Marketing Mathematics in Early Eighteenth-Century England: Henry Beighton,Certainty,and the Public Sphere

Early in Beighton's editorship (1714–43), the Ladies' diary's circulation was about 6,000 (see 1718, p. 18). Its annual sales gradually increased, peaking at 30,000 in the 1750s. In 1761 the Diary was still England's third bestselling almanac; in 1789 it was still in the top five. See Capp Bernard , Astrology and the popular press: English almanacs 1500–1800 (London and Ithaca, NY, 1979).

The Ladies' diary, or Woman's almanack (1729, p. 2). Beighton's collecting had been made “agreeably” redundant, he explained, by the 1728 publication of Ephraim Chambers's thorough Cyclopaedia, which immediately “stopp'd my collections and eas'd me that further trouble my curiosity would have led me to”.

Stewart Larry , The rise of public science: Rhetoric, technology and natural philosophy in Newtonian Britain, 1660–1750 (Cambridge, 1992) and Golinski Jan , Science as public culture: Chemistry and enlightenment in Britain, 1760–1820 (Cambridge, 1992) both piqued scholarly interest in public science. See also Stewart , “Other centres of calculation, or, Where the Royal Society didn't count: Commerce, coffee-houses and natural philosophy in early modern London”, The British journal for the history of science, xxxii (1999), 133–53; Schaffer Simon , “A social history of plausibility: Country, city and calculation in Augustan Britain”, in Wilson Adrian (ed.), Rethinking social history: English society 1570–1920 and its interpretation (Manchester and New York, 1993); and Walters Alice , “Conversation pieces: Science and politeness in eighteenth-century England”, History of science, xxxv (1997), 21–54. Brewer John has explored eighteenth-century England's growing state bureaucracy of mathematical measurement, especially the gauging of ale casks, in The sinews of power (London, 1989), bringing a governmental sense of “public” to the literature on public science and adding taxation to the economic themes of exchange and consumerism prevalent in this literature.

Beighton was also one of the first in England to collect meteorological data. See Cook's Alan article on Beighton Henry in the New dictionary of national biography (Oxford, forthcoming).

See Stewart , The rise of public science (ref. 3), especially pp. 242–51. Beighton also worked closely with John Theophilus Desaguliers, the foremost Newtonian public lecturer of the early eighteenth century. On Beighton's mathematization of technology and his work with Desaguliers see my “‘Reduced to a mathematicall calculus’: Beighton Henry , the Newcomen engine, and a new role for geometry in early industrial England” (forthcoming).

The Ladies' diary is cited parenthetically throughout this article; the cover of each issue is counted as page 1. For issues missing from the Bodleian Library's nearly complete collection, I have relied on the Diarian miscellany (London, 1775), five volumes of riddles, mathematical problems and selected commentary compiled from past issues of the Ladies' diary by its then editor, Hutton Charles . Citations for those issues give the year of the original Diary and, in brackets, the abbreviation “DM” along with the appropriate volume and page number of Hutton's 1775 compilation.

The Diary sponsored an annual exchange of mathematical questions, verbal riddles, geographical puzzles and their answers. An annual supplement called the Palladium and a rival almanac, the Gentleman's diary — Both begun in the 1740s — Printed similar mathematical questions, but before the 1740s the Ladies' diary was the only mathematical periodical in existence. Although mathematical contents occasionally appeared in journals such as the Royal Society's Philosophical transactions or other question-and-answer periodicals such as the Athenian Mercury or the British Apollo, this occurred rarely, far too infrequently for such publications to be termed “mathematical”. The same can be said for the widely read Gentleman's magazine, begun in the 1730s.

Jones Colin , “The Great Chain of Buying: Medical advertisement, the bourgeois public sphere, and the origins of the French Revolution” in The French Revolution: The essential readings, ed. by Schechter Ronald (London, 2001), 138–74. Jones criticizes the recent fashion for emphasizing the abstract, discursive features of the Habermasian public sphere at the expense of the bourgeois basis of the original theory. See Habermas Jürgen , The structural transformation of the public sphere: An inquiry into a category of bourgeois society , transl. by Burger Thomas with Lawrence Frederick (Cambridge, 1989). On print and the spread of scientific ideas see also Broman Thomas , “The Habermasian public sphere and ‘Science in the Enlightenment’”, History of science, xxxvi (1998), 123–49, and Johns Adrian , The nature of the book: Print and knowledge in the making (Chicago, 1998).

It should be noted that, despite its extreme popularity, the Ladies' diary was not an enormous source of income to Beighton. The Company of Stationers, a London guild with exclusive rights to publish English almanacs, retained the vast majority of the profit. An estimate of £10 for Beighton's annual stipend seems reasonable, since at the peak of the Diary's popularity in the 1750s, its editor received under £11 — About 3% of the overall revenue from the sale of the Ladies' diary (Capp, Astrology and the popular press (ref. 1), 243). On the economy of English almanacs see Blagden Cyprian , The Stationers' Company: A history, 1403–1959 (London, 1960). For the effect of the Company's almanac monopoly on printing as a profession see Johns , The nature of the book (ref. 8), 259–62.

Costa Shelley , “The Ladies' diary: Gender, mathematics and civil society in early eighteenth-century England”, Osiris, xvii (2002), 49–73.

On features of enlightened mathematics see Frängsmyr Tore Heilbron J. L. Rider Robin E. , (eds), The quantifying spirit in the eighteenth century (Berkeley, CA, 1990); the work of Alder Ken Rusnock Andrea Terrall Mary — The contributions of all three, for example, in Clark William Golinski Jan Schaffer Simon (eds), The sciences in enlightened Europe (Chicago, 1999); and Daston Lorraine , Classical probability in the Enlightenment (Princeton, NJ, 1988). See also Calinger's Ron explanation of esprit systématique as compared with esprit géométrique in his Classics of mathematics (Englewood Cliffs, NJ, 1995), 434.

As Schaffer Simon has put it, “attention to the cosmopolitan public sphere addresses issues of central concern both for Enlightenment itself, and for our own sociology of knowledge. Recent sociological analyses have rightly stressed the local, situated character of knowledge and its production. The wider grip of different knowledges is then accounted as liaisons between these locales, the multiplication of the contexts in which specific techniques work and are compelling”. “A social history of plausibility”, op. cit. (ref. 3), 138.

Their personal connection is evidenced by Beighton's later reference to his predecessor as “my good friend Mr. Tipper, … whose ingenuity recommended him to the world, as his piety, modesty, and candour did to those who knew him” (1717, p. 20).

A 1709 editorial provides the best evidence of John Tipper's commitment to the general reader: “I have received several arithmetical questions which are very unfit for this place; my design being not to puzzle, but to please; not to perplex the understanding, but to exercise the wit, and a moderate knowledge in numbers; and therefore those who are pleased to send me any arithmetical questions, I desire they may be very pleasant, and not too hard” (1709, p. 29).

Pennant Thomas , The journey from Chester to London (London, 1782), 184.

See the summary of Gregory King's 1688 table of income distribution in Hay Douglas Rogers Nicholas , Eighteenth-century English society: Shuttles and swords (Oxford and New York, 1997), 19.

Porter Roy , English society in the eighteenth century (London, 1982), 29. Porter summarizes Gregory King as asserting “that the least a family … could live on, without getting into debt or taking poor relief or charity, was about £40 a year” (p. 28).

Foul-smelling tobacco.

The careful recording of weather-related statistics was one of Beighton's many occupations. He made several meteorological reports to the Royal Society. See Cook , “Henry Beighton” (ref. 4).

Unlike Tipper, who discoursed on astronomy, Beighton did not include instruction in any subject.

Beighton may have used the language of public service to assert his status as a freeholder. Paul Langford has discussed the various public duties of landed gentlemen at length in Public life and the propertied Englishman 1689–1798 (Oxford, 1991).

Jones Meredith Mr. wrote to Beighton in November 1716 that “I know this day many eminent men that owe (as I have heard them to confess it) their knowledge in those [mathematical] mysteries to the ingenious Mr. Tipper, deceas'd; I mean owe it so far, as his Diary was the first occasion of applying themselves that way” (1718, p. 19).

Beighton frequently drew from Patrick Gordon's Geography anatomiz'd: Or, A compleat geographical grammar (London, 1693) to provide his readers with entertaining geographical “paradoxes”.

Precision is the ability of a tool to give the same result consistently. Accuracy is the ability of a tool to give a true result or, in social terms, to meet an accepted standard of truth. Beighton wished his readers to believe in the truth, i.e. the accuracy, of his measurements, but the inability of anyone to know a priori the true proportions of the English countryside — And the need to set his results apart from previous measurements — Meant that he had to assert the accuracy of his data by other means. The distinction between precision and accuracy is discussed in the editor's introduction to Wise M. Norton (ed.), The values of precision (Princeton, 1995), 7–9.

Schaffer , “A social history of plausibility” (ref. 3), 142.

The Warwickshire County Record Office, Warwick, possesses several manuscripts by Beighton — Including memoranda, field notes and invoices — That show that he performed the official surveys of Attleborough and Nuneaton (both very close to his home village of Griff) between 1731 and 1733. Warwickshire County Record Office (hereafter Warwickshire CRO), MSS CR 3221/2–4, 6, 8–10, 12–13.

The economic historian Wordie J. R. estimates that 37% of England was enclosed during the seventeenth and eighteenth centuries. Nearly two-thirds of this occurred during the seventeenth century, but the visibility of Parliamentary legislation for enclosure during the eighteenth has led most historians erroneously to assume that more enclosure occurred during the eighteenth century. Wordie J. R. , “The chronology of English enclosure, 1500–1914”, Economic history review, xxxvi (1983), 483–505.

In the early seventeenth century a pamphleteer had denounced all who attended an enclosing landlord: “the surveyor is his quartermaster which goes like a bear with a chain at his side, and his two or three parishioners who walk with him help him to undo themselves”. Harleian miscellany, ix, cited in Darby H. C. , “The agrarian contribution to surveying in England”, Geographic journal, lxxxii (1933), 529–35. The image of the chain refers not just to a trained bear, but also to the standard tool of the surveying chain.

Sharing or distributing land was the subject of, for example, Questions 63 (1718), 69 (1719) and 108 (1724). Eight other problems before 1725 also involved the measurement of land.

Advertisements in almanacs were placed at the discretion of authors. Revenue from them was not necessary to publication since the Stationers' Company supplied the capital. See ref. 9, above.

See, for example, Dear Peter , “Totius in verba: Rhetoric and authority in the early Royal Society”, Isis, lxxvi (1985), 145–61, and Biagioli Mario , Galileo, courtier: The practice of science in the culture of absolutism (Chicago, 1993).

The Royal Society of Arts, founded in 1755, offered prizes for land surveying done with the most accurate instruments available. Parliamentary legislation for the enclosure of common lands also notably increased after mid-century. In addition, military interest in mapping Scotland after the Jacobite revolt of the 1740s led to a specialization in mapmaking for the British government's Board of Ordnance from the 1780s. Feldman Theodore , “Barometric hypsometry”, Historical studies in the physical sciences, xv (1985), 127–97.

Feldman , ibid., 156, 157. On surveying instruments of the period and their relationship to mathematical theory see Bennett J. A. , “The challenge of practical mathematics”, in Science, culture, and popular belief in Renaissance Europe, ed. by Pumfrey Stephen (Manchester, 1991), 176–90, and Bennett , The divided circle (Oxford, 1987).

Harley J. B. , “The re-mapping of England, 1750–1800”, Imago mundi, xix (1965), 56–67, cited in Feldman, op. cit. (ref. 32).

Pennant Thomas declared that “for elegance, accuracy, and expedition, [Beighton] had few equals” in surveying. The journey from Chester to London (London, 1782), 184.

Warwickshire CRO MS CR 3221/12.

On contemporary problems with magnetism and land measure see Fara Patricia , Sympathetic attractions (Princeton, 1996), especially pp. 97–98.

This book was an example of a longstanding trend in English geography, the practice of “chorography”, or detailed description of a county or other small region. See Cormack Lesley B. , “‘Good fences make good neighbors’: Geography and self-definition in early modern England”, Isis, lxxxii (1991), 639–61.

Between 1716 and 1728 Beighton produced views of the Coventry Cross, two county churches and seven county manors for the new Antiquities of Warwickshire.

Beighton reported these dates in the Ladies' diary (1728, p. 37).

Woodward David , “English cartography, 1650–1750”, in Thrower Norman (ed.), The compleat plattmaker: Essays on chart, map and globe making in England in the seventeenth and eighteenth centuries (Berkeley, 1978), 159–93. Woodward here cites Elizabeth Rodgers, The large scale county maps of the British Isles, 1596–1850, 2nd edn (Oxford, 1972).

“Before 1750 only a dozen or so counties had been mapped on a scale of one mile to the inch or larger. By 1775, however, almost half the country had been surveyed and mapped at the one-inch scale, and by 1800 only the highlands of Wales and Scotland still remained unsurveyed.” Feldman, “Barometric hypsometry” (ref. 32), 159.

“… the total production cost of the average map might be £20. Since [small county maps] were sold at sixpence uncolored, a shilling colored, the publisher would have to sell about 400 colored impressions to recover his manufacturing costs.” Woodward, “English cartography, 1650–1750” (ref. 41), 166.

“… the etching and graving is now finished (which is no small pleasure to see) by the hand of that curious artist Mr. Elisha Kirkall, and the most neatly etch'd I ever saw any” (1728, pp. 37–38).

“In 1679, a piece of copper for John Adams's map of England and Wales cost £1 5s.” Woodward, “English cartography, 1650–1750” (ref. 41), 166.

“… subscriptions … are taken in, and receipts given, by Collyer Mr. [sic] at Stationers-Hall, Mr. Senex, Bookseller, in Fleetstreet; Mr. King, Bookseller, in Westminster-Hall, London; Mr. Hurt and Mr. Ratton, Booksellers in Coventry; Mr. Fancourt, Bookseller, at Stratford on Avon; Mr. Parkes, Bookseller, in Birmingham; and by the author in his progress thro' the county” (1724, p. 40).

Vickery Amanda points out that “mercantile elites” in provincial England “belonged to the same clubs and libraries, pursued a similar interest in agriculture and inventions … and enjoyed the same public assemblies and private parties” as landed gentry. “The crucial social divide was seen to run between genteel commerce and retail trade, between the polite and the vulgar, not between land and trade as such.” Vickery, The gentleman's daughter: Women's lives in Georgian England (New Haven, 1998), 34.

Beighton Henry , “The reducing and transcribing the map fit for the graver took above four months time more than I expected, the graving which I thought most proper to have done by two hands, viz. the landscape churches, houses, rivers, &c. to be etched, to imitate a soft and beautiful drawing, the letters and lines to be graved, which have taken a much longer time than was expected” (1727, p. 39).

Beighton Henry to the Royal Society, “The heads of some papers design'd for the R. Society”, 10 June 1736; BL Add. MSS. 4433, f. 273 (verso). The proposed description of the plane table was one of twenty topics he offered to the Royal Society in this letter. It was submitted a few years later and published in the Philosophical transactions, xli (1741), 747–61.

Ibid.

“Apparently this instrument was in common use in the early eighteenth century, as seen from its inclusion in Chambers's Cyclopedia (1727–1741).” Woodward, “English cartography, 1650–1750” (ref. 41), 164.

Henry Beighton to the Royal Society, “An easy and cheap method of making a large quadrant or arch capable of taking the latitude of a place very exactly”, 24 May 1739; BL Add. MSS. 4432, ff. 182–3.

The chaise-wheel perambulator was “made by that ingenious artist, Mr. Tho. Eayre of Kettering, from whom we may expect to see the most accurate map of Northamptonshire” (1724, p. 39).

Woodward , “English cartography, 1650–1750” (ref. 41), 171.

This holds not only for tools of physical measurement, but also for psychometric tools such as standardized examinations.

Shapin Steven , A social history of truth: Civility and science in seventeenth-century England (Chicago, 1994).

Prize questions in the Ladies' diary were often written by the editor, though they were usually not attributed in the text.

This can be seen in, for example, the answers to Questions 10, 17 and 47 that appeared, respectively, in the 1710, 1712 and 1717 issues of the Ladies' diary.

Consider John Tipper's response to this phenomenon in 1713: “To the prize question proposed last year, I received abundance of letters … out of which there were but four true answers…. And that so many were mistaken in their answers, there are two reasons. First, in Sir Jonas Moor[e]'s and some other catalogues, that star (call'd by Kepler in his Rudolphine Tables Tertia ab Extrema in Cauda Draconis) is accounted of the 3d [rather than of the second] magnitude, and those who had recourse to these tables, took the middle star in the great bear, or the guard-star in the little bear's shoulder, to answer the question…. A second reason was, (tho' the difference is inconsiderable) some astronomers say the prescesion [sic] of the equinox is 48, and others 50 seconds in a year” (1714 [DM i, p. 94]). This commentary was printed in an issue which was begun by Tipper and finished by Beighton after his predecessor's unexpected death. Its style, together with the fact that the deadline for answers to the question was more than two months before his death, implicate Tipper as its author.

Most precise.

Beighton , op. cit. (ref. 49). This treatise does not appear to have been written.