The Impact of Ballistics on Mathematics
On 23 August 1774, the economist and politician
Anne-Robert-Jacques Turgot
(1727-1781) wrote to Louis XVI:
The famous Leonhard Euler, one of the greatest
mathematicians of Europe, has written two works which could be very useful to
the schools of the Navy and the Artillery. One is a Treatise on the
Construction and Manoeuver of Vessels; the other is a commentary on the
principles of artillery of Robins . . . I propose that your Majesty order
these to be printed; . . . [Quoted, in English, by Clifford Truesdell, An
Idiot's Fugitive Essays on Science (1984), p. 337]
Turgot had reason to know about these books, for at the time
he was Ministre de la Marine. He was aware of the impropriety of translating a
work without the author's permission so urged the king to compensate Euler with
5,000 francs from the secret accounts of the Navy.
Works by Benjamin Robins
1726: "A Demonstration of the 11th
Proposition of Sir Isaac Newton's Treatise of Quadratures. By Mr. Benjamin
Robins
Benjamin Robins, Isaac Newton," Philosophical Transactions (1683-1775), Vol. 34, 1726 - 1727 (1726 -
1727), pp. 230-236.
1735: A discourse concerning the nature and certainty of Sir
Isaac Newton’s methods of fluxions, and of prime and ultimate ratios. By
Benjamin Robins. London, Printed for W. Innys and R.
Manby, 1735. ii, 78 p. 20 cm. Columbia:
SMITH 517 1735 R55
1739: Remarks on Mr. Euler’s Treatise of motion, Dr. Smith’s
Compleat system of opticks, and Dr. Jurin’s Essay upon distinct and indistinct
vision. By Benjamin Robins, F.R.S. London :
printed for J. Nourse, 1739. vi,112p. : ill. Columbia's Butler Microforms, 401B:
Eighteenth century ; reel 9682, no. 06. F a4254 reel 9682, no.06.
1740: "A full confutation of Dr. Jurin's Reply to the remarks on his Essay
upon distinct and indistinct vision. By Benjamin Robins, F.R.S.,"
printed for J. Nourse, 1740.
1742: New principles of gunnery: containing the
determination of the force of gun-powder, and an investigation of the difference
in the resisting power of the air to swift and slow motions.
London, J. Nourse, 1742. Copy at NYPL.
1743: Paper in Phil Trans
1747: A proposal for increasing the strength of the British navy,
by changing all the guns, from the eighteen pounders downwards, into others of
equal weight but of a greater bore. By Benjamin Robins,
... London : printed for J. Nourse, 1747. vii,[1],24p. Columbia's Butler
Microforms, 401B: Eighteenth century ; reel 7626, no. 03. F a4254 reel 7626, no. 03.
1749: "Observations on the Height to
Which Rockets Ascend; By Mr. Benjamin Robins F. R. S."
Philosophical Transactions (1683-1775), Vol. 46, 1749 - 1750 (1749 -
1750), pp. 131-133.
1761: Mathematical tracts of the late Benjamin Robins Published
by James Wilson, M.D. London, J. Nourse, 1761. 2 v. 3 pl. (1 fold.) diagrs.
21 cm. USMA Special Collections: WPT 510.4 R553. Not in electronic
catalog.
1783: Nouveaux principes d’artillerie
/ de M. Benjamin Robins ; commentés par M. Léonard Euler
; traduits de l’allemand, avec des notes, par M. Lombard ... , A Dijon
: Chez L.N. Frantin ... ; Et se trouve a Paris ; Chez Jombert fils aîní
..., 1783. Off-site at NYPL.
1805: New principles of gunnery: containing the
determination of the force of gun-powder, and an investigation of the difference
in the resisting power of the air to swift and slow motions, with several other
tracts on the improvement of practical gunnery / by Benjamin Robins... with an
account of his life and writings by James Wilson.
London : F. Wingrave, 1805. New ed. / corrected, and enlarged
with the addition of several notes, by Charles Hutton. xlvi, [2], 341 p., [2]
folded leaves of plates : ill. ; 24 cm. Signatures: a-c8A-X8Y4. USMA Special
Collections: UF144 .R6 1805.
The following is probably an error:
Benjamin Robins, “New Principles in Gunnery”, London (1807).
The only copy available in the United States is the 2nd Edition (1842) at the
United States Military Academy, West Point, NY.
REFERENCES:
Ackroyd, J. A. D., "Sir George Cayley, the father
of aeronautics. Part 1. The invention of the aeroplane," Notes
and Records of the Royal Society, Volume 56, Number 2 / May 22,
2002, pp.167 - 181.
This paper, in two parts, seeks to describe
and assess Cayley's technical development of his invention,
the fixed-wing aeroplane. Particular attention is paid to such
scientific results as were known to Cayley at that time. Part
1 deals with the invention of the aeroplane itself, this being
prefaced by a biographical sketch outlining his wide-ranging
interests, both scientific and humanitarian; part 2 will show
how Cayley was not only able to develop his invention but
through this was also able to demonstrate many of the basic
principles of fixed-wing flight. The paper is based on the
author's Cayley Lecture to the Royal Aeronautical Society in
April 2000.
Allibone, T. E., "Edmond
Halley and the Clubs of the Royal Society,"
Notes and Records of the Royal Society of London, Vol. 28, No. 2 (Apr.,
1974), pp. 195-205.
Barkla, H. M., "Benjamin Robins and the resistance of air,"
Annals of Science, vol. 30, no. 1, March 1973, pp. 107 - 122.
Bektas, M. Yakup and Crosland,
Maurice, "The
Copley Medal: The Establishment of a Reward System in the Royal Society,
1731-1839," Notes and Records of the Royal
Society of London, Vol. 46, No. 1 (Jan., 1992), pp. 43-76.
Burckhardt, J. J., "Leonhard
Euler, 1707-1783, Mathematics Magazine,
Vol. 56, No. 5 (Nov., 1983), pp. 261-273.
Cajori,
Florian, "Frederick
the Great on Mathematics and Mathematicians."
American Mathematical Monthly, Vol. 34, No. 3 (Mar., 1927), pp. 122-130.
Grattan-Guinness, Ivor, "The interest of G. H. Hardy, F.R.S., in the
philosophy and the history of mathematics," Notes and
Records of the Royal Society, Volume 55, Number 3 / September 22, 2001, 411
- 424.
Laudan, L. L., "The
Vis viva Controversy, a Post-Mortem,"
Isis, Vol. 59, No. 2 (Summer, 1968), pp. 130-143.
Matthews, Michael R.; Gauld,
Colin, and Stinner, Arthur, "The Pendulum: Its Place in Science,
Culture and Pedagogy,"
Science & Education,
Volume 13, Numbers
4-5 / July, 2004, pp. 261-277. Journal not at USMA.
Abstract The
study and utilisation of pendulum motion has had immense scientific,
cultural, horological, philosophical, and educational impact. The
International Pendulum Project (IPP) is a collaborative research effort
examining this impact, and demonstrating how historical studies of pendulum
motion can assist teachers to improve science education by developing
enriched curricular material, and by showing connections between pendulum
studies and other parts of the school programme especially mathematics,
social studies and music. The Project involves about forty researchers in
sixteen countries plus a large number of participating school teachers.The
pendulum is a universal topic in university mechanics courses, high school
science subjects, and elementary school programmes, thus an enriched
approach to its study can result in deepened science literacy across the
whole educational spectrum. Such literacy will be manifest in a better
appreciation of the part played by science in the development of society and
culture.
Radelet-de Grave, P., "La diatribe du Docteur Akakia, Médecin
du pape,"
www.fyma.ucl.ac.be/files/UCL-IPT-97-10.pdf I think there is a
very interesting story to be followed up here.
Saintsbury, George, "François
Marie Arouet De Voltaire (1694-1778)," Encyclopedia Britannica, 11th
edition, vol 28, pp. 199-205. On line at
http://www.1911encyclopedia.org/Francois_Marie_Arouet_De_Voltaire . Very
nice biography of Voltaire. Good connections with Emilie du Chatelet, Frederick,
and Voltaire. Euler and Robins not mentioned.
Steele,
Brett D., "Muskets and Pendulums: Benjamin Robins, Leonhard Euler, and the
Ballistics Revolution," Technology and Culture, Vol. 35, No. 2 (Apr., 1994), pp. 348-382.
Steel, Brett D., "Military "Progress" and Newtonian Science in the age of
Enlightenment," pp. 361-390 in The heirs of Archimedes : science and
the art of war through the Age of Enlightenment, edited by Brett D. Steele
and Tamera Dorland, Cambridge, Mass. : MIT Press, c2005.
Steel, Brett D., my article on Leonhard Euler's interior ballistics analysis
and its influence on both military and engineering thinking in the late
eighteenth century was published in Gunpowder, Explosives, and the
State: A Technological History, edited by Brenda Buchanan, Aldershot,
England; Burlington, VT : Ashgate, c2006.
Swerdlow, N. M., "Montucla's
Legacy: The History of the Exact Sciences,"
Journal of the History of Ideas, Vol. 54, No. 2 (Apr., 1993), pp. 299-328.
Available in JSTOR.
Thomas, J. M., "Sir Benjamin Thompson, Count Rumford and the
Royal Institution," Notes and Records of the Royal Society, Volume 53,
Number 1 / January 22, 1999, 11 - 25.
On 19 September 1798, there arrived in London from Munich a
45-year-old, tall, blueeyed, handsome, American-born, opportunistic man of
action. A former soldier and statesman, he was, by all accounts, ruthless and
arrogant, callously cunning and devious, an unprincipled spy and a calculating
womanizer; but he was also a philanthropist, a brilliantly effective social
reformer, an ingenious inventor and an exceptionally innovative scientist. His
name was Benjamin Thompson, better known as Count von Rumford of the Holy
Roman Empire. He would found the Royal Institution.
Truesdell, C., review of “Exterior Ballistics” by E. J.
McShane, J. L. Kelley, and F. V. Reno, Scripta Mathematica 20 (1954), 172-174.
Not surprisingly, Truesdell is caustic (p. 56 "is the ugliest page I have ever
seen). He is surprised that these distinguished authors did not do better. Yet
he praises the 50 page historical appendix. He praises the book for this alone.
USMA: UF820 .M248. R. A. Rankin has a long review in Mathematical Reviews
(MR0060355) that predicts, correctly, that the book will become a classic.
Truesdell, C. A., "Published Works of Clifford Ambrose Truesdell III,"
Journal of Elasticity,
Volume 72, Numbers
1-3 / July, 2003, 1-27. Journal not at USMA.
Voltaire, François Marie Arouet
de, "Traité de paix conclu entre M. le Président et M. le Professeur,"
dated 1 January 1753. On line copy at
http://www.voltaire-integral.com/Html/23/08DIAL.htm
. Search for "Euler".
Some of the clauses here are quoted from Robins's critique of Euler. Need to
look into this. Would be nice to track down an English translation.
Wicher, Enos, "Ballistics pendulum," American Journal of Physics, vol
45, no. 7, 681-682, July 1977.
___
The two notebooks of Benjamin Robins
Johnson, W., "The Woolwich professors of mathematics (1741-1900),"
Journal of mechanical working technology,
18(2), 145, 1989. Journal available at SIBL branch of NYPL.
Johnson, W., "Charles Hutton, 1737-1823: The prototypical Woolwich Professor
of Mathematics," Journal of mechanical
working technology, 18(2), 195, 1989. Journal available at SIBL branch of
NYPL.
Johnson, W., "The origin of the ballistic pendulum : the
claims of Jacques Cassini (1677-1756) and Benjamin Robins (1707-1751),"
International journal of mechanical sciences, 1990, vol. 32, no4, pp. 345-374 (22
ref.)
Johnson W., "In search of the end of the life, in India, of
Benjamin Robins, F.R.S," International journal of impact engineering,
1991, vol. 11, no4, pp. 547-571.
Johnson W., "
Benjamin
Robins, F.R.S. (1707-1751): New Details of His Life,"
Notes and Records of the Royal Society of London, Vol.
46, No. 2 (Jul., 1992), pp. 235-252.
Johnson W., "Benjamin robins (18TH century founder of scientific
ballistics) : some European dimensions and past and future
perceptions," International journal of impact engineering,
1992, vol. 12, no2, pp. 293-323.
Johnson, W., "Encounters between Robins, and Euler and the
Bernoullis ;
artillery and related subjects," International journal of mechanical sciences,
1992, vol. 34, no8, pp. 651-679.
Johnson, W., "Benjamin
Robins during 1739-1742: 'Called to a Publick Employment... A Very Honorable
Post," Notes and Records of the Royal
Society of London, Vol. 48, No. 1 (Jan., 1994), pp. 31-42.
Johnson W., "Congreve's Details of the rocket system and
the artillery museum in the Rotunda at Woolwich, London," International
journal of impact engineering, Vol. 15, no. 6, pp. 833-842. 1994
William Congreve, Jnr (1772-1828), in a 40-page booklet,
describes the various applications of his rocket system. This is partially
and briefly summarized below, mostly using some of Congreve's figures. The
contents of the booklet, accompanied by an essay by Captain Boxer, also
appear in a recent Canadian facsimile reproduction, a short summary being
included in the Notes. The second portion of this paper is concerned with
the artillery museum in the Rotunda, Woolwich, established about 170 years
ago. We mention the inception of the new museum and recommend it for
visiting by students of impact engineering. Our first two Notes suggest or
show that the renowned 18th century British pair, Benjamin Robins and
Charles Hutton (founders of early ballistic theory), were well acquainted
with the widely known Henry Pemberton and Sir William Congreve Snr
respectively.
Johnson W., "Edward
Gibbon and George Grote: A Bicentenary in Common,"
Notes and Records of the Royal Society of London, Vol. 48, No. 2 (Jul.,
1994), pp. 221-22.
Johnson W., "A note on James Wilson M.D
(1690-1771): Biographer and editor of some of the works of
Pemberton, Robins and Newton," International journal of
impact engineering, Volume 21, Number 8, September 1998, pp.
707-710.
Johnson W., "Aspects of the live and works of Martin
Folkes (1690-1754),"
International Journal of Impact Engineering, Volume 21, Number 8,
September 1998, pp. 695-705.
Johnson W., "Early
bridge consultants, Benjamin Robins, FRS and Charles Hutton, FRS and mis-judged
bridge …,"
International Journal of Mechanical Sciences, 1999
Johnson W., "Short unpublished manuscripts of Benjamin
Robins,"
International Journal of Impact Engineering, Volume 24, Number 4,
April 2000, pp. 417-428.
Johnson W., "Benjamin Robins, Tobias Smollett and
fictional Roderick Random: expeditions to Portobello (1739),"
International journal of impact engineering,
Johnson W., "The Watts Academy, 1715–1750: Robins’
probable involvements and opportunities," International journal of impact
engineering,
http://pixe2004.ijs.si/proceedings/htm/pdf/1201.pdf
[CITATION] All guns blazing. Collected works
on Benjamin Robins and Charles Hutton, by W. Johnson
A McConnell - NOTES AND RECORDS-ROYAL SOCIETY OF
LONDON, 2004 - UNIVERSITY PRESS
Web Search -
BL Direct
How Galileo solved the problem of maximum projectile
range without the calculus
Herman Erlichson 1998 Eur. J.
Phys. 19 251-257 doi:10.1088/0143-0807/19/3/007
Herman Erlichson
Department of Applied Sciences, The College of Staten Island, City
University of New York, 2800 Victory Blvd, Staten Island, NY 10314, USA
Abstract. The
maximum range of a projectile in a vacuum is easily derived from the range
formula or the calculus, but Galileo solved this problem in the 1600s
without knowledge of either. This paper decribes his method and provides
the first detailed study and discussion in the literature (to this
author's knowledge) of Galileo's work on the maximum range problem.
http://www.ias.ac.in/currsci/apr102004/1033.pdf
Robins-Magnus effect: A continuing saga
-
group of 2 »
TK Sengupta, SB Talla - Current Science, 2004 - ias.ac.in
... only experimental device at that time and ballistic pendulum for ... In
writ- ing the
book on ballistics 2 , he ... 4. Anderson, J. D., A History of Aerody- namics
and ...
http://www.srim.org/SRIM/History/HISTORY.htm
http://www.americanyc.com/sailing/cruising/navigation/Celestial/pix/MoskowitzSextants.pdf
http://www.cmste.uncc.edu/new/Document%20Hold/Wind%20Tunnels%20-%20Paper.doc
http://www.ciar.org/ttk/mbt/papers/ijie01/ijie_25_315.pdf
