledge, he commenced teacher of the mathematics. But the business of teaching, which required confinement, not suiting his active disposition, he gradually declined it, and engaged in business that required more exercise. Hence he tried many laborious experiments in gunnery, from the persuasion that the resistance of the air has a much greater influence on swift projectiles than is generally imagined. Hence also he was led to consider the mechanic arts that depend on mathematical principles; as the construction of mills, the building of bridges, the draining of fens, the rendering of rivers navigable, and the making of harbours. Among other arts, fortification much engaged his attention; and he met with opportunities of perfecting himself by viewing the principal strong places of Flanders, in some tours which he made with persons of distinction.

Upon his return from one of these excursions, he found the learning amused with Dr Berkeley's work entitled "The Analyst," in which an attempt was made to explode the method of fluxions. Mr Robins was therefore advised to clear up this subject by giving a distinct account of Sir Isaac Newton's doctrines, in such a manner as to obviate all the objections that had been made, without naming them. Accordingly he published, in 1735, "A Discourse concerning the Nature and Certainty of Sir Isaac Newton's Method of Fluxions;" and, some exceptions being made to his manner of defending Newton, he afterwards wrote two or three additional discourses. In 1738, he defended the same great philosopher against an objection contained in a note at the end of Baxter's Matho, sive Cosmotechnia puerialis; and the following year printed Remarks on Euler's Treatise of Motion, on Dr Smith's System of Optics, and on Dr Jurin's Discourse of distinct and indistinct Vision, annexed to Smith's work. In the mean while, Mr Robins did not solely confine himself to mathematical subjects; for in 1739 he published, without his name, three pamphlets on political affairs. Two of them, relating to the convention and negotiation with Spain, were so highly esteemed as to occasion his being employed in a very honourable post: on a committee being appointed to examine into the past conduct of Sir Robert Walpole, he was chosen their secretary.

In 1742, Mr Robins published a small treatise entitled "New Principles of Gunnery," containing the result of many experiments; and a discourse being published in the Philosophical Transactions, in order to invalidate some of his opinions, he thought proper, in an account which he gave of his book in the same Transactions, to take notice of those experiments. In consequence of this discussion, several of his Dissertations on the Resistance of Air were read, and the experiments exhibited before the Royal Society, for which he was presented by that honourable body with a gold medal.

In 1748 appeared Lord Anson's Voyage round the World, which, though Mr Walter's name is in the title, has been generally thought to be the work of Robins. Walter, chaplain on board the Centurion, had brought it down to his departure from Macao for England, when he proposed to print the work by subscription. It was however, it is said, thought proper that an able judge should review and correct it, and Robins was appointed; when, upon examination, it was resolved that the whole should be written by Robins, and that Walter's papers should only serve as materials. Hence the introduction entire, and many dissertations in the body of the work, it is said, were composed by him, without receiving the least assistance from Walter's manuscript, which chiefly related to the wind and the weather, the currents, courses, bearings, distances, the qualities of the ground on which they anchored, and such particulars as generally fill up a sailor's account. No production of this kind ever met with a more favourable reception: four large impressions were sold within a twelvemonth; and it has been translated into most of the languages of Europe. The fifth edition, printed at London in 1749, was revised and corrected by Robins himself. In the corrigenda and addenda to the first volume of the Biographia Britannica, printed in the beginning of the fourth volume of that work, it is however stated that Robins was only consulted with respect to the disposition of the drawings, and that he had left England before the book was printed. Whether this be the fact, as it is asserted to be by the widow of Mr Walter, it is not for us to determine.

Robins was soon afterwards desired to compose an apology for the unfortunate affair at Prestonpans. It was prefixed as a preface to "The Report of the Proceedings of the Board of General Officers on their Examination into the conduct of Lieutenant-General Sir John Cope;" and this preface was esteemed a masterpiece in its kind. He afterwards, through the interest of Lord Anson, contributed to the improvements made in the Royal Observatory at Greenwich. Having thus established his reputation, he was offered the choice of two considerable employments; either to go to Paris as one of the commissaries for adjusting the limits of Acadia, or to be engineer-general to the East India Company. He chose the latter, and arrived in the East Indies in 1750; but the climate not agreeing with his constitution, he died there the year following.