Mathematical practitioners and instruments in Elizabethan England

This article was downloaded by: [George Mason University]On: 10 October 2014, At: 13:51Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK

Annals of SciencePublication details, including instructions for authors andsubscription information:http://www.tandfonline.com/loi/tasc20

Mathematical practitioners andinstruments in Elizabethan EnglandStephen Johnston aa The Science Museum , London, SW7 2DD, U.K.Published online: 23 Aug 2006.

To cite this article: Stephen Johnston (1991) Mathematical practitioners and instruments inElizabethan England, Annals of Science, 48:4, 319-344, DOI: 10.1080/00033799100200321

To link to this article: http://dx.doi.org/10.1080/00033799100200321

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the“Content”) contained in the publications on our platform. However, Taylor & Francis,our agents, and our licensors make no representations or warranties whatsoever as tothe accuracy, completeness, or suitability for any purpose of the Content. Any opinionsand views expressed in this publication are the opinions and views of the authors,and are not the views of or endorsed by Taylor & Francis. The accuracy of the Contentshould not be relied upon and should be independently verified with primary sourcesof information. Taylor and Francis shall not be liable for any losses, actions, claims,proceedings, demands, costs, expenses, damages, and other liabilities whatsoever orhowsoever caused arising directly or indirectly in connection with, in relation to or arisingout of the use of the Content.

This article may be used for research, teaching, and private study purposes. Anysubstantial or systematic reproduction, redistribution, reselling, loan, sub-licensing,systematic supply, or distribution in any form to anyone is expressly forbidden. Terms &Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions

http://www.tandfonline.com/loi/tasc20

http://www.tandfonline.com/action/showCitFormats?doi=10.1080/00033799100200321

http://dx.doi.org/10.1080/00033799100200321

http://www.tandfonline.com/page/terms-and-conditions

http://www.tandfonline.com/page/terms-and-conditions

ANNALS OF SCIENCE, 48 (1991), 3 1 9 - 3 4 4

Mathematical Practitioners and Instruments in Elizabethan England

STEPHEN JOHNSTON

The Science Museum, L o n d o n SW7 2DD, U.K.

Received 26 January 1991

Summary A new culture of mathematics was developed in sixteenth-century England, the culture of'the mathematicalls'. Its representatives were the self-styled mathematical practitioners who presented their art as a practical and worldly activity. The careers of two practitioners, Thomas Bedwcll and Thomas Hood, are used as case studies to examine the establishment of this culture of the mathematicalls. Both practitioners self-consciously used mathematical instruments as key resources in negotiating their own roles. Bedwell defined his role in contrast to mechanicians and he secured patronage in military engineering and the service of the commonwealth; Hood worked in the commercial setting of London as a teacher, author, chartmaker, and retailer. Working in new contexts and dealing with new audiences of gentlemen and mechanicians, Bedwell and Hood used instruments to construct a public consensus on the status and aims of mathematics.

Contents 1. Establishing the mathematicalls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319 2. Thomas Bcdwell's 'profession of the mathematicalls'. . . . . . . . . . . . . . . . . . . . . . 320

2.1. Career and patronage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 2.2. Locating the practitioner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 2.3. The indispensable citizen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327

3. Thomas Hood: mathematics in public . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330 3.1. Mathematics and medicine as careers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 3.2. Audiences and instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334 3.3. London locations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337

4. Mathematical cultures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341

1. Establishing the mathematicalls The fortunes of mathematics underwent a remarkable t ransformat ion in sixteenth-

century England. F r o m being little known and less studied, the mathematical arts and sciences were pushed towards public prominence. This t ransformat ion was principally due to the vocal advocacy of the self-styled mathemat ical practitioners. Most visibly, these practit ioners used the technology of print to publicize their concept ion of mathematics as a collection of practical arts dependent on arithmetic and geometry. One of their c o m m o n collective terms for subjects such as as t ronomy, navigation, surveying, gunnery, architecture, and mensura t ion was ' the mathematicalls ' .

The mathematical ls were not, however, merely a collection of interlinked arts. The idea included a part icular evaluation of their character: they were por t rayed as plain and profitable, pleasurable and certain, fit for bo th the private individual and the commonweal th . This characterizat ion was the ou tcome of the practit ioners ' a t tempts to defuse the hostility (or simple indifference) of their contemporaries. There were

0003-3790/91 $3-00 �9 1991 Taylor & Francis Ltd.

Dow

nloa

ded

by [

Geo

rge

Mas

on U

nive

rsity

] at

13:

51 1

0 O

ctob

er 2

014

320 Stephen Johnston

various common perceptions to be overcome: mathematics might be classed as a dry and difficult pursuit, and mathematicians as a vain or solitary breed, with little sense of civic duty. In post-Reformation England there was also the more dangerous accusation that mathematics was a popish and superstitious activity, bound up with illicit and occult practices. 1 The idea of the mathematicalls was intended to undermine and ultimately replace such perceptions.

But how were contemporaries actively persuaded of the merits of the mathematicalls? How were their interests enlisted and doubts assuaged? By setting out a vision of the scope and character of the mathematical arts, texts such as John Dee's well-known Mathematicall Praeface (1570) played a major part. But this paper follows a different route in examining how the claims of the mathematical practitioners were established. Rather than taking the vernacular literature of the mathematicalls as a starting point, it demonstrates that mathematical instruments were a key resource for the practitioners. Of course, mathematical instruments had many uses beyond presenting the mathematicalls as a legitimate and publicly-acceptable domain. They became part of the daily equipment of the self-consciously progressive surveyor and were essential to the novel astronomical observations of a mathematician such as Thomas Digges. They could, moreover, serve as collectors items and objects of conspicuous consumption. In the economic sphere, they were the basis of the emerging trade of the mathematical instrument maker. However, despite such diversity, the focus of this paper will be on the ways in which instruments were used to convince Elizabethan audiences of the dignity, utility and pleasure of the mathematicalls.

Rather than proceed by means of a general survey, two case studies will be used to display and interpret the strategic uses of instruments. 2 The two practitioners selected for investigation are Thomas Bedwell and Thomas Hood, both of whom devoted considerable attention to mathematical instruments in the 1580s and 1590s. Although Hood's work has featured in a number of historical discussions, neither he nor Bedwell has previously been studied in depth. The case studies present new interpretations of their careers and demonstrate their self-conscious deployment of instruments, revealing how instruments were used to negotiate the character and status of the mathematicalls. Moreover, in contrast to the well-researched but idiosyncratic figure of John Dee, for example, Bedwell and Hood give a much more representative indication of the contours of mathematical practice. By studying their careers we can recover the work which they invested in building public consensus on the mathematicalls and in establishing appropriate roles for the mathematical practitioners.

2. Thomas Bedwell's 'profession of the mathematicalls' Mathematical instruments played an important part in the career of Thomas

BedweU (c. 1547-1595). He designed two instruments and wrote a pair of accompanying tracts to explain their respective uses. His first instrument, a carpenter's rule, was conceived early in his career and, although not widely known in Bedwell's own lifetime, was publicized in the seventeenth century by his nephew, the Arabic scholar and

1 For one practitioner's response to these charges, see Edward Worsop, A Discoverie ofsundrie errours (London, 1582).

2 Much of the material for a larger study can be found in E.G.R. Taylor, The Mathematical Practitioners of Tudor and Stuart England (Cambridge, 1954).

Dow

nloa

ded

by [

Geo

rge

Mas

on U

nive

rsity

] at

13:

51 1

0 O

ctob

er 2

014

Elizabethan mathematical practitioners and instruments 321

Figure 1. Thomas Bedwell's carpenter's rule, as made in the 1630s by John Tompson.

ma thema t i ca l a u t h o r Wi l l i am Bedwell (see F igure 1). 3 Some years after devis ing the carpenter ' s rule, T h o m a s crea ted ano the r rule, s imi lar in pr inc ip le and a ppe a ra nc e to its predecessor , bu t for the qui te different pu rpose of gunnery. These two ins t ruments , t a i lo red to the p rac t ica l ar ts of mensu ra t ion a n d ar t i l lery, a l low us to locate Bedwell f irmly wi thin the c o n t e m p o r a r y deve lopmen t of the mathemat ica l l s . 4 Bedwell was himself qui te self-conscious of his role as a ma the ma t i c a l p rac t i t ioner , reflecting in la ter life on the t ime when he first appl ied himself to the 'profess ion of the mathemat ica l l s ' . 5

In this case s tudy I examine how Bedwelrs in s t rumenta l concerns fit in to the larger pa t t e rn of his career , how they suppor t his concep t ion of the 'profess ion of the mathemat ica l l s ' , Three pa r t i cu la r topics will be addressed , each of which depends on. Bedwel rs use of ins t ruments : the bu i ld ing of his own career; the open ing-up of a social space for the ma thema t i ca l pract i t ioners ; and the a t t e m p t to present himself to con tempora r i e s as an indispensable citizen. T a k e n together , Bedwell 's ins t rumenta l s trategies a r t icu la te and just i fy his role as a ma the ma t i c a l prac t i t ioner .

2.1. Career and patronage T h o m a s Bedwell first appears a t C a m b r i d g e Univers i ty as a successful g r adua t e

elected to a fel lowship at Tr in i ty CoUege. 6 A p a r t f rom be long ing to the small minor i ty of ma t r i cu lan t s who comple ted the full ar ts curr iculum, he appea r s nei ther dis t ingu- ished nor unusual . H e could easily be classed as a s tuden t seeking a s t a n d a r d career such as preferment in to the Church. But Bedwell went in a very different direct ion. 7 After leaving Tr in i ty in a b o u t 1574 he is no t hea rd of aga in unt i l 1582, when he became

For William Bedwell's pubfications on Thomas' carpenter's rule, see Eileen Harris, British Architectural Books and Writers 1556-1785 (Cambridge, 1990).

41 know of no surviving examples of either rule. The brief tract on the carpenter's rule is Bodleian Tanner 298 (4) (referred to hereafter as Tanner); it is bound with several printed works. The text on the gunner's rule is Bodleian MS Laud 618 (hereafter referred to as Laud).

s MS Laud fol. 1L Bedweil is using 'profession' in the sense of an occupation from which he earns a living; his comment should not be taken to refer to a coherent community of practitioners with common standards and training.

Bedwell's Trinity details are: matriculated as a sizar (1562), B.A. (1566--7), fellow (1569), and M. A. (1570). See John Venn and J. A. Venn, Alumni Cantabrigienses, Partl, 4 vols (Cambridge, 1922-27), I, 124. The first recorded payment to him appears in the Bursar's Books for 1570, and he continued to be paid until at least 1574. See H. M. Innes, Fellows of Trinity College Cambridge (Cambridge, 1941), p. 25. Note that there are no surviving records for 1575 (ibid., p.7).

7 Charles Henry Cooper and Thompson Cooper (Athenae Cantabrigienses, 3 vols (Cambridge, 1858- 1913), n (1861), 539), state that Bedwell became a minister in London. The statement was repeated by Venn and Venn (footnote 6) and made its way into the Dictionary of National Biography. However, Bedwell does not appear in G. Hennessy, Novum Repertorium Ecclesiasticum Parochiale Londinense (London, 1898). While the possibility that Bedwell was briefly a minister cannot be ruled out, it should be discounted until some supporting evidence can be found. The statement may have arisen from a misinterpretation of a passage written by his nephew William Bedwell in A Brief Description of the town of Tottenham High-Cross in Middlesex (London, 1631), chapter 8.

Dow

nloa

ded

by [

Geo

rge

Mas

on U

nive

rsity

] at

13:

51 1

0 O

ctob

er 2

014


a technical consultant and supervisor at Dover harbour, s Bedwell's involvement with this major project meant that he was no longer moving in academic circles, but among Privy Councillors, gentlemen, craftsmen, and labourers. 9

For much of his subsequent career Bedwell continued to serve on construction projects, finding a particular place in the realm of military engineering. After the work at Dover he turns up in the Earl of Leicester's 1585 expedition against the Spanish in The Netherlands. He acted there as colonel of the pioneers, directing the unarmed men who built ramparts, threw up earthworks, and dug trenches.l~ By the time of his return to England his reputation had spread more widely, and he was in demand for tasks such as the surveying of fortifications. 11 During the Armada crisis of 1588 he was again pressed into service, co-operating with the Italian engineer Federico Genebelli on strengthening the defences of the River Thames. 12 After this succession of separate projects he successfully petitioned in 1589 for a permanent position as Keeper of the Ordnance Store at the Tower of London, an office that he held until his death in 1595. ~ 3

Bedwell's career was therefore played out largely against a background of military necessity and national defence. He served as a vigorous participant in the field, on the move from one activity to another until eventually he took up residence at the Tower. Although working for the ultimate benefit of the crown, he was not to be found at court, and he cannot readily be identified as a court mathematician; rather, Bedwell established himself as an administrator and technical expert in the emerging nation- state.

However, BedweU's career poses us with a problem. For there was no obvious connection between the opportunities and expectations of a young scholar of the 1570s and the world of construction and military engineering which Bedwell entered in the 1580s. How did he make the transition between these two spheres? BedweU lacked the training and experience of the typical military engineer, who had either learnt his trade as a craftsman (a mason, for example), or had picked it up as a military gentleman exercised in the art of war. ~* He therefore needed to establish his credibility by presenting an alternative set of qualifications, which could persuasively demonstrate his expertise. His need to bridge a perceived credibility gap would have been particularly acute at the outset of his career, when he was least experienced; it is therefore to Bedwell's earliest documented efforts to seek employment that we must turn in order to examine his claims to technical competence.

Many of the transactions of Elizabethan society were conducted through networks of patronage, and Bedwell's participation in major construction projects depended on securing the support of an influential figure, preferably one of the statesmen who made

s Bedwell's first involvement with this protracted project was probably in April 1582 (Public Record Office, State Papers, SP 12/153/27-29). He was still offering suggestions and estimates in March 1583 (PRO SP12/159/9).

9 The best modem account of the Elizabethan harbour works at Dover is by J. Summerson in The History of the Kino's Works, edited by H. M. Colvin, 6 vols (London, 1963-82), IV, 755-64.

lo Calendar of State Paper, Foreign, June 1586 to March 1587 (London, 1927), p. 319. He is presumably the 'beduwel' listed in the Dutch records as a follower of Leicester; see R. Strong and J. A. van Dorsten, Leicester's Triumph, Publications of the Sir Thomas Browne Institute, special series, 2 (Leiden, 1964), p.110. For the duties of the pioneers see C. G. Cruickshank, Elizabeth's Army, second edition (Oxford, 1966), p.25.

11 PRO SP12/199/22; Earl of Sussex to Lord Burghley, from Portsmouth, 10 March 1587. 12 The History of the King's Works (footnote 9), Iv, 604. 13 Bedwell was buried on 30 April 1595, see M. S. R., Notes and Queries, 2nd series, 10 (1860), 74--5. 14 For the diffuse but recognizable role of the military engineer, see The History of the King's Works

(footnote 9), Iv, 409-14.

Dow

nloa

ded

by [

Geo

rge

Mas

on U

nive

rsity

] at

13:

51 1

0 O

ctob

er 2

014


up the Privy Council. Bedwell sought out just this support from Lord Treasurer Burghley when the planned works at Dover harbour were being considered by the Privy Council. In April 1582, Bedwell submitted a memorandum to Burghley in which he set out the credentials which he hoped would capture the Lord Treasurer's attention and favour.1 s The memorandum began with a note of some devices and techniques which could be applied in the harbour works. However, Bedwell's submission was not restricted to the particular matter in hand, for he appended an additional three points to his document. These points were evidently intended to show the breadth of his concerns: he offered to make a water clock to find the longitude during oceanic navigations; he expected successfully to conclude ballistic investigations into the 'course of the bullet of great ordnance'; and he had devised an instrument for measuring timber and stone, 'the easiest and most perfect that hath been or can be invented'. Each of these points--longitude, artillery, and mensuration--fell within the domain of the mathematicalls. Although nothing more is known of the water dock, the measuring instrument is his carpenter's rule, and the concern with ordnance presages the development of his later gunner's rule. 16 It was thus through practical mathematics that Bedwell sought to convince Burghley of his suitability for employment in the harbour works. Indeed, his use of the water clock and his own carpenter's rule indicate that Bedwell gambled on mathematical instruments as the most impressive way to convince the Lord Treasurer of his merits. The success of Bedwell's strategy is evidence that the carpenter's rule was a significant asset in achieving preferment and patronage, and in the founding of a novel career.

Bedwell's use of instruments to procure patronage was not limited to his engagement in the Dover works. At the end of the 1580s he repeated the tactic when he sought out a permanent position to pursue and complete his studies of ordnance.

The Dover memorandum indicated that Bedwell was already occupied with artillery problems in 1582. But it was not until about five years later, after returning from The Netherlands, that he designed his gunner's rule. ~7 The device was to have a twin purpose: it could be used both for the correct elevation of artillery pieces and also for determining the range of fire for any given elevation. The engraving of scales for elevation was a problem of geometry and calculation, and gave the rule an outward appearance similar to the earlier carpenter's rule. However, Bedwell's second purpose, to make the rule serve as a ready reckoner for artillery ranges, posed a more taxing problem. A practical solution to the problem of predicting artillery ranges was being sought throughout Europe at this time. Niccol6 Tartaglia had promised to publish tables giving just these data, but his promise went unredeemed. ~8 Bedwell was thus broaching one of the major unresolved technical issues of the day, and, although historians seeking Galilean precursors will find little reward in Bedwell's work, his method is of considerable interest.

15 PRO SP12/153/27. 16 Water clocks may appear unlikely candidates for the determination of longitude. However Bedwell

was not alone in rating their possibilities highly: William Oughtred was another who considered that they offered the likeliest method for establishing longitude differences. See his Circles of Proportion and the Horizontal Instrument, translated by W. F., edited by A. H. (Oxford, 1660), pp.140-3

7 The following account is based on the introductory sections of the tract on the gunner's rule. 18 See the dedication to his Nova Scientia, in Mechanics in Sixteenth-Century Italy, edited and translated

by Stillman Drake and I. E. Drabkin (Madison, 1969), p. 65. For a more general account of gunnery in this period, see A. R. Hall, Ballistics in the Seventeenth Century (Cambridge, 1952).

Dow

nloa

ded

by [

Geo

rge

Mas

on U

nive

rsity

] at

13:

51 1

0 O

ctob

er 2

014


From his account, it would seem that he began by assuming a particular form for the projectile's trajectory and that on this basis he then calculated theoretical range results. But he was dissatisfied with a purely theoretical procedure. Bedwell wanted some way of verifying or refining his results, and he therefore planned to carry out a systematic series of experimental artillery trials. However, his limited means as a private individual did not stretch to so expensive an undertaking: in order to see his investigations through, he needed access to powder, shot, and artillery. Bedwell's appointment as Keeper of the Ordnance Store at the Tower of London in early 1589 placed him in direct control of the national stocks of exactly those resources which he required. 19 Furthermore, even without Bedwell's intervention, the artillery did not lie undisturbed in store, but was regularly used for training purposes. 2~

How did Bedwell secure this post, so finely tuned to his explicitly stated needs? As at Dover, Bedwell's appointment was effectively granted by Lord Burghley, but in this case Bedwell was able to press his suit through an appropriate intermediary, the Earl of Warwick, Master of the Ordnance. 21 The arguments in his tract on the gunner's rule show that Bedwell used the instrument in his bid for preferment. Claiming that a programme of experimental trials would give him a test of his otherwise uncertain rule, he held out the prospect of an exact instrument. Moreover, he declared that he would be able to determine the 'perfect protract of the bullet's range in the air, which is very corruptly imagined, supposed and described by all that have written thereof hitherto'. 22

These inducements helped Bedwell to secure his permanent position as storekeeper. At both Dover and the Tower he obtained office and employment by using one of his own mathematical instruments to capture the favourable interest of noble patrons; mathematical instruments were crucial to the building of his career.

2.2. Locating the practitioner Bedwell and his instruments were embedded within the complex patronage

network surrounding the Privy Council, and it would be possible to trace more fully his relations with a succession of noble lords throughout the 1580s. However, I want now to turn away from the realm of patronage and towards the humbler level of mechanicians, to the artificers who were envisaged by Bedwell as the pr imary users of his instruments. Although these instruments were ostensibly devised to help the mechanician, they actually played a more subtle role in opening up a social space for the mathematical practitioner. For these instruments figured prominently in his efforts to sanction the intellectual and social elevation of the mathematical practitioner at the

19 Bedwell's patent as storekeeper is dated 15 January 1589, see O. F. G. Hogg, The Royal Arsenal, 2 vols (London, 1963), I, 169, n.lll.

20 British Library, Sloane MS 871, fol. 150 ~-v. 21 Warwick to Burghley, 17 January 1588/9, BL Lansdowne MS 59/5. 22 Laud fol. I v. It is unclear whether Bedwell's tract was itself used to gain patronage, or whether it merely

represents arguments that he had already put forward. The tract was certainly written about the time of his appointment in January 1589, but whether just before or after cannot be confidently determined. Cyprian Lucar's 1588 translation of Tartaglia had already appeared when Bedwell was writing, and he states that it was two years since he had returned from The Netherlands. However, the date of his departure from The Netherlands is not known (although the Earl of Leicester first returned to England at the end of 1586). The issue is complicated by an obscure hint of the Earl of Warwick that Bedwell may have been marked out for the post of Storekeeper a good deal earlier than his actual appointment.

Dow

nloa

ded

by [

Geo

rge

Mas

on U

nive

rsity

] at

13:

51 1

0 O

ctob

er 2

014


expense of the mechanician. The humble mechanician was to have a double dependence on the mathematical practitioner, for the practitioner was both to provide the expertise which mechanicians lacked and was also to act as an intermediary between mechanicians and their social superiors. In his engineering work, Bedwell became accustomed to leading and directing the work of labourers and artificers; when discussing the uses of his instruments he implicitly justified this superior position, while the instruments themselves provided a material embodiment of his claims to recognition and status.

Bedwell sought to accomplish his displacement and demotion of mechanicians by a two-step process. First, he emphasized the manifold errors common in daily practice. Then he offered his instruments as reliable replacements for the current devices and procedures. The strategy was in essence a simple one: having highlighted existing disorders and abuses, the mathematical practitioner steps in to offer ready means for their reformation. This tactic was employed with both the carpenter's and gunner's rules. When writing on the carpenter's rule Bedwell gave an example of an artificer who, given a measure of breadth, will desire to find out what length of the material is needed to make up a square foot. But, 'because they know not how to do it truly or at least not readily, my purpose is by this instrument to show them how to perform the same with reasonable exquisiteness and marvellous speed and celerity'. 23 In the case of the gunner's rule Bedwell sketched a similar situation. Gunners measured the elevation of their pieces of great ordnance in inches and had a special form of rule for this task. It seemed to Bedwell that this procedure bred confusion and complexity. For, as each piece of ordnance was typically of a different length, mounting different pieces to the same elevation meant that each piece had to be raised to a different number of inches. In contrast, Bedwell's ruler was universally applicable and used not inches but degrees as a standard measure of elevation. 2+ As with the carpenter's rule, Bedwell was here diagnosing faults in contemporary craft practice and offering a mathematical resolution of them. The prime element in the reformation of errors was the replacement of familiar craft instruments with those newly devised by the mathematical practitioner.

Bedwell presumed that the errors in craft practice arose from the mechanicians' lack of arithmetic and geometry. He likewise did not expect such artificers to understand the construction of his new instruments: 'it is enough for them to know that it is so, although they be altogether ignorant why it is so'. 2s Bedwell claimed that their ignorance was no disparagement to artificers. In this he was more than a little disingenuous. At the very least, an aspiring artisan would have been sharply stung by Bedwell's critical comment, since it provided the precise rationale for the existence and superior status of the mathematical practitioners. 26 It is therefore no accident that the

23 Tanner, fol. 2'. 24 Laud foi. 3 '-v. Bedwell was aware of the gunner's quadrant proposed by Tartaglia which also measured

elevation in degrees or in equal parts of a geometrical square. However, Bedwell offers a reason for favouring his ruler. The quadrant is a much more dangerous instrument for its user since elevation is measured at the cannon mouth. If, as with his ruler, the elevation can be taken at the breech end of the piece, the gunner need not be exposed to enemy fire in combat.

25 Tanner, fol. 1 r. 26 Robert Norman, the mechanician responsible for discovering the dip of the magnetic needle, certainly

felt arguments of this sort to be a disparagement to his status as an expert artisan. He defended himself against the learned, who wished to reduce the mechanician to no more than a drudge incapable of any intellectual contribution. See The Newe Attractiue (London, 1581), sig. Bi v.

Dow

nloa

ded

by [

Geo

rge

Mas

on U

nive

rsity

] at

13:

51 1

0 O

ctob

er 2

014


theme of 'vulgar errors' is so common to the practitioners' vernacular literature of mathematics. Not only was the theme proclaimed within texts, but it was even broadcast on title pages. On the subject of surveying there is Edward Worsop's A Discoverie of sundrie errours and faults daily committed by Landmeaters, ignorant of A rithmetike and Geometrie (1582); a more famous example is Edward Wright's Certaine Errors in Navigation (1599), and instances both in England and abroad could be multiplied.

Bedwell's manoeuvre against the common sort of artificer (if not necessarily the more able) should make us suspicious of Christopher Hill's overly narrow alignment of the interests of mathematical practitioners and craftsmen. 27 We should not assume that the revaluation of the mechanical arts enforced a positive revaluation of all mechanicians. 2a Newly engaged, with affairs that had previously been the exclusive concern of mechanicians, practitioners such as Bedwell used the theme of craft errors as a powerful weapon with which to dislodge craft interests and justify their own claims.

What was the response of mechanicians to the cultural politics of the mathematical practitioners? We have no record of the views of the vast majority of artisans; however, a significant number of the most able and.articulate shifted their allegiance to the mathematicalls and accepted the claims of the mathematical practitioners. We can see the implications of this new affiliation in the case of one Richard More who, in 1602, published a book on mensuration which, like Edward Worsop's surveying text before it, at tempted to mediate between existing vernacular texts of mathematics and craft practice. Again, like Worsop, More accepted and promoted the programmatic rhetor ic of the mathematicalls. Even in his title he adopts familiar themes: The Carpenters Rule. . . With a Detection of Sundrie great errors, generally committed by Carpenters and others in measuring of Timber. However, unlike Bedwell, More was no graduate, but rather a craft member of the Carpenters ' Company. 29 But More's authorities were no longer his brethren in the Carpenters Company; instead they were the mathematical authors to whom he was subordinate in learning and status, a~ According to More 's recommendation, aspiring artificers should attend the recently-founded Gresham College to directly meet their new masters, al

Thus More did not dispute the legitimacy of the mathematical practitioners' position. Indeed, his work is indirect evidence of the practitioners' success in carving out a space for themselves. Bedwell, one of the architects of this success, was also ultimately a beneficiary, for More was to publicize the carpenter's rule after Bedwell's death:

While this book was in printing I came to the sight of a ruler sometime invented by one Master Bedwell; which, as it is easy, so it is most speedy, and not less

27 Intellectual Origins of the English Revolution, corrected edition (Oxford, 1980), chapter 1, 'London Science and Medicine'.

2a Paoio Rossi, Philosophy, Technology and the Arts in the Early Modern Era, translated by S. Attanasio (New York, 1970), pp. 29-30. Rossi distinguishes the general process of the revaluation of the mechanical arts from the particular changes in the status of mechanicians. Rossi's stress on upward mobility and harmonious co-operation between artisans and intellectuals should be qualified by a more extensive consideration of strategies such as Bedwell's.

29 More identifies himself as a carpenter on his title page. For his membership of the company, see A. M. Millard, Records of the Worshipful Company of Carpenters, vn, Wardens' Account Book 1592-1614 (London, 1968), where he is indexed as Richard Moore.

30 See his citation of authors in The Carpenters Rule (London, 1602), p.56. 31 Ibid., sig. A4".

Dow

nloa

ded

by [

Geo

rge

Mas

on U

nive

rsity

] at

13:

51 1

0 O

ctob

er 2

014


certain (being truly made), for the measuring of timber and board; which I expect and hope will be shortly published for the common good. 32

More is therefore a representative of those mechanicians who sought an alliance with the mathematical practitioners. The crucial point is that he did so on the practitioners' terms: he stood to gain from the newly-fashioned prestige of the mathematicalls only by accepting the programme and values of the practitioners. More takes up the task of preaching the mathematicalls and reforming craft errors from within.

Bedwell's conception of the mathematical practitioner's role thus had major repercussions for the status of mechanicians. Bedwell presented himself in a space between gentlemen and artificers, between patrons and craftsmen. In doing so he marked out the boundaries of his own independent cultural territory, characterizing those mechanicians unable or unwilling to come to terms with the programme of the mathematicalls as inferior in status and authority. Such men were required to accept the guidance of the practitioner, just as those who did not understand why the practitioners' instruments worked 'must leave (the reason) unto the learned in the mathematical arts'. 33

2.3. The indispensable citizen Bedwelrs efforts to achieve a secure career and to annex an area of cultural terrain

for the mathematical practitioners were largely successful. But his task was not complete. For, once defined, how was the position of the mathematical practitioner to be safeguarded and maintained? How could the practitioner remain in constant demand, rather than being an occasional contributor of ingenious inventions which would then be appropriated by others? How did BedweU prevent his instruments from being absorbed into craft culture and reproduced there, leaving him a redundant and marginal figure? As we have just seen, the longer-term solution was to negotiate a settlement with the leading mechanicians. In the short term, Bedwell's solution to the problem was to make himself indispensable by controlling both the manufacture of his instruments and the knowledge of their use. When writing about his instruments he gives explicit attention to both these issues--production and dissemination--and makes clear his wish to become an obligatory passage point to which all users had to resort.

Bedwell experienced a tension between the wish to publicize his devices and to retain control over their fate, a tension that was particularly acute in the case of the carpenter's rule. The title page of his tract on the instrument suggests his anxiety to capture as wide a readership as possible. He considered that it would serve for

architects, carpenters, masons, bricklayers, joiners, glaziers, painters, tailors & diverse other artificers, as also for geographers, hydrographers, surveyors, landmeaters, and generally for all gentlemen and others taking pleasure in any of these faculties.

32 Ibid. Bedwelrs ruler continued to be used, even before it was advertised and described in print by his nephew William Bedwell. It was probably part of the instrumental repertoire of contemporary mathematicians. Certainly, Henry Briggs was offering instruction on its use in 1607: Briggs to Ralph Clarke in Correspondence of Scientific Men of the Seventeenth Century, edited by Stephen Jordan Rigaud, 2 vols (Oxford, 1841), i, 1-3

33 Tanner, fol. 1".

Dow

nloa

ded

by [

Geo

rge

Mas

on U

nive

rsity

] at

13:

51 1

0 O

ctob

er 2

014


These aspirations towards an almost universal audience were not uncommon among mathematical practitioners, yet Bedwell held this text back from the press and relied on a more restricted manuscript circulation. 3a He explained his decision not to print the manuscript (which contained neither an illustration not details of construction) by his desire to regulate the making and use of the instrument:

I have not set down the order of making it because as the invention of it was very secret, so the description of it must be very exquisite: which cannot well be done by any common mechanic or handicrafts man; therefore I thought it good as yet to let it go, only by tradition from one to another, a5

Thus, in order to control the manufacture of the instrument, Bedwell employed a crude, but perhaps effective, tactic: he simply kept its delineation a secret. Bedwell envisaged himself as the sole supplier of his carpenter's rule: withholding the instrument's construction was meant to prevent any unauthorized copying, a6 He was not alone in this ambition. When Galileo eventually had his treatise on the sector printed in 1606, he used exactly the same tactic in an (unsuccessful) attempt to retain complete control over his invention. 37

Bedwelrs success is harder to gauge. He probably had good reason to doubt the copying abilities of an ordinary, unsupervised mechanician. Richard More, the carpenter who commended Bedwell's ruler (providing it was truly made), indicates that carpenters usually made their own rulers by copying another workman's. When the copying was done blindly, without an understanding of the instrument's construction, the result was a ruler whose scales for measuring board and timber were inaccurately engraved and graduated, as Bedwell, in reserving to himself the privilege of making his own form of carpenter's rule, was evidently trying to circumvent just such problems of craft practice. As a consequence, anyone who wished to use the ruler, whether artificer or gentleman, had to acquire an example from Bedwell himself. Bedwell's continuing monopoly not only helped to secure his livelihood, it also maintained him in the role of mathematical practitioner, separate from craft practice. In addition, by preventing the appearance of unlicensed and inaccurate examples he preserved his reputation from discredit.

These same issues of production and distribution were also at the heart of Bedwell's decision not to print his tract on the gunner's rule. First of all, he targeted a very

34 Tanner is evidently the work of a copyist: it ends 'Finis 1596', the year after Bedwell's death. Laud is a neat copy, presumably prepared by a scrivener and possibly corrected by Bedwell himself. It does not have a dedication, but may have been intended for presentation. There are two manuscripts in the collection of the Earl of Macclesfield 'for the delineation of Bedwell's ruler'. These treat the carpenter's rule, but may be adaptations of Bedwelrs tract or, more probably, independent compositions dealing only with the construction of the instrument. See Rigaud (footnote 32), I, 3.

35 Tanner, fol. I r. 36 He may have actually made the instruments himself. He appears to suggest this when writing on the

gunner's rule: 'I have made some of the plates differing in some small points from this form' (Lau d, fol. 3*). However, within the conventions of sixteenth-century authorship, this could equally be taken to mean that Bedweli had closely supervised the making of slightly variant forms of the rule.

37 Operations of the Geometric and Military Compass, 1606, translated by Stillman Drake (Washington, D.C., 1978), p. 41, and Drake's introduction pp. 24-5.

3s More (footnote 30), p. 2. 'As those strikes and divisions agree not with the truth, so upon diverse rules you shall find them to disagree one from another, yea, hardly shall you see two rules that do everywhere agree. Neither is this error insensible, and so not to be respected; but apparently gross, and therefore not to be tolerated . . . . Neither is this error rare and in some alone, but so general as that ifa man would examine them he should be forced to say that true rules are very scant.' (Ibid.)

Dow

nloa

ded

by [

Geo

rge

Mas

on U

nive

rsity

] at

13:

51 1

0 O

ctob

er 2

014


particular audience for text and instrument. The treatise was 'to be communicated only with those whom it shall most especially concern', this being taken to include faithful English gunners and officers of the ordnance, 'such as are devoted to her Majesty ') 9 Certainly, neither text nor instrument were to be carelessly distributed. Bedwell tried to ensure that only authorized users could benefit from the device:

I have purposely not set down upon the ruler any floes, marks or ciphers to declare the uses of the lines or of the moving plate or scale, whereby any man that shall find this ruler by chance shall never know to what end or use it is made. . , except he shall understand it by this description, or by tradition. Which I have done partly to avoid confusion among the lines and figures, but chiefly for that I would not have this invention over readily to be known or spread into other nations. 4~

Even the use of the vernacular could thus be justified on grounds of national security: writing in English made the text more accessible to unlearned compatriots but much more difficult for foreigners. 41 More generally, the absence of any explanatory inscriptions on the instrument was designed to restrict its use to those who had either received direct instruction from Bedwell or who had been allowed access to a copy of the accompanying manuscript. As with the carpenter's rule, the manuscript contains no account of the instrument's construction and, in particular, no account of the all- important engraving of its lines and scales. While the determined historian can readily grasp the principles of the instrument, its complete reconstruction would require more numerical examples than Bedwell was prepared to give. His contemporaries would have had no more luck in divining its detailed form. 42

Bedwell's attempts to define and establish the role of the mathematical practitioner thus comprised various elements: securing patronage; revaluing the status of unlearned mechanicians; displacing their instruments; and controlling the manufacture and use of his replacements. In combination, these elements were intended to ensure that Bedwell should be treated as an indispensable citizen and practitioner. What consequences for the perception of mathematics were occasioned by the full range of Bedwell's strategies? The reader of his texts or the user of his instruments was not to imagine their author as a conjuring astrologer, or a solitary and uncivil scholar, removed from the affairs of the commonwealth. Rather, mathematics was to be seen as plain and profitable, fit for the pressing demands of the state or the needs of the individual. More particularly, mathematics was to be construed as a body of procedural rules relevant to worldly affairs. It was a contemporary commonplace to define an art as a system of ru les . 43 But in Bedwell's usage 'rule' is used interchangeably to refer both to geometrical and

39 Tanner, fols 1", 2". 40 Laud, foi. 2 r. 41 Note that Thomas Digges also decided to restrict his future writings on artillery to the vernacular:

Pantometria, second edition (London, 1591), p. 176. 42 BedweU's secrecy and reluctance to publish indicate that it was not only craftsmen who were unwilling

to divulge the secrets of their trade. This aspect of Bedwell's work requires more sustained attention and a larger comparative context than is possible here. For general comments, see Elizabeth Eisenstein, The Printing Press as an Agent of Change, 2 vols in 1 (Cambridge, 1980), chapter 6, 'Technical literature goes to press'.

43 Petrus Ramus, for example, repeated Galen's definition: 'Ars est systema praeceptorum universalium' (cited by W. Tatarkiewicz, 'Classification of the Arts', in Dictionary of the History of Ideas, edited by Philip P. Wiener, 5 vols (New York, 1973-4), I, 456-62 (pp. 456, 459). Note that Edward Worsop has one of the participants in his dialogue realize that 'Euclid's Elements is a book of mathematical rules, and that by the knowledge of those rules mathematical operations are performed' (footnote 1, sig. G2").

Dow

nloa

ded

by [

Geo

rge

Mas

on U

nive

rsity

] at

13:

51 1

0 O

ctob

er 2

014

330 Stephen Johns ton

arithmetical rules and to their embodiment as instruments. Through this blurring of the intellectual content of mathematics and its material rules, mathematics itself takes on the character of an instrument. Presenting the mathematical ls as instrumental reason, the mathematical practit ioners were able to persuasively argue that their form of expertise was essential to the state.

3. Thomas Hood: mathematics in public Thomas H o o d (c.1557-1620) seems at first sight to have had a career remarkably

similar to that of BedweU" they were both graduates and then fellows of Trinity College, Cambridge, before passing on to ' the profession of the mathematicalls ' . Moreover , as with Bedwell, mathematical instruments were crucial resources in H o o d ' s activity as a mathemat ical practitioner. However, these similarities mask large differences in their practice of the mathematical arts. While I shall no t pursue a point-by-point compar i son of their work, my account of Bedwell sets the agenda for that of Hood . Wha t emerges is an alternative definition of the practi t ioner 's role, a role grounded in the public and commercial context of London.

3.1. M a t h e m a t i c s and medicine as careers

H o o d has been identified as one of Elizabethan London ' s successful mathemat ical practitioners, the range of his activities qualifying him as an exemplary figure: he was the city's first public mathemat ical lecturer (1588-1592), and during the 1590s he worked as author , editor, and translator of mathemat ica l texts, as well as devising instruments and producing navigational charts. 44 It is just these activities that I want to interpret. Yet I want to begin with a broader view of his career, which the focus on his work as a mathematical practi t ioner has hitherto obscured. By making this initial detour I hope to clarify the nature of his commi tment to the mathematicalls.

Hood ' s career began at Cambridge where, after receiving his M.A. in 1581, he became the university's mathematical lecturer for the academic year 1581-2. 45 He then moved on to medicine in which he gained his university licence to practise in December 1584. 46 This degree enabled H o o d to practise as a physician anywhere in England

44 Taylor (footnote 2), pp. 40-1, 179; Francis R. Johnson, Astronomical Thought in Renaissance England: A Study of the English Scientific Writings from 1500 to 1645 (Baltimore, 1937), pp. 198-205; D. W. Waters, The Art of Navigation in England in Elizabethan and Early Stuart Times, second edition (Greenwich, 1978), pp. 185-201; Hill (footnote 27), pp. 33-4. Even Mordechai Feingold, whose interpretations often sharply differ from those of Taylor, Johnson, Waters, and Hill, agrees that Hood 'embarked upon a successful career as a mathematical practitioner in London', see The Mathematicians' Apprenticeship: Science, Universities, and Society in England, 1560-1640 (Cambridge, 1984), p. 50.

,,5 Hood's formal education actually began under Richard Mulcaster at Merchant Taylors' School on 7 November 1567 (C. J. Robinson, Register of the Scholars admitted into Merchant Tailors' School 1562-1874, 2 vols (1882), I, p. 10). Hood's father, also called Thomas Hood, died before his son reached school age. His will is dated 24 June 1563, and it was proved 3 July 1563 (PRO PCC 27 Chayre). Hood's early Cambridge details are: matriculated pensioner 1573, scholar 1575, B.A. 1578, fellow 1579, and M.A. 1581, see Venn and Venn (footnote 6), n (1922), 402. Hood's tenure of the mathematical lectureship is recorded in Grace Book Delta, edited by J. Venn (Cambridge, 1910), p. 356 and in Cambridge University Archives, University Accounts, 2 (1), p. 279. For the lectureship from the 1560s to the 1640s, see Feingold (footnote 44), pp. 50-3; on its earlier history, see Paul Lawrence Rose, 'Erasmians and Mathematicians at Cambridge in the Early Sixteenth Century', Sixteenth Century Journal, 8 (Supplement) (1977), 47-59.

46 Grace Book Delta (footnote 45), pp. 388-9. Hood continued to receive his fellowship money from Trinity at least until 1583 and probably during 1584, though the Bursar's Books are missing for the latter year, see Innes (footnote 6), p. 7.

Dow

nloa

ded

by [

Geo

rge

Mas

on U

nive

rsity

] at

13:

51 1

0 O

ctob

er 2

014

El izabethan mathemat ica l pract i t ioners and instruments 331

except for London , which was regula ted by the Roya l Col lege of Physicians. H o o d ' s activit ies in the next few years are no t recorded. However , by 1588, ma themat i c s was again at the centre of his a t ten t ion and in N o v e m b e r of tha t year he began his publ ic ma thema t i ca l lec tureship in London ; for the next four years he was active in the capi ta l as a ma thema t i ca l prac t i t ioner . Nevertheless , be tween 1593 a n d 1595 he was back in Cambr idge , where he t o o k up his medica l studies again; when he once more m a d e his way to L o n d o n it was now with the tit le D o c t o r in Physic. Yet, in L o n d o n from 1595 to 1597, H o o d was work ing as a ma themat i ca l ra ther than medica l p rac t i t ioner and it was only after this two-year pe r iod tha t he set t led as a physic ian , the occupa t ion in which he appa ren t ly con t inued unt i l his dea th more than twenty years later. 47

W h a t becomes evident f rom even this briefest of out l ine sketches is tha t H o o d d id no t devote himself solely to the pract ice of mathemat ics , bu t r a the r shut t led back and forth be tween ma thema t i c s and medicine. F o r his con tempora r i e s , this pa t t e rn of deve lopmen t would have been nei ther ent irely unfami l ia r n o r dis turbing. O n the Cont inent , professors of medic ine typica l ly had p re l iminary teaching experience of ma thema t i ca l discipl ines such as a s t ronomy. 48 Closer to home, the physic ians Rober t Recorde and Wi l l i am C u n i n g h a m p rov ided no tab l e precedents th rough their ver- nacu la r ma thema t i ca l pub l ica t ions of the 1540s and 1550s. Clearly, the pursu i t of medic ine as a career d id no t exclude the cul t iva t ion of ma themat ics . Yet I want to argue that , in fashioning the role of ma themat i ca l p rac t i t ioner , H o o d was a t t empt ing to pursue the ma themat i ca l l s no t as an act ivi ty c o m p l e m e n t a r y to medicine, but as an independen t a l ternat ive. Ma thema t i ca l pract ice was to p rov ide a l ive l ihood in itself, and when H o o d became publ ic ma themat i ca l lec turer in late 1588, he was e m b a r k i n g on a novel venture which ran con t r a ry to the t ide of expec ta t ion , peer pressure, and advice which his C a m b r i d g e educa t ion provided . 49 But if, as I suggest, H o o d was indeed commi t t ed to the ma themat ica l l s in this way, it might be a sked why he m o v e d so frequently between medic ine and mathemat ics . Before examin ing H o o d ' s ins t rumenta l

47 Hood's will was made on 14 March 1620 and proved 23 April 1620 (Woreester Record Office, Probate vol. 7, lois 296v-297~). Hood describes himself as 'doctor in Physic dwelling within the city of Worcester' (though he also had a house in the village of Shrawley, 8 miles distant). John Aubrey states more positively that Hood practised physic at Worcester ('Brief Lives', chiefly of Contemporaries, set down by John Aubrey, between the years 1669 and 1696, edited by Andrew Clark, 2 vols (Oxford, 1898), l, p. 409). It does seem likely that Hood acted as a physician in and around Worcester, but we have no idea when and why he left London.

48 On the general European pattern of connection between the roles of mathematicus and medicus, see R. S. Westman,'The Astronomer's Role in the Sixteenth Century: A Preliminary Study', History of Science, 18 (1980), 105-47.

49 By the 1580s, Cambridge was established as a small but effective centre of medical training, and the medical faculty students could look forward to a secure career as either a country or London physician. See Margaret Pelling and Charles Webster, 'Medical practitioners', in Health, medicine and mortality in the sixteenth century, edited by Charles Webster (Cambridge, 1979), pp. 165-235 (p. 200). One of Hood's older Cambridge contemporaries, Lancelot Browne, provides an example of the more standard career that Hood could have chosen to follow. Browne was university mathematical lecturer from 1568 to 1570, before medicine fully occupied his studies. His licence to practise came in 1570 and his M.D. in 1576. Thereafter he moved to London where he was elected a member of the Royal College of Physicians in 1584. However, Browne's successful pursuit of a London medical career did not rule out the amateur cultivation of his earlier mathematical interests: as late as 1602 he assisted Thomas Blundeville in his Theories of the Seven Planets and he received the dedication of Thomas Oliver's De rectarum linearum parallelismo et concursu doctrina geometries (1603). The mathematical arts thus remained worthy of the occasional attention of the learned physician, but they did not provide a career. For Browne, medicine offered the best route for the ambitious graduate and he recommended its study to Gabriel Harvey, even giving him a reading list. See Dictionary of National Bio#raphy, Athenae Cantabrigienses (footnote 7), Feingold (footnote 44), p. 50, and Pelling and Webster (above), pp. 193, 2(14-5.

Dow

nloa

ded

by [

Geo

rge

Mas

on U

nive

rsity

] at

13:

51 1

0 O

ctob

er 2

014


concerns in detail, some explanation of the convoluted path of his career should be offered.

The place to begin is with the mathematical lectureship. Hood's first lecture of 4 November 1588 was given at the house of one of the main backers, the merchant Thomas Smith. Afterwards, the venue moved to the Stapler's Chapel in the Lcadenhall where it was to remain. However, the lectureship was not indefinitely guaranteed, and Hood first brought it up for renewal after an initial period of two years. With some vigorous lobbying of the Privy Council and the City of London, he secured an extension for a further two years.5~ But in 1592, Hood was not successful in prolonging his tenure, and by the end of the year he had ceased to call himself the city's mathematical lecturer. 51 Yet he almost certainly did not give up this position willingly. Five years later the mathematical author and divine William Barlow lamented the lack of mathematical teachers in London; he continued in melancholy vein:

But greater is the grief unto diverse well willers of that noble City, and lovers of good Arts, that whereas not many years since there was a Mathematical Lecture erected.., and furnished with a learned man of sufficiency answerable, of very honest and courteous behaviour, affable to resolve beginners of their doubts; the party was afterwards dismissed and the thing (that began to be so great a commendation to the founders, so principal an ornament to the City and a commodity both unto it and the whole Realm in general) was notwithstanding without all regard basely suffered to sink and vanish in the end unto nothing. 52

Why was Hood "dismissed'?. The ostensible reason was given by John Stow in his Survey of London: the mathematical lectureship was displaced out of its home in the Stapler's Chapel when it and the rest of the Lcadenhall was taken over and used as a storehouse for goods from a captured 'Spanish' carrack, s3 Once 900 tons of plunder were accommodated, there was no room left for Hood and his listeners. No doubt the reasons for the leetureship's demise ran deeper than Stow knew, and ultimately Hood must have failed to persuade the city authorities that he deserved their further support. Ironically, although it may have been due to lack of civic will (or deliberate desire to save the city the cost of Hood's wages), the pretext was provided by the success of English oceanic navigation and the triumphs of privateering.

After the end of the lectureship, Hood briefly continued with private teaching. But, with the removal of a major source of income, he did not long sustain his role as mathematical practitioner; instead, he returned to Cambridge to resume his study of

no Hood to Burghley, BL Lansdowne Ms 101/12, printed in A Collection of Letters Illustrative of the Progress of Science in England, edited by James Orchard Halfiwell (London, 1841), p. 31.

51 By contrast with his earlier publications, Hood's title is conspicuously absent in his 1592 edition of William Bourne's Regiment for the Sea, which was entered in the Stationers' Register on 20 December 1592.

s2 William Barlow, The Navigators Supply (London, 1597), sig. K2 v. s3 John Stow, The Survey of London, edited by A. M. (London, 1618; first published 1598), p. 122. Stow's

brief notice of the mathcmatieal lecture has come to be regarded as unreliable because he garbled the chronology of its foundation. He was, however, well informed on the end of the lectureship. The carrack was actually the Portuguese Madre de Digs, captured by Walter Ralegh's privateering fleet and brought back to Dartmouth on 7 September. Various contemporary accounts of the action leading to the capture of the ship and its immensely valuable cargo survive: see Kenneth R. Andrews, English Privateering Voyages to the West Indies 1588-1595, Hakluyt Society (Cambridge, 1959), p. 188, n. 1. Hakluyt gives an inventory of merchandise stored at the Leadenhall, dated 15 September 1592 (R. Hakluyt, Principal Navigations, 12 vols (Glasgow, 1903~}, wl, 116). This is a misdating and should be corrected against BL Lansdowne 70/89, dated 15 December 1592.

Dow

nloa

ded

by [

Geo

rge

Mas

on U

nive

rsity

] at

13:

51 1

0 O

ctob

er 2

014


medicine. These Cambridge studies were successfully prosecuted, and it was now as Dr Hood that he made his way back to London in 1595, with the intention of establishing himself as a London physician. In order to practise in London, Hood ' s 1584 Cambridge medical licence was insufficient, and he needed to obtain a fresh licence from the Royal College of Physicians. If Hood had expected medicine to provide a more permanent and secure career than mathematical practice could offer, he was to be rudely shaken. Examined on 17 October 1595, he was refused a licence by the College and ordered to improve his knowledge of Galen.54 Faced with this setback, and expressly forbidden to earn a livelihood as a physician, Hood was placed in a difficult position. He compared himself to Odysseus, whose harsh reception on returning to the island of Aeolia did not match the fond farewell he had previously been given. 5s

Some said they could not, some durst not for fear, and some answered they would not help to repair that loss which the unkind Nor thern blast had enforced me to . . . . I suffered it all, and bare it out, not lying still as a man careless, but knowing mine head and hands (under God) to be my best friends, I set them to their old occupation again, teaching the mathematical arts, and penning or translating such books as I thought most convenient for that purpose. 56

Hood 's return to the mathematicalls in 1595 was, therefore, not by choice but from urgent necessity. As before, his living came from private teaching, chartmaking and, most visibly, publication: he had two new texts printed and reissues of two earlier works also appeared. However, Hood still sought to become a properly licensed physician and, after again failing to demonstrate a satisfactory knowledge of Galen on 25 February 1597, he was finally granted a conditional licence on 5 August 1597. s7 Clearly, Hood ' s mathematical work during this period was undertaken as a stopgap measure until he could convince the Royal College of Physicians of his Galenic orthodoxy. Once legitimately able to act as a London physician, Hood 's stream of mathematical publications dried up. His last new text, a book on the mathematical instrument known as the sector, must have been written in the summer or autumn of 1597 and was entered in the Stationers' Register on 5 December 1597. 5a There is no need to assume that Hood suddenly lost all interest in the mathcmaticalls for, as has been shown above, mathematics was perfectly compatible with the practice of medicine. But mathematical authorship had been part of his livelihood as a mathematical practitioner and, once established as a physician, Hood no longer had pressing reasons for publication. His only subsequent item to come from the press was a 1601 reissue of his edition of William Bourne's Regiment f o r the Sea, in which Hood promised a larger

54 George Clark, A History of the Royal College of Physicians of London, 3 vols (Oxford, 1964-72), 1, 165. Hood is referred to as 'Dr Thomas Hudd of Cambridge', though he is later termed Dr Hood. This is the only definite evidence that he received his M.D. from Cambridge, where almost no official records of the university survive for the period 1589 to 1601 (J. Venn and J. A. Venn, The Book of Matriculations and Degrees... in the University of Cambridge from 1544 to 1659 (Cambridge, 1913)).

s5 Odyssey, translated by E. V. Rieu (Harmondsworth, 1946), Book 10, pp. 155-7. 56 Dedication to Hood's translation of Christian Urstitius' The Elements of Arithmeticke (London, 1596).

Hood is described on the title page as "Doctor in Physic, and well-wilier of them which delight in the Mathematical Sciences'.

s7 Clark (footnote 54), pp. 165-6. ss Short Title Catalogue, second edition. The title was The Making and Use of the Geometricall

Instrument, called a Sector (London, 1598).

Dow

nloa

ded

by [

Geo

rge

Mas

on U

nive

rsity

] at

13:

51 1

0 O

ctob

er 2

014


navigational text of his own, T h e M a r i n e r ' s E a s e . 59 Significantly, this promise of further publication was not fulfilled, and nor were the others which he had made through the 1590s. 6~

Reviewing Hood's career, it becomes clear that only during the period 1588 to 1592 did he attempt to build a permanent role for himself as a mathematical practitioner. Aside from the temporary and unplanned return to mathematical practice in the mid- 1590s, it is therefore Hood's four years as public lecturer which provide the best evidence of his perception and practice of the mathematicalls. It is therefore on this short period that the remainder of this case study will primarily focus.

3.2. A u d i e n c e s a n d i n s t r u m e n t s

For the period 1588 to 1592, Hood had a new kind of audience: not the group of readers to whom an author would appeal, but an assembly gathered to listen to his public mathematical lectures. During these four years he was principally accountable to the 'friendly auditors of the mathematical lecture' and, perhaps paradoxically, it was to them as listeners rather than to the reader that his published prefaces were typically directed.

The circumstances of the lecture's foundation determined the original character of Hood's auditory. As a result of the Armada crisis of 1588 a civil militia had been hastily formed to defend London in case of invasion. The youthful captains of these 'trained bands' had little experience, and the mathematical lecture was part of their programme of training. The lectureship was approved by the Privy Council, and its establishment marks an important stage in the official acceptance of the mathematical arts. However, Hood did not significantly respond to the military circumstances of the lecture's origins: he never taught subjects such as fortification, gunnery, or the ordering of soldiers in the field. Not that he was unaware of these topics: in his first lecture he mentioned gunnery and martial affairs, but gave them no more prominence in his sketch of the mathematicalls than was accorded to geography, topography, hydrography, surveying, mining, and water conducting. 61 Indeed, it is Hood's distance from the military context which is striking. The Armada crisis saw Thomas Bedwell mobilized to strengthen Gravesend blockhouse. Hood's 'mobilization' was of less immediate military relevance: in his first lecture he laid greatest stress on the intellectual value of astronomy and the service it rendered to physic, navigation, and the almanac.

However, it is Hood's regular teaching rather than his preliminary discourse that requires examination. During his tenure of the lectureship, he published four texts suitable for use in the lectures, of which three dealt with instruments. He wrote on his improvements to two versions of the cross-staff, 62 on his own pair of printed celestial maps, 63 and on the use of the celestial and terrestrial globes, the last text commissioned

59 William Bourne, A Regiment for the Sea, edited by Thomas Hood (London, 1601), fol. 19. 6o Hood undertook at various times to publish a full text (with demonstrations) of Ramus' geometry, a

treatise on dialling, a manuscript on Mercator's projection of the sea chart, and a completed translation of Simon Stevin's Geometrical Problems.

61 A Copie of the Speache: Made by the Mathematicall Lecturer (London, 1588). 6~ The use of the two Mathematicall instruments, the cross staffe . . . and the Jacob's staffe (London, 1590);

entered in the Stationers' Register 27 January 1590 (S/C, second edition). 6a The Use of the Celestial Globe in Piano, set forth in two hemispheres (London, 1590); entered in the

Stationers' Register on 4 September 1590 (S/C, second edition).

Dow

nloa

ded

by [

Geo

rge

Mas

on U

nive

rsity

] at

13:

51 1

0 O

ctob

er 2

014


to accompany the globes of Emery Molyneux. 64 His fourth publication from this period, intended to act as a handy epitome since it included neither demonstrations, diagrams nor accompanying text, was a translation of the propositions in the 27 geometrical books of Ramus' Scholae Mathematicae. 65 These publications indicate that in his lectures Hood drew his principal themes from geometry and cosmography. 66

From his publications it is clear that instruments played the major, though not exclusive, role in setting the didactic tone of Hood's lectures. Instruments defined and gave concrete embodiment to his chosen topics and were intended to make his teaching plain and accessible. 67 Does this mean that the lectures were immediately applicable to practical problems? Certainly, the improved cross-staff was designed to make solar and stellar observations easier and more accurate, while the 'Jacob's staff' version was expressly for tasks such as surveying. But the evidence suggests that we need a broader definition of 'use' to accommodate Hood's presentation of instruments.

Hood expected that his auditors would be moved as much by considerations of pleasure and polite accomplishment as practicality. In discussing his celestial maps he devoted many pages to the 'poetical fables' of the constellations represented in his two plates. These fables were devised

to make men fall in love with Astronomy, for many times it falleth out so among us, that albeit we are not willing to give ear unto a matter or to read a discourse because it is profitable, yet will we give ear unto it and take pains to read or hear it because it is pleasant. 6s

Hood's audience required more than practical and vocational stimulus. Knowledge of the globes evidently became a fashionable ornament, and acquaintance with the sumptuous sets issued by Emery Molyneux a gentlemanly obligation. 69 It is in just these terms that the pupil in Hood's dialogue expresses his desire to learn their use: 'forsomuch as they are now in the hands of many with whom I have to do, I would not be altogether ignorant in those matters'. ~~ These globes were not for the daily use of the

64 The Use of both the Globes, Celestiall, and Terrestriall (London, 1592). 65 The Eleraentes of Geometrie (London, 1590). Hood also wrote a now lost tract in 1591 in response to a

pamphlet by the astrologer Simon Forman, The groundes of the longitude (London, 1591). Forman claimed to have a method of finding the longitude, but he did not reveal his secret; Hood's reply was presumably dismissive. The existence of this pamphlet is known from two sources: Forman's diary records that on 'the 6 of July [1591] I put my book of the longitude to press .... The 22 of November Mr Hoods book came out Against me'; and Thomas Harriot refers to 'Forman's book oftbe longitudes..[and].. Hood's Answer to the same'. See David B. Quinn and John W. Shirley, 'A Contemporary List of Hariot References', Renaissance Quarterly, 22 (1969), 9-26 (p. 22). Hood's work was evidently polemical rather than didactic, and thus would not give direct evidence for the content of the mathematical lecture. Note that he also refers slightingly to Forman in the preface to The Use of Both the Globes (1592).

66 Hood lectured on at least two other texts, both of which confirm the teaching emphasis of his own books. Before the appearance of his own work on the globes he used Charles Turnbull's A perfect and easie Treatise of the Use of the coelestiall Globe (London, 1585) (see Globe in Piano (footnote 63), pp. 1 "-2 r, 13", 42r). Hood also used Francis Cooke's The Principles of Geometrie, Astronomie, and Geographie (London, 1591), a translation from Georg Henisch whose title page advertised that the text was "appointed publicly to be read in the Stapler's Chapel at Leadenhall by the Wor[shipful] Tho. Hood, Mathematical Lecturer of the City of London'.

67 For general comments on the didactic importance of instruments in the mathematical arts, with a particular study of John Aubrey's educational scheme of 1683/4, see A. J. Turner, 'Mathematical Instruments and the Education of Gentlemen', Annals of Science, 30 (1973), 51-88.

6s Globe in Plano (footnote 63), fol. 23 v. 69 On the Molyneux globes, see Anna Maria Crin6 and Helen Wallis, 'New researches on the Molyneux

Globes', Der GIobusfieund, 35-37 (1987), pp. 11-18, with references to earlier literature. 70 The Use of both the Globes (footnote 64), sig. BV.

Dow

nloa

ded

by [

Geo

rge

Mas

on U

nive

rsity

] at

13:

51 1

0 O

ctob

er 2

014


aspiring artisan or earnest craftsman, but were for the personal prestige and domestic display of wealthy gentlemen and merchants:

For it will be unto you a great disgrace, especially in this our travelling age, not to be cunning in these things; which cunning you may easily attain unto if you do but furnish your study with the globes and now and then as your leisure serveth look upon them. 71

Who then made up the audience for the lectures? When reviewing his first two years Hood remarked that 'in this time I have been diligent to profit not only those young gentlemen whom commonly we call the captains of the city, for whose instruction the lecture was first undertaken, but also all other whom it pleased to resort unto the same'. 72 The character of Hood's teaching made the lectures more useful to the captains as gentlemen than as military leaders. The fresh listeners drawn in by Hood would have found the cosmographical emphasis relevant to interests in navigation, trade and English expansion rather than martial prowess. 73 Whatever the initial intentions behind the lecture s , they were quickly tailored to those mariners, merchants, or gentlemen with a stake 'in this our trav.elling age'.

Hood's teaching was not restricted to the public lectures. During his time as lecturer he advertised his availability for private lessons, TM and after the end of the lectureship he continued this activity. Hood aimed at the same audience and used the same means as in the public lectures. For example, at the end of 1592 he brought out a new edition of William Bourne's Regiment for the Sea to which he appended an addition of his own, The Mariner's Guide. This was a short analysis of one of the navigator's principal 'instruments', the sea chart. While the text is more overtly practical than previous writings, Hood was not targeting a much more humble audience. His preface, 'To the industrious sailor's health and prosperity', immediately qualifies the identity of his expected reader by beginning 'Gentlemen sailors.. ?.75 Moreover, the pupil in the ensuing dialogue is not an ordinary mariner but someone of higher standing who has been to sea and wants to know about the charts which seamen use.

Unfortunately, aside from Hood's published comments, it is difficult to establish who would have resorted to Hood as a private teacher. By chance, however, the identity of one of his pupils is known because, in December 1595, Hood made an arrangement with the diarist Arthur Throckmorton, Walter Ralegh's brother-in-law. Throckmorton was no youth but a man probably a few years older than Hood himself--a substantial if not flamboyant or pre-eminent figure in court circles. Throckmorton's diary recorded the deal that was struck:

I bargained with Mr Thomas Hood to read geometry to me and do give him 20s. from this day weekly. Paid him for 3 pair of compasses 18d. the piece, and for a ruling compass 8d., and for one spring brass compass 14d. 76

71 Ibid. sig. M[8] r. 72 Elementes of Geometrie (footnote 65), dedication to Sir John Hart, Lord Mayor, and the Aldermen of

the City of London. 73 Hood himself appears to have been a backer of a proposed voyage by Ralegh, see The Roanoke

Voyages, 1584-1590, edited by David Beers Quinn, Hakluyt Society, 2 vols (London, 1955), n, 570. 74 Globe in Piano (footnote 63), foL 43", Use of both the Globes (footnote 64), sig. A4 *, M[8] r. 75 The Mariner's Guide (London, 1592), sig. Aiii r. Hood republicized his private availability as a teacher in

this work. 76 A. L. Rowse, Ralegh and the Throckmortons (London, 1962), p. 197. Shortly afterwards Throckmorton

put down a deposit of 5 shillings on a 'sphere' worth s (ibid.).

Dow

nloa

ded

by [

Geo

rge

Mas

on U

nive

rsity

] at

13:

51 1

0 O

ctob

er 2

014


Throckmorton's evidence not only confirms that Hood's teaching was directed at men of elevated social rank, but also re-emphasizes the primary role of instruments in Hood's didactic practice. Hood used instruments to appeal to a gentlemanly audience with a form of mathematics which was at once accessible, profitable, and pleasant.

3.3. London locations An important theme in the career of Thomas Bedwell was his attempt to position

himself socially between the roles of patrons and mechanicians, and within a steady sphere of military and state employment. Thomas Hood's cultural location is only partly captured by emphasizing the gentlemanly audience whose interests he engaged. To fully characterize Hood's role, we need to examine a broader range of his relationships. But rather than tackling the issue head on, it can be approached indirectly by first seeking Hood topographically rather than culturally.

How could Hood be found in London? He deliberately made it easy for his readers by notifying his whereabouts in print. For the duration of the mathematical lecture he could be found at Stapler's Chapel in Leadenhall where his books could be bought as well as his lectures attended. From 1590, he also began to give notice of his own address, first 'at my poor lodging in Abehurch Lane' and then, in 1592, 'a little beneath the Minories without Aldgate between the sign of the Red Lion and the Elm Tree'. Gentlemen and mariners seeking private instruction or wishing to purchase books, instruments, and charts therefore had exact directions for finding Hood.

Can we place Hood in the context of London life as readily as we can track down his addresses? Hood publicized his locations in order to advertise the items which he had for sale. He therefore occupied a space that was public and commercial. With whom did Hood negotiate working relationships? Whose trade and professional territories did his activities border? The range is extensive, from printers, chartmakers, engravers, and instrument makers to the teachers of arithmetic and accounts who pasted their advertising sheets around the city. 77 In this paper it is appropriate to examine just one aspect of the whole network of connections which Hood had to manipulate and sustain: his relations with instrument makers.

The mathematical instrument makers working in brass with whom Hood dealt were practitioners of a trade only recently established in London. 7a The boundaries of the craft were not drawn rigidly, and the makers found frequent employment engraving plates for books and maps as well as producing instruments. It was engraving and metalwork which formed the boundary between Hood and the craftsmen with whom he collaborated. On Hood's side of the boundary was not just writing and teaching, but

77 For the arithmetic and accounts teachers, see John W. Shirley, Thomas Harriot: A Biography (Oxford, 1983), pp. 73-4. As colleagues and competitors, Hood also established relations with other mathematical practitioners. Thomas Harriot was an associate (Quinn and Shirley (footnote 65), p. 13) and Hood became involved in a dispute with Simon Forman (see above, footnote 65). In The Use of Both the Globes, Hood also defended himself against the alleged slanders of Abraham Kendall.

7s G.L'E. Turner, 'Mathematical instrument-making in London in the sixteenth century', in English Map- Making 1500-1650, edited by Sarah Tyacke (London, 1983), pp. 93-106.

Dow

nloa

ded

by [

Geo

rge

Mas

on U

nive

rsity

] at

13:

51 1

0 O

ctob

er 2

014

Stephen J o h n s t o n 338

Figure 2. Thomas Hood as engraver (from The use o f the two Matheraaticall instruments, the cross staffe...and the Jacob's staffe). (Copyright the British Library.)

a lso d ra f t smansh ip : H o o d inves ted t ime a n d effort deve lop ing his d r a w i n g skill a n d he b e c a m e a n accompl i shed ch a r t ma k e r . 79 As well as t e ach ing the use of sea cha r t s he ac ted as a retailer , sel l ing examples of his o w n w o r k a l o n g wi th i n s t r u m e n t s such as

79There are three known charts signed by Hood: a 1592 chart of the West Indies (reproduced in F. Kunstmann, K. yon Spruner and Georg M. Thomas, Atlas zur Entdeckungsgeschichte Amerikas (Munich, 1859), pl. 13); a 1592 chart of the North Atlantic (engraved by Augustine Ryther for Hood's The Mariner's Guide; reproduced in A Regiment for the Sea and other writings on navigation by William Bourne, edited by E. G. R. Taylor, Hakluty Society (Cambridge, 1963), facing p. 130); and a 1596 chart of the Bay of Biscay and the English Channel (reproduced in D. Howse and M. Sanderson, The Sea Chart (Newton Abbott, 1973), pp. 46- 7). There are also two doubtful attributions: an English chart of the North Atlantic (BL Add. Ms 17938B), unsigned and undated (attributed by Henry Harisse, D~couverte et Evolution Cartographique de Terre-Neuve (London and Paris, 1900), p. 303n.); and a chart signed 'TH' (reproduced in R. A. Skelton and John Summerson, A Description of Maps and Architectural Drawings in the Collection made by William Cecil First Baron Burghley now at Hatfield House (Oxford, 1971), p. 39 and pl. 15). The last chart, which differs in a number of respects from Hood's standard practice and was made for Trinity House ('TH'?), was afterwards engraved and appeared with a royal proclamation of 1605 (STC, second edition, 10019). On charts or sea plats as instruments, see Robert Norman's dedication to his translation of The Safegarde of Saylers, or great Rutter (London, 1590): navigation or hydrography use 'many notable instruments, as Compass, Astrolabes, Plats, Quadrants... ' (sig. A2r).

Dow

nloa

ded

by [

Geo

rge

Mas

on U

nive

rsity

] at

13:

51 1

0 O

ctob

er 2

014


Figure 3. Augustine Ryther's engraving of the northern hemisphere of Thomas Hood's celestial map. (Copyright the British Library.)

Robert Norman's new variation compasses, s~ However, he did not seriously challenge the expertise of the makers in metalwork. Hood produced one crude diagrammatic cut for his book on the cross-staff and Jacob's staff (Figure 2). But this attempt was not intended to supplant the instrument makers and engravers. Rather, Hood relied on several such craftsmen. For example, his book on the sector may actually have been a collaborative venture with the instrument maker Charles Whitwell. Whitwell was advertised on the book's title page as the maker of the instrument and he may have

a~ Regiment for the Sea (London, 1592), fol. 71".

Dow

nloa

ded

by [

Geo

rge

Mas

on U

nive

rsity

] at

13:

51 1

0 O

ctob

er 2

014


commissioned Hood to write the text)1 But the detailed negotiation of respective roles between Hood and the instrument makers is most sharply evident in his relations with Augustine Ryther. s2

Hood twice worked with Ryther. On both occasions their collaboration was close although each performed separate and well-defined tasks: Hood did the drawing and Ryther the engraving. The relationship is encapsulated in the sea chart which accompanied Hood's Mariner's Guide (1592). The simple inscription reads 'T Hood descripsit, A Ryther sculpsit 1592'. Two years earlier they had also worked together in the production of Hood's two celestial maps (Figure 3). Hood defined his own responsibility in the book which described the use of the maps.

Inthe Hemisphere I have inscribed the stars and drawn the constellations with mine own hand, because I would be sure to have them rightly placed: and in that respect, if in the figures everything be not so exquisite as you would wish, excuse the matter because they were drawn by a scholar and not by a painter. 83

The mathematical practitioner has had his own drawings of the constellations copied on to the plate by the engraver and has even, it seems, gone so far as to inscribe the plate itself with the stars' positions.

Whereas Bedwell tried to define his role as a dominant one, controlling and supervising the work of mechanicians, a different and more cooperative model is required for Hood. Within his network of associates, colleagues, and competitors, Hood worked on the basis of a division of labour which left both himself and craftsmen such as the instrument makers independent. These considerations return us to the final issue raised by the work of Thomas Bedwell: how to create a role that made the mathematical practitioner an indispensable figure. Hood dearly did not succeed in this task. But the contrast with Bedwell helps to illuminate the reasons for his failure.

Bedwell's strategy was to control his audience by centralizing knowledge and status on himself. Within his relatively restricted milieu he aligned himself with the interests of gentlemen, patrons, and military administrators, and rhetorically placed himself between these social superiors and mechanicians such as gunners, carpenters, and masons. In contrast, Hood operated within an extended network of public associations. To span the diversity of this network, Hood needed social, financial, and personal skills in addition to the mathematical and technical competence which his role more obviously demanded. Like Bedwell he attracted the attention of gentlemen; but on a basis of practical accomplishment and pleasure rather than binding military necessity. His relationships with instrument makers, engravers, and printers were reciprocal: while enlisting them to serve his role as a mathematical practitioner, he was also contributing to their success. Moreover, with the discontinuance of the mathematical

sl The sector has often been credited as Hood's invention, independent of (and possibly earlier than) Galileo's similar device. But Hood made no claim to have devised the instrument and instead referred to it as an already familiar device: he described the instrument as it was 'commonly' made (The Making and Use of the Geometrical Instrument called a Sector (London, 1598) ft.5 v, 28v). There is a sector of this type by Robert Beckit, dated 1597, in the Museum of the History of Science, Oxford (illustrated in Turner, footnote 78). On Whitwell, see Joyce Brown, Mathematical Instrument-Makers in the Grocers' Company 1688~1800, with notes on some earlier makers (London, 1979), pp. 24, 60--1. Note that an additional engraving by Lenaert Terwoort of a cylindrical dial (dated 1591) was also used in Hood's book on the sector.

s2 On Ryther, see Brown (footnote 81), pp. 58-60, and Arthur M. Hind, Engraving in England in the Sixteenth and Seventeenth Centuries, 3 vols (Cambridge, 1952-64), l, 138-49. Note that in 1590, when Hood was lecturing at the Stapler's Chapel in the Leadenhall, Ryther's shop was 'a little from Leadenhall next to the Signe of the Tower',

s3 Celestial Globe in Piano (footnote 63), sig. A4 r.

Dow

nloa

ded

by [

Geo

rge

Mas

on U

nive

rsity

] at

13:

51 1

0 O

ctob

er 2

014


lectureship, Hood was addressing an uncertain market of buyers, users, and potential pupils. He was now dependent on an audience which he could not manage or regulate. At this point Hood gave up the attempt to persuade his contemporaries that, as a mathematical practitioner, he was personally indispensable to the commonwealth.

Should Hood's brief career from 1588 to 1592 be considered simply as a failure? I suggest that it should not. Although I have reinterpreted the course of Hood's career, I do not wish to diminish his recognized place within the contemporary culture of mathematics. Instead, I want to insist on the distinction between his personal career and his perceived role in promoting mathematics. Hood's prominent public advocacy of mathematics in the 1590s gave much greater currency to the mathematicalls than did the 'successful' career of Bedwell. To those contemporary readers personally unfamiliar with Hood, his publications formed a major point of reference in defining the character of mathematics. While Bedwell secured a position for the mathematical practitioner within the internal organization of the state, Hood's work became a resource for the public culture of the mathematicalls.

4. Mathematical cultures What conclusions can be drawn from these case studies of Thomas Bedwell and

Thomas Hood? Rather than simply summarize, this final section draws out the implications of their careers in order to more fully map the terrain of mathematics in Elizabethan England.

Having hitherto concentrated on just two practitioners, we should now take a wider view of the personnel of mathematical practice. The initial impression is of diversity: a mathematical practitioner might be an esquire or an expert artisan. That the practitioners were not restricted to a narrow range of the social scale can be simply demonstrated. For example, a perfunctory survey of authors might include Thomas Digges, a substantial landed gentleman and political figure; John Blagrave, a minor member of the gentry who briefly served in a noble household; William Bourne, citizen, gunner, and sometime port-reeve (mayor) of Gravesend; and Robert Norman, a sailor who became a compass and chart maker. Compared to this diversity, the Cambridge origins of Bedwell and Hood are all but identical; yet despite this indistinguishable training their careers followed quite distinct paths. We should, therefore, not expect to isolate any ideal or archetypical practitioners: there is no single role which encom- passes the full range of their backgrounds and livelihoods. But while recognizing the very considerable differences in their activities, audiences, and styles, it is equally important to insist on the common elements that united them.

The framework which tied together the practitioners was the idea of the mathematicalls. The seemingly all-inclusive list of arts--from geometry to surveying, navigation, gunnery, and a host of other disciplines--acted as an umbrella under which individuals with different areas of expertise could come together. Beyond the basic definition of a common domain, the sense of a joint project was fostered by the programmatic rhetoric of the mathematicalls. Differing expectations and aspirations could be settled by reference to a shared perception of mathematics as a vernacular, practical, accessible, and worldly activity. Commitment to these ideals was not just a matter for prefaces and declarations of faith, but could be demonstrated through the promotion and use of instruments. Indeed, instruments served as concrete embodi- ments of the practitioners' values.

Dow

nloa

ded

by [

Geo

rge

Mas

on U

nive

rsity

] at

13:

51 1

0 O

ctob

er 2

014


The mathematicalls thus became the practitioners' medium for public consensus on the aims of mathematics. But we need to go beyond the practitioners' perspective to determine both the success and the limits of the mathematicalls. From the point of view of wider public acceptance, success was neither rapid nor general: the culture of the mathematicalls would have had little impact on the illiterate majority in the rural population or the labouring poor. Rather, the audience was largely restricted to gentlemen and the literate urban classes of merchants and master craftsmen. Indeed, through Bedwelrs displacement of unlearned mechanicians, we can see mathematics contributing to a sharper distinction between the popular culture of the 'vulgar' and the perceptions of both the learned and middling sort. Moreover, despite emerging as the dominant public form of mathematics in the late sixteenth and early seventeenth centuries, the mathematicalls did not command universal assent from active matbema- ticians. One example will have to suffice to indicate that the culture of the mathematicalls was not all-embracing and that not every mathematician can be assimilated to it.

Henry Savile (1549-1622) is perhaps the most notable Elizabethan mathematician whose work was inspired by values quite different from those of the mathematicalls. In his lectures at Oxford (1570-5) and on his Continental tour (1579-82), Savile contributed to the restoration of mathematics and to the scholarly collection, collation, and emendation of manuscripts, s4 In this emphasis he is comparable to Italian mathematical humanists such as Commandino. s5 However, Savile's chief concern was with astronomy and his detailed technical and textual work aligns him with northern Europeans such as his correspondent Johannes Praetorius. s6 Savile did not publish his work and hence did not challenge the vernacular, practical, and instrumental character of the contemporary mathematicalls. Moreover, he sub- sequently moved on from mathematics to antiquarian, Biblical, and patristic studies. But his early mathematical work does indicate that despite the public consensus of the printed texts the culture of the mathematicalls was a limited and local phenomenon.

Savile's distance from the mathematicalls is additionally apparent in his attitude to r the practitioners' instruments. In 1619, he endowed professorships in geometry and astronomy at Oxford. John Aubrey recounts a story about Savile's recruitment of a suitable incumbent for the chair of geometry. Savile eventually appointed Henry Briggs, but only after he had first considered Edmund Gunter, then in London but originally an Oxford graduate. Gunter had responded to Savile's summons:

he came and brought with him his sector and quadrant, and fell to resolving of triangles and doing a great many fine things. Said the grave knight "Do you call this reading of geometry? This is showing of tricks, man!" and so dismissed him, with scorn, and sent for Briggs, from Cambridge. s7

a4On Savile, see Feingold (footnote 44), pp. 124-130. s5 See P. L. Rose, The Italian Renaissance of Mathematics (Geneva, 1975). s6 On Praetorius, see Robert S. Westman, 'Three Responses to the Copernican Theory: Johannes

Praetorius, Tycho Brahe, and Michael Maestlin', in The Copernican Achievement, edited by Westman (Berkeley, 1975), pp. 285-345.

a7 Aubrey (footnote 47), n, p. 215.

Dow

nloa

ded

by [

Geo

rge

Mas

on U

nive

rsity

] at

13:

51 1

0 O

ctob

er 2

014


For Savile, mathematics was primarily the demonstrative and textual work of the scholar. The instruments of mathematical practitioners such as Gunter appeared to Savile as trivial and superficial toys. ss

Once we begin to differentiate between distinct conceptions and forms of mathematics, then a number of thorny historical problems become more tractable. Among these is the much debated question of the universities' role in the teaching and practice of mathematics. The evidence from Bedweil and Hood points to the conclusion that the mathematicalls were to be found elsewhere. This is not to fall back on the caricature of the universities as sclerotic and tradition-bound institutions. There is no doubt that both BedweU and Hood came in contact with mathematics at university. In addition, Savile's teaching shows that advanced mathematics was possible at Oxford and Cambridge. But it was not part of the universities' function to produce mathematical practitioners. Accordingly, as even an apologist for the universities concedes, those graduates who participated in the culture of the mathematicalls did so after leaving their colleges for employment or livings elsewhere, s9 Bedwell and Hood are early representatives of this pattern, which can be seen in the careers of contemporaries and successors such as Thomas Harriot, Edward Wright, Henry Briggs, William Oughtred, and Edmund Gunter.

Where, then, did the mathematical practitioners work? On the Continent, and especially in Germany, royal courts provided an important answer. But England did not have a court culture which could offer substantial support to the activities of a mathematician. There was no equivalent in Elizabethan England to the courts of William IV of Hesse-Cassel or Rudolf II of Prague. At such European courts, the most able mathematicians and instrument makers secured patronage. 9~ In contrast, even John Dee, often referred to as Queen Elizabeth's astrologer, was unable to obtain the rewards and status which he felt were his due . 91 Rather than to a court milieu, historians rejecting the role of the universities have traditionally turned to London and its craft practitioners. Yet the case studies of this paper do not justify a step back to so simple a polarization. Certainly, with its instrument makers and printshops, London provided the chief location for the practice of mathematics. It also offered a new market for the products and teaching of the practitioners. However, the London audience for the mathematicalls was made up not just of craftsmen, but also, and of at least equal importance, of gentlemen. Moreover, as Hood discovered, plying the trade of mathematical practitioner did not bring easy rewards. There were no guarantees of success within the complex commercial world of London. Besides, London did not have a monopoly on the mathematicalls: as Bedwell's career shows, the mathematical practitioner was often on the move, engaged on a variety of projects.

sa Aubrey's anecdote may be exaggerated or apocryphal; Savile did in fact include reference to practical geometry in his statutes, see Mordechai Feingold, 'The Universities and the Scientific Revolution: the Case of England', in New Trends in the History of Science, edited by R. P. W. Visser et al. (Amsterdam, 1989), pp. 29- 48 (p.41). However, instruments were at the heart of other disputes on the character and teaching of mathematics. For the controversy between William Oughtred and Richard Delamain, see Turner (footnote 67).

89 Feingold (footnote 44), pp. 168-70. 9o Bruce T. Moran has published a number of articles on German princely courts, see for example

'German Prince-Practitioners: Aspects in the Development of Courtly Science, Technology, and Procedures in the Renaissance', Technology and Culture, 22 (1981), 253-74.

91 Nicholas H. Clulee, John Dee's Natural Philosophy: Between Science and Relioion (London, 1988), pp. 189-199.

Dow

nloa

ded

by [

Geo

rge

Mas

on U

nive

rsity

] at

13:

51 1

0 O

ctob

er 2

014

344 Elizabethan mathematical practitioners and instruments

Rather than seeking a single institutional or geographical home for the mathematical practitioners, it is therefore their cultural location which we should chart. This holds true not just for the Elizabethan incarnation of the mathematical arts. Once established in the sixteenth century, the essential form of the mathematicalls remained in place up to the nineteenth century. However, this subsequent history of the mathematical arts has largely been lost in the shadows of the histories of science, technology, and mathematics. Yet, although the name may have dropped out of fashion (the seventeenth century preferred 'the mathematicks'), the same constellation of disciplines and the same rhetoric continued to be employed. Moreover, the locations highlighted in the careers of Bedwell and Hood were also to be the major arenas for later mathematical practice. For example, in the operations of the state, Bedwell's position in the Ordnance Office is echoed by seventeenth-century careers such as that of Jonas Moore. 92 Hood's tentative steps as writer, chartmaker, retailer, and teacher were to be built on in the London marketplace of the seventeenth and eighteenth centuries. Once established, these locations regulated and directed the cultural and economic opportunities open to mathematical practice.

Acknowledgments I would like to thank Jim Bennett, Tim Boon, J.V. Field, and Frances WiUmoth for

their comments on drafts of this article.

92 See Frances Willmoth's paper in this issue of Annals of Science.

Dow

nloa

ded

by [

Geo

rge

Mas

on U

nive

rsity

] at

13:

51 1

0 O

ctob

er 2

014

Documents

Mathematical practitioners and instruments in Elizabethan England