Robins, Benjamin

(1707-1751), mathematician and military engineer

by Brett D. Steele

© Oxford University Press 2004 All rights reserved

Robins, Benjamin (1707-1751), mathematician and military engineer, was born in Bath, the only son of John Robins (1666-1758), a tailor, and his wife, Sarah Broughton, Quakers of modest means. Although largely self-taught, Robins soon demonstrated his talents for literature, language, and mathematics, especially Euclidean geometry. To acquire respectable teaching credentials Robins studied under Dr Henry Pemberton in London. A prominent Newtonian who edited the third edition of the Principia, he directed Robins's study in both ancient and contemporary mathematics. Robins was elected a fellow of the Royal Society in 1727. He published his demonstration of the final proposition of Newton's treatise on quadratures in the society's Philosophical Transactions (1727) and his refutation of Johann Bernoulli's theory of elastic collisions in The Present State of the Republic of Letters in 1728. Such early success initiated a lifelong taste for polemics. With a reputation as a rigorous defender of Newton's geometrical approach to the calculus, he secured employment as a mathematics tutor to prospective Cambridge students.

Robins also conformed to Baconian ideals by applying Newtonian reasoning to engineering domains. By the early 1730s he was investigating bridges, harbours, mills, and navigable rivers, with the encouragement of William Ockenden. Fortifications and artillery emerged as his central engineering concern, however, after he had rejected his Quaker heritage. While touring northern France and the Netherlands he became influenced especially by the fortress designs of Menno van Coehoorn, the famous seventeenth-century Dutch military engineer. The publication of Bishop George Berkeley's Analyst (1734), a critique of the ontological and logical inconsistencies of Newton's calculus, brought Robins's attention back to basic mathematics. In a lengthy debate with his fellow Newtonian James Jurin, Robins argued for ridding the calculus of all infinitesimal terms, relying on Newton's prime and ultimate ratios instead. To avoid Berkeley's objections, he grounded this technique on the Archimedian method of exhaustion in A discourse concerning the nature and certainty of Sir Isaac Newton's principles of fluxions, and of prime and ultimate ratios (1735). Robins's success is indicated by the similar approach of Colin Maclaurin in Treatise of Fluxions (1742), the most authoritative calculus text in eighteenth-century Britain. Robins continued his polemical dispute with Jurin in Remarks on M. Euler's Treatise of motion; on the Compleat system of optics written by Dr. Smith, master of Trinity College, Cambridge; and on Dr. Jurin's Discourse of distinct and indistinct vision (1739). He also exposed the logical inconsistencies of Euler's Mechanica, sive, Motus scientia analytice exposita (1736), the pioneering treatise of analytical mechanics.

Robins's polemics extended to parliamentary issues. He published three pamphlets that severely criticized the administration of Walpole, especially over its relations with Spain: Observations on the Present Convention with Spain, A narrative of what passed in the common hall of the citizens of London assembled for the election of a lord mayor, and An address to the electors and other free subjects of Great Britain occasioned by the late secession; in which is contained a particular account of all our negociations with Spain and their treatment of us for above ten years past. Such works helped pressure Walpole into declaring war on Spain in 1739. It also secured tory patronage for Robins after that prime minister's fall from power in 1741. He served as a secretary for a secret committee investigating Walpole's prior conduct. Robins's zeal in that position proved to be a liability, however, when his application to teach at the new Royal Military Academy at Woolwich failed. He published New Principles of Gunnery (1742), based on course material he prepared unsuccessfully for the application.

New Principles of Gunnery transformed ballistics into a Newtonian science. Galileo's vacuum theory was the only practical theory before 1742, but only for low-velocity mortars as demonstrated in Bélidor's Le bombardier français (1731). Robins made it applicable for gunpowder weaponry in general. His key contribution was the invention and utilization of the ballistic pendulum. With Huygens's law of pendulum motion and Newton's law of linear momentum, he deduced the bullet's impact velocity from the subsequent swing angle. Robins then used the ballistic pendulum to verify his interior-ballistics theory, relying on Boyle's law, the thirty-ninth proposition from book one of the Principia, and the pneumatic chemistry techniques of Francis Hauksbee the elder and Stephen Hales. By applying Newton's second law of motion to velocity measurements at varying ranges, Robins also obtained the air-resistance force acting on musket balls. This revealed the significant limitations of Galileo's vacuum ballistics theory and of Newton's air-resistance function when approaching the speed of sound.

Robins furnished the necessary experimental data for the numerical analysis of high-speed trajectories required for the computation of artillery range tables. He conducted such analysis in Of the resistance of the air; together with the method of computing the motions of bodies projected in that medium (1746). He provided a convenient gunnery table, and demonstrated its utility with heavy-artillery data. Robins also investigated low-speed air resistance with the whirling arm, another fundamental aerodynamic research innovation, as described in An account of experiments relating to the resistance of the air, exhibited at different times before the Royal Society, in the year 1746 (1747). In addition to spheres, he investigated the resistance of pyramids and inclined planes to further demonstrate the limitations of Newton's fluid mechanics theories. Robins described range tests, as well, where he related the lateral deflection of musket balls to the direction of their angular velocity, a phenomenon now known as the Magnus effect. Robins employed such research to address practical artillery issues. In Of the force of fired gunpowder, together with the computation of the velocities thereby communicated to military projectiles (1747) he criticized military research efforts to optimize gunpowder charges and barrel lengths to maximize the projectile's muzzle velocity. Instead, artillerists should set the barrel length and charge weight to provide the minimum muzzle velocity to destroy only the target in question. In A Proposal for Increasing the Strength of the British Navy (1747) Robins proposed a new naval gun design based on these considerations. His arguments helped inspire the invention of the carronade in 1778. In Of the Nature and Advantage of Rifled Barrel Pieces (1747) he argued for the ballistic merits of rifled over smooth-bore projectiles in terms of air resistance. Robins summarized his gunnery reform proposals in Practical maxims relating to the effects and management of artillery, and the flight of shells and shot. In recognition of his new science of ballistics, the Royal Society awarded him the Copley medal in 1747.

Robins's artillery reform agenda reflected the patronage of Lord George Anson, following the latter's lucrative circumnavigation of the world. Robins earned £1000 for writing Anson's highly acclaimed A Voyage Round the World, though formal credit went to Richard Walter, the chaplain of the voyage who initiated the project. Likewise, Robins received material aid from Anson for ballistic investigations of heavy ordnance. Robins briefly served as a military engineer for the Dutch during the final phase of the siege of Bergen op Zoom in 1747. Another indication of his growing military as well as literary reputation was his employment to write a defence of Sir John Cope's military leadership at Prestonpans. His final appointment was as engineer general for the British East India Company in 1749. Upon arriving in India, Robins began designing new fortifications for Fort St David at Cuddalore, and Fort St George in Madras. He died, unmarried, a year later on 29 July 1751, at Fort St David, of a fever, presumably malaria. In accordance with Quaker custom, he received a simple burial and never had his likeness made.

The influence of Robins's research and reform proposals was pervasive. Leonhard Euler translated New Principles of Gunnery into German in 1745, and added an extensive commentary and mathematical analysis. Patrick D'Arcy verified Robins's experimental results in France during the late 1740s, and Le Roy translated New Principles of Gunnery for the Paris Académie des Sciences in 1751. Robins directly affected Piedmontese artillery investigations during the mid-1740s, and appears to have helped inspire the Liechtenstein artillery reforms of Austria. Prince Josef Wenzel zu Liechtenstein furnished the first heavy yet mobile field-artillery system. His protégé Gribeauval also employed Robins's arguments during his subsequent artillery reform efforts in France. Dupuy published another French translation of New Principles of Gunnery in 1771; Lombard followed suit with Euler's analysis and commentaries in 1783. The Royal Artillery and Engineering Academy of Piedmont-Savoy began formally teaching Robins's ballistics theories during the 1760s. This trend was followed by its counterparts in France and England during the 1770s, and in Austria and Prussia during the 1780s and 1790s, respectively. An experimental fluid mechanics tradition grew from Robins's work, as indicated by the ballistics studies of D'Arcy, Papacino D'Antoni, Charles Hutton, and Benjamin Thompson; the hydraulics studies of Charles de Borda; and the aerodynamics studies of John Smeaton and George Cayley. Robins's substantial accomplishments in mathematical theory, scientific discovery, technical practice, and literary production place him at the forefront of the British Enlightenment. As a British artillery officer wrote in 1789, Robins 'was in gunnery what the immortal Newton was in philosophy, the founder of a new system deduced from experiment and nature' (A. V. P. d'Antoni, A Treatise on Gunpowder, a Treatise on Fire-Arms, and a Treatise on the Service of Artillery in the Time of War, trans. Captain Thomson, 1789, xvii).

BRETT D. STEELE

Sources  
Mathematical tracts of the late Benjamin Robins, ed. J. Wilson, 2 vols. (1761)
B. D. Steele, 'The ballistics revolution: military and scientific change from Robins to Napoléon', PhD diss., University of Minnesota, 1994
B. D. Steele, 'Muskets and pendulums: Benjamin Robins, Leonhard Euler, and the ballistics revolution', Technology and Culture, 35 (1994), 348-82
W. Johnson, Collected works on Benjamin Robins and Charles Hutton (2002)
H. M. Barkla, 'Benjamin Robins and the resistance of air', Annals of Science, 30 (1973), 107-22
M. P. Charbonnier, Essais sur l'histoire de la balistique (1928)
F. L. Robertson, 'New principles of gunnery' and 'The carronade', The evolution of naval armament (1921), 112-24, 125-39
K. Alder, 'Design and deployment', Engineering the revolution: arms and enlightenment in France, 1763-1815 (1997), 87-124
W. Bareris, 'Cavalleria e artigliera: orizzonti dell conservazione nobiliare e idee di modernità', Le armi del principe: la tradizione militare sabauda (1988), 139-238
A. Semek, 'Die Artillerie unter Liechtenstein, 1746-1772', Die Geschichte der Artillerie, ihr Werdegang, ihre Entwicklung bis heute (1908), 37-71
D. M. Jesseph, 'The aftermath of the Analyst', Berkeley's philosophy of mathematics (1993), 231-95
F. Cajori, 'Jurin's controversy with Robins and Pemberton', A history of the conceptions of limits and fluxions in Great Britain: from Newton to Woodhouse (1919), 96-148
N. Guicciardini, 'The controversy on the foundations of calculus', The development of Newtonian calculus in Britain, 1700-1800 (1989), 38-51

Archives  
RS, papers

Wealth at death  
approx. £100: W. Johnson, 'In search of the end of the life, in India, of Benjamin Robins, F.R.S.', International Journal of Impact Engineering, 11/4 (1991)


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