manners unfaulted

I recently finished reading Hilary Mantel's new book, Bring Up the Bodies, and I liked it, every page. She's a marvelous writer, so good that it's difficult to pin down what she's doing that's so much better than anyone else does. Putting her work into the "historical fiction" warehouse doesn't make sense; it isn't genre, it's simply literature.

My affection for the book comes partly from my interest in the lives of early modern Englishmen who did not receive a university education. I've been studying one of them, the mathematician John Collins, and Mantel's subject, Thomas Cromwell, is another. The lives of the two men were very different. Cromwell lived a full century and a half before Collins and achieved wealth and power as an able politician and chief minister to a king (Henry VIII). Collins attained neither wealth nor power. He was a clerk, teacher, author, accountant, and, on the side, an "Ingenious Obstetrix of the Press promoting the laudable Design of getting Learned Men to impart their Labours to be Printed; and exciting others to encourage the same, as being of singular Use and advantage to the Republick of Learning; through the want whereof many Learned Mens Works of much worth have been lost, suppressed or long delayed."[1]

Nonetheless they were in some ways similar. Both were born "of low estate," Cromwell as son of a blacksmith and small businessman and Collins as son of a poor clergyman who was barred from preaching in any church. Both left England while young and, while on the Continent, gained knowledge and skills that served them well on their return home. Both were largely self-taught, learning more by experience than education. On returning to England both attracted the notice of high-placed men and used these contacts to advance themselves. Both married only once and were devoted to their wives and families.

I don't mark up books I'm reading, or turn down corners -- none of that. But I do occasionally write out something -- a phrase, line, paragraph, or page -- that seems especially meaningful and this I chose to scribble into my Moleskine from Bring Up the Bodies. In it we see Cromwell's thoughts about his son:

Gregory is a good boy, though all the Latin he has learned, all the sonorous periods of the great authors, have rolled through his head and out again, like stones. Still, you think of Thomas More’s boy: offspring of a scholar all Europe admired, and poor young John can barely stumble through his Pater Noster. Gregory is a fine archer, a fine horseman, a shining star in the tilt yard, and his manners cannot be faulted. He speaks reverently to his superiors, not scuffling his feet or standing on one leg, and he is mild and polite with those below him. He knows how to bow to foreign diplomats in the manner of their own countries, sits at table without fidgeting or feeding spaniels, can neatly carve and joint any fowl if requested to serve his elders. He doesn't slouch around with his jacket off one shoulder, or look in windows to admire himself, or stare around in church, or interrupt old men, or finish their stories for them. If anyone sneezes, he says, “Christ help you!”

I was able to copy and paste this quote, rather than key it, because a reviewer chose to quote it as well. Writing in the New Yorker on May 7, James Wood uses the paragraph to show how Mantel uses a "cunning universalism" to link Cromwell with modern parents, indeed any parents, whose concern about their children leads them to catalog their strengths and weaknesses.

I did not see this aspect of the quote. For me it shows in glorious detail some of the main attributes of the "gently-" as against the "meanly-" born young men of early modern England. Cromwell and Collins were "of mean birth" and by their attainments came to be known as gentlemen. As adults they mastered the forms of address, techniques of polite conversation, and deportment sufficiently well to be accepted among the gently born. By contrast Cromwell's son Gregory, as Mantel presents him, was raised from childhood to be "courteous" in the original sense of the word.[2]

Spenser gives this sense of "courtesie" in the Faerie Queene.

Of Court, it seemes, men Courtesie doe call
For that it there most useth to abound :
And well beseemeth that in Prince's hall
That vertue should be plentifully found
Which of all goodly manners is the ground.
And roote of civill conversation.
-- Spenser, Faerie Queene, VI, i, i.

It's implied that Gregory knows how to behave in Court, that is the chambers where royals and nobles gather. He knows how to restrain any of his impulses which might be considered impolite, he shows deference to his betters, and possesses a confident demeanor which frees him from distasteful arrogance. His manners are easy and graceful. This ease and grace is the basis of what Spenser calls "civill conversation."[3]

Mantel puts most of Gregory's courtly achievements as negative virtues — bad habits he has had to overcome — and this is typical of the many books of polite manners that appeared in the centuries after the invention of the printing press. She and they take it as given that people are born with unsocial impulses which must be restrained if they are to get along well with each other. It's also implicit that those belonging to the courtly classes have advantages which others lack — chiefly wealth (or at least credit) and leisure. To them being industrious is not a virtue, and, although many of the gently born do work hard, they are encouraged not to make a show of it. Their leisure is not one of idleness, ideally, but their energy should be expended in sport (tilting or hunting) and social engagements (such as riding and dancing) rather than any effort that would appear busy.

Gregory is not literally "gently born." Writers of courtesy books divided pretty much evenly over those who equated gentility with good breeding and those who said it could be acquired as well as bred, but they all acknowledged that people were accepted as gentles either way. They also implicitly or explicitly accepted that this characterization — gently born — applied pretty much equally to all those who belonged in the upper classes, from the lowest of gentry through to the highest of nobles and royals. The gap between people of mean birth and those of gentle birth was, in this instance at any rate, more significant than the gap between a poor but well mannered landowner and a duke or earl. Men like Cromwell and Collins breached the first sort of gap, but they did not do so easily and their hold on their new status was tenuous. I suspect they hoped their sons would, as men, be able to accept gentility with unselfconscious ease.

{Cromwell by Holbein from the Frick Collection; source: wikipedia}

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Some sources:

The ideal of a gentleman; or, A mirror for gentlefolks, a portrayal in literature from the earliest times by Abram Smythe Palmer (Routledge; New York, Dutton)

"The English Gentleman," by Sir George Sitwell in The Ancestor, No. I (Westminster, April 1902)

Peacham's Comple'at Gentleman (1634), with an introduction by G. S. Gordon (Oxford, 1906)

Rhetoric and Courtliness in Early Modern Literature by Jennifer Richards (Cambridge, Cambridge University Press, 2003)

From Civilitas to Civility: Codes of Manners in Medieval and Early Modern England by John Gillingham, Transactions of the Royal Historical Society, Sixth Series, Vol. 12 (2002), pp. 267-289. Stable URL: http://www.jstor.org/stable/3679348.

Invitation to a Beheading, The Thomas Cromwell novels of Hilary Mantel, a review by James Wood in The New Yorker, May 7, 2012.

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Notes:

[1] ... -- The sphere of Marcus Manilius [by Marcus Manilius], made an English poem with annotations and an astronomical appendix by Edward Sherburne, squire (1675).

Sherburne says:
We should be injurious to him, if we did not farther inlarge, by telling the World how much it is obliged for his Pains in exciting the Learned to publish their Works, and in acting the Part of an Ingenious Obstetrix at the Press, in correcting and in drawing of Schemes; So that he hath been Instrumental in furnishing the World with the many learned Mathematical Books here lately published (for which, his chief Reward hitherto hath been to obtain from the Learned the Title of Mersennus Anglicanus) and many more may be expected, if moderate Encouragements towards Printing such Works, and Leisure for such an Affair be not impeded through the necessary Avocations for a livelyhood, and though it be besides my Design, yet I cannot but digress in giving him and others like minded (which are very rare to be found) their due commendations, in promoting the laudable Design of getting Learned Men to impart their Labours to be Printed; and exciting others to encourage the same, as being of singular Use and advantage to the Republick of Learning; through the want whereof many Learned Mens Works of much worth have been lost, suppressed or long delayed.

a Barnabas among those mathematical apostles, his tact and
devotion in calming the headstrong and drawing out the reticent
being above all praise.

[2] "Courteous" comes from the 14th-century French word curteis and it then meant "having courtly bearing or manners." The phrases I put in quotes were common in early modern England. In the 16th and 17th centuries a literature, quite a large literature, grew up giving instructions on courtesy.

[3] As one source says, Spenser took the term "civill conversation" from an Italian work of 1574 in which gentles are shown as harmoniously intermingling with an unselfconscious grace. (The Spenser Encyclopedia by Albert Charles Hamilton (Taylor & Francis, 1990)).

rules and other mathematical instruments

Rules matter: both the ones used, as Cleopatra says, by "Mechanic slaves / With greasy aprons, rules, and hammers" and the ones used by mathematical practitioners, as I wrote a little while ago.[1] We think of the simple straight edge — a ruler — that we used at school. The one I remember looked like this.


In the 16th and 17th centuries most rules probably were easily identifiable as ancestors of the school ruler of the 1950s. This one comes from a carpenter's toolbox aboard a warship that was sunk during a sea fight in 1545.

{From a group of carpenter's tools, including a mallet, drill handle, and plane, found in chests stowed in one of the main deck cabins of the Mary Rose, one of Henry VIII's warships which was sunk in battle in 1545; source: wikipedia}

From Shakespeare's time forward, however, rules could be and often were both more precise and more versatile. Here is a folding rule used by a ship's carpenter in during the first half of the 17th century.[2]

Front

Back

Extension arm

{17th Century English Three-Fold Ship Carpenter’s Rule, a two foot rule, made of boxwood and brass. Front has four scales (inch, two sets of lines for setting a ship's mast, and a scale for making octagon shapes — use of the octagon scale is described here). Back was used for timber and board measure and contains scales for measuring areas and volumes. The extension arm carries a logarithmic line of numbers 1-10 and would have been used with a pair of dividers. Source: http://www.teodolite.it/arch_carp_rule.htm in antichi strumenti topografici. (I have reproduced this image under fair use provisions of US copyright law.)}

The scales on the back of this rule are for estimating how much wood is needed for a given construction project, whether as timber or board measure. Timber measure was given in cubic feet or yards; board measure in square feet or yards. These scales accord with instructions given by Leonard Digges in 1556. Here is a page from Digges' book, A booke named Tectonicon, brieflie shewing the exact measuring, and speedie reckoning all manner of land, squares, timber, stone, steeples, pillers, globes, etc..

{A booke named Tectonicon, brieflie shewing the exact measuring, and speedie reckoning all manner of land, squares, timber, stone, steeples, pillers, globes, etc. ... With other things pleasant and necessarie, most conducible for surveyers, landmeaters, joyners, carpenters, and masons by Leonard Digges (London, Imprinted by F. Kyngston, 1605); first published in 1556}

Here is Digges' template for a carpenter's rule showing the timber scale and another one to be used for calculating board measure.[3]

This handsome example of a two-foot folding carpenter's rule has the Digges scales on its first arm (the arm having inch measure 1 to 12). The second arm continues the lumber measure scales and labels them. There are also degree markings on its hinged joint permitting the rule to be used as a sector for measuring distances and heights. It is nicely detailed and worth a close look (as usual, click to view full size).

{Folding Rule, Brass, 305 mm in radius, signed by Humfrey Cole, 1575, London; source: Museum of the History of Science, Oxford (I have reproduced this image under fair use provisions of US copyright law.)}

It's a safe bet that most of Digges' readers would use his instructions to obtain wooden rules like the ship's carpenter's version not shiny brass ones. The latter would be too expensive for most of the men whom Digges called artificers to afford. In writing the book, Digges addressed himself expressly to such men, those who could read but only in English and who could count money (as most men could) but whose knowledge of mathematics was limited.

In his prefatory remarks Digges says others before him have written books on surveying, carpentry, and related subjects, but they wrote in inaccessible languages (as he says, "locked up in strange Tongues") and assume knowledge of mathematics (that is, they require the "art of numbring"). For these reasons, he says, they have little value for British artificers: "they doe profit (or have furthered) very little the most part: Certes nothing at all, the Landmeater, Carpenter, Mason, wanting the aforesaid".[4]

Digges' book serves his readers well. It's written clearly in an informal style and gives many useful examples. The surveyors, carpenters, masons, and other workmen who followed his advice, giving it a first reading "confusely," then closely, and finally with diligence, "wittely to practise: so few things shall be unknowe."

Writing a whole century later, John Collins does much the same for seamen, makers of sun dials, and students of navigation.

In a book called Navigation by the mariners plain scale new plain'd he gives basic lessons in elementary geometry with many illustrations, provides detailed instructions for applying this mathematical knowledge in navigation at sea, and shows many demonstrations from actual experience. He tells his readers how to account for changes in vessel speed and in compass readings due to magnetic variation and how to adjust for the drift of a vessel due to wind and currents, and he discusses problems resulting from cloud covers obscuring the sun or stars, and the like.[5] He also acknowledges that seamen are hampered most of all through not having accurate charts for their points of destination: "unless the true Longitudes and Latitudes of Places be known, their true Courses and Distances cannot be found, whence it will unavoidably follow, that no true reckoning can be kept." This chapter concludes: "Notwithstanding the imperfections and uncertainties that arise in the practick part, yet it should be our endeavour to render this excellent Art as easie and certain as we can, which is the thing I am at, and the Instrument here used being the Plaine Scale, is, as I said before, in every mans power."[6]

The Plaine Scale to which Collins referred is a rule which he shows thus:


On this scale,

C is the scale of secants
S the scale of sines
C the scale of chords
R the scale of rhumbe
P the scale of semi-tangents, and
L the scale of tangents

Collins' plain scale is a version of Gunter's scale. Invented by Edmund Gunter and first described in a book he wrote in 1624,[7] this scale eventually became so common on sailing ships as simply to be called the Gunter by its users.[8] This is a detail from a common two-foot version of the scale. Its top line of numbers shows inches. I don't know what the next scale is. Below it you find rhumbe, chord, sine, tangent, semi-tangent.

{Detail from a Gunter's scale. You can vier the whole scale here. Source: KRING HISTORISCHE REKENINSTRUMENTEN}

Like Digges, Collins addresses readers of, in his words, the "meanest sort," i.e., those who possess few or no advantages of wealth and education. To that end he includes engraved plates showing the plain scale and other tools which readers could make for themselves. Aside from them, the only tools needed were a straight edge and a pair of dividers, or as he put it "a pair of Compasses and a bare Ruler."

A few years ago there was a Gresham lecture which brings out points similar to the ones I'm making here about the production and use of mathematical instruments and those who made them, about those who instructed others about these instruments, and about those who actually put them to use. It's History from Below: mathematics, instruments and archaeology, a lecture by Stephen Johnston, Museum of the History of Science, Oxford University, Thursday, 3 November 2005.

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Some sources:

A booke named Tectonicon, brieflie shewing the exact measuring, and speedie reckoning all manner of land, squares, timber, stone, steeples, pillers, globes, etc. ... With other things pleasant and necessarie, most conducible for surveyers, landmeaters, joyners, carpenters, and masons by Leonard Digges (London, Imprinted by F. Kyngston, 1605); first published in 1556

Navigation by the mariners plain scale new plain'd, or, A treatise of geometrical and arithmetical navigation; wherein sayling is performed in all the three kindes by a right line, and a circle divided into equal parts. Containing 1. New ways of keeping of a reckoning, or platting of a traverse, both upon the plain and Mercators chart ... 2. New rules for estimating the ships way through currents, and for correcting the dead reckoning. 3. The refutation of divers errors, and of the plain chart, and how to remove the error committed thereby ... as also a table thereof made to every other centesm. 4. A new easie method of calculation for great circle-sayling, with new projections, schemes and charts ... 5. Arithmetical navigation, or navigation performed by the pen, if tables were wanting ... By John Collins of London, Pen-man, accomptant, philomathet (London : printed by Tho. Johnson for Francis Cossinet, and are to be sold at the Anchor and Mariner in Tower-street, as also by Henry Sutton mathematical instrument-maker in Thread needle street, behinde the Exchange, 1659)

Digges, Leonard in the galileo Project at Rice Univ.

Folding Rule, signed by Humfrey Cole, 1575, London
Brass, 305 mm in radius, Inventory no. 49631, Epact number: 79726

A Late 17th-Century Armed Merchant Vessel in the Western Approaches by Neil Cunningham Dobson, Odyssey Marine Exploration, Tampa, USA, and Sean A. Kingsley, Wreck Watch Int., London, United Kingdom (pdf)

Like father, like son? John Dee, Thomas Digges and the identity of the mathematician by Stephen Johnston, Museum of the History of Science, University of Oxford

The Logarithms and Rules on the Calculating Tools page of the History of Computers web site

Gunter's rule, one step before the Slide Rule, on the History of Computing web site

The description, nature and general use, of the sector and plain-scale briefly and plainly laid down; as also a short account of the uses of the lines of numbers, artificial sines and tangents by Edmund Stone (Printed for Tho. Wright; and sold by Tho. Heath mathematical instrument maker, next the Fountain Tavern in the Strand., 1721)

An introduction to the theory ... of plane and spherical trigonometry ... including the theory of navigation by Thomas Keith (London, Longman, Hurst, Rees, Orme, and Brown, 1816)

On the history of Gunter's scale and the slide rule during the seventeenth century by Florian Cajori (Berkeley, Univ. of California Press, 1920)

History from Below: mathematics, instruments and archaeology, a lecture by Stephen Johnston, Museum of the History of Science, Oxford University, Thursday, 3 November 2005


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Notes:

[1] The post is men holding rules, Secondat, January 21, 2012.

[2] Full caption: "17th Century English Three Fold Ship Carpenter’s Rule — The two foot rule, made of boxwood and brass SCALES 1. Side A has four scales: -a. An inch scale [0]-18, divided to unit, half, quarter, eighth and numbered by 1 to 18. This continues to 24 on the brass leg. -b. A pair of sectoral lines, used for setting out the taper of a ship’s mast. The inner sector lines on each of the boxwood legs are graduated P, 3Q, 2Q, 1Q and MH, representing Partners, third, second, and first Quarters, and Masthead. The function of this sector is to provide a series of diameter measurements. The second, or outer set of the two sector lines are designated S, 3Q, 2Q, 1Q and YA, for Slings, third, second, and first Quarters, and Yardarm. -c. the octagon scale, to left and right of the rule joint, scaled 0 to 28 Side B for timber and board measure was designed to be used for measuring areas and volumes. This particular format was established during the 17th century as an adaptation of a design first published by Leonard Digges in 1556 Side B has three elements: -a. The line of board measure running from 9 to 36. The scale ends 4in from the end of the leg (4 x 36 = 144 = 1ft square). -b. The line of timber measure from 11 to 33. -c. A table of timber undermeasure. This is continuous with the timber line and supplies values for 1 to 8in, which the rule cannot accommodate on the scale line. The edge carries a logarithmic line of numbers 1-10. The logarithmic line of numbers on the edge was first published by Edmund Gunter in the 1620s. In the form found here, which appeared on a range of instruments in the 17th century, it would have been used with a pair of dividers."

[3] Note that Digges puts the lumber scales are on the front side of the rule he describes, along with a 12-inch scale. The back side of his rule has a scale for use in measuring angles and distances (a quadrant). Note also that he calls the device a ruler not a rule. The terms seem to have been interchangeable at the time. And finally, notice that the printer has done Digges wrong: the numbers by the side of the timber and board hash marks are grossly misplaced.

[4] The landmeater measured land, apparently with less skill than the surveyor. Here is Digge's address to the reader in full:

L. D. to the Reader — Although many have put forth sufficient and certain rules to measure all manner of superficies, etc., yet in that the art of numbring hath been required, yea, chiefly those rules hid and as it were locked up in strange tongues, they doe profit or have furthered very little, for the most part, yea, nothing at all, the landmeater, carpenter, mason, wanting the aforesayd. For their sakes I am here provoked not to hide but to open the talent I have received, yea, to publish in this our tongue very shortly if God give life a volumne containing the flowers of the sciences mathematicall largely applied to our outward practise profitably pleasant to all manner men. Here mine advice shall be to those artificers, that will profit in this or any of my bookes now published, or that hereafter shall be, first confusedly to read them through, then with more judgement, read at the third reading wittily to practise. So, few things shall be unknowne. Note, oft diligent reading joyned with ingenious practise causeth profitable labour. Thus most hartely farewell, loving reader, to whom I wish myselfe present to further thy desire and practise in these.

[5] Leonard's son, Thomas Digges, was John Dee's foster son wikipedia: "Thomas was the son of Leonard Digges, the mathematician and surveyor. After the death of his father, Thomas grew up under the guardianship of John Dee, a typical Renaissance natural philosopher."

[5] This discussion of the "uncertainties of navigation" includes description of the parallax error that occurs when the sun is at the horizon. Since readings are taken at noon, this problem only occurs during winter in northern latitudes.

[6] Collins gives this definition: "By a Plain Chart, is meant a Chart drawn on Paper or Pasteboard, lined with Meridians and Parallels, making right Angles each with other, and numbered with degrees both of Latitude and Longitude, each equal to other, and what is commonly performed in casting up a Traverse on such a Chart, we shall perform on a Blank of Paper."

[7] Gunter's book is The description and use of the sector, cross-staff, bow, quadrant, and other instruments (London, 1624) republished in The works of Edmund Gunter : containing the description and use of the sector, cross-staff, bow, quadrant, and other instruments. with a canon of artificial sines and tangents to a radius of 10,00000 parts, and the logarithms from an unite to 10000 ... and some questions in navigation added by Mr. Henry Bond ... To which is added, the description and use of another sector and quadrant, both of them invented by Mr. Sam. Foster ... furnished with more lines, and differing from those of Mr.Gunters both in form and manner of working by Edmund Gunter, ed. by William Leybourn (London, Printed by A.C. for Francis Eglesfield, 1673).

[8] Gunter's navigational scale was used by the Royal Navy up to the 1840s. The historian of mathematics, Florian Cajori, gives this description:

We begin with Anthony Wood's account of Wingate's introduction of Gunter's scale into France.

In 1624 he transported into France the rule of proportion, having a little before been invented by Edra. Gunter of Gresham Coll. and communicated it to most of the chiefest mathematicians then residing in Paris: who apprehend[ed] the great benefit that might accrue thereby...

Gunter's scale, which Wingate calls the "rule of proportion," contained, as described in the French edition of 1624, four lines: (1) A single line of numbers; (2) a line of tangents; (3) a line of sines; (4) a line, one foot in length, divided into 12 inches and tenths of inches, also a line, one foot in length, divided into tenths and hundredths.

men holding rules

Shakespeare puts words in Cleopatra's mouth that tell more about class attitudes in his time than in hers:

                                      Mechanic slaves
With greasy aprons, rules, and hammers shall
Uplift us to the view. In their thick breaths,
Rank of gross diet, shall we be enclouded.
And forc'd to drink their vapor.
              (AC. V. ii. 209-13)

She's telling an attendant how she feels about the prospect of being acclaimed by plebeian Romans. Though less pungently, Coriolanus said much the same. So did Puck, quoted in my last post.[1]

It's not easy to generalize with any confidence about the attitudes of any class toward another. The attempt to locate the boundaries that separate the "us" of one class from the "them" of another can likewise be a daunting one. To Cleopatra the odiferous mass were all one. To themselves, they were many distinct groups.[2]

I'm interested in the mechanic who's holding a rule. One can imagine him as a carpenter or builder, maybe a shipwright or gunner, or he might have been a surveyor, navigator, or excise officer. Or he might have been a man who made rules — a person who made tools for a living. Or, still, he might have been one who taught others how to make and use the instruments of the trade.

In Shakespeare's time, to many of those who were gently born, these mechanic slaves holding rules would have been men who were presumed not to amount to much simply because they worked with their hands. But although many surely did, as apprentices and journeymen whose daily drudge was limited to performing tasks the master assigned, approximate this description, other men — the masters themselves — also held rules in their hands. They were builders, architects, land surveyors, gunnery officers, and others who used mathematical tools — rules — in their work. This, for example, shows a gentlemanly-looking surveyor (at right) and equally-well-decked-out helper (left) with an early version of the theodolite (described as a "Semy Circle set upon a perfeck square"), some levels (one of them using water boxes), and a target stick.

{Illustration of surveyors with their equipment from The English Improver Improved or the Survey of Husbandry Surveyed by Walter Blith (London, 1652); source: MSU.edu hst425}

This illustration shows a Portuguese navigator using a similar device (a forerunner of the sextant called a cosmolabe) to help draw a nautical chart. His instrument could not be used at sea, but more portable versions might be found on the distant ships, to be used with his charts when landmarks ashore were out of sight.

{A navigator and his instruments from the late sixteenth century; source: Os oitavos na História blog}

Another set of men holding rules were the men who made them. They were self-employed craftsmen or masters of small shops who possessed skill akin to goldsmiths or clock-makers or even, in those times, many plebeian artists, composers, and literary authors.

You can tell something of the skill possessed by one of these craftsmen, Henry Sutton, from this account by John Collins. Notice that Sutton needed no more than a verbal description in order to make a complex mathematical instrument. A mathematician "intimated his desires" and the craftsman, an engraver, "speedily found out the drawing" without further instruction. [3]

{From: The sector on a quadrant, or, a treatise containing the description and use of three several quadrants Accommodated for dyalling, for the resolving of all proportions instrumentally, and for the ready finding the hour and azimuth; with large cuts of each quadrant, printed from the original plates graved by Henry Sutton, by John Collins (printed by J.Macock, to be sold by George Hurlock, William Fisher and Henry Sutton mathematical instrument maker, 1658)}

This is Sutton's quadrant, made from a plate he engraved for Collins' book.

{source: Royal Museums, Greenwich}

Sutton was acclaimed one of the best, but others like him were skillful instrument makers, the technicians of their time. Here's one (quite late) description of their trade.[4]

{This reads: "Of the Mathematical and Optical Instrument, and Spectacle-Maker.

"THE Mathematical-Instrument-Maker makes all kind of Instruments constructed upon Mathematical Principles, and used in Philosophical Experiments: He makes Globes, Orrerys, Scales, Quadrants, Sectors, Sun-Dials of all Sorts and Dimensions, Air-Pumps, and the whole Apparatus belonging to Experimental Philosophy. He ought to have a Mathematically turned Head, and be acquainted with the Theory and Principles Upon which his several Instruments are constructed, as well as with the practical Use of them. He employs several different Hands, who are mere Mechanics, and know no more of the Use or Design of the Work they make, than the Engines with which the greatest Part of them are executed; therefore the Master must be a thorough Judge of Work in general.

"The Optical-Instrument-Maker is employed in making the various sorts of Telescopes, Microscopes of different Structures, Spectacles, and all other Instruments invented for the Help or Preservation of the Sight, and in which Glasses are used. He himself executes very little of the Work, except the grinding the Glasses: He grinds his Convex-Glasses in a Brass Concave Sphere, of a Diameter large in proportion to the Glass intended, and his Concave-Glasses upon a Convex Sphere of the same Metal: His Plane-Glasses he grinds upon a just Plane, in the same Manner as the common Glass-Grinder, mentioned Chap. XXXII. Sect. 4. He grinds them all with Sand and polishes them with Emery and Putty. The Cases and Machinery of his Instruments are made by different Workmen, according to their Nature, and he adjusts the Glasses to them.

"It is a very ingenious and profitable Business, and employs but a few Hands as Masters; The Journeymen earn, a Guinea a Week, and some more, according as they are accurate in their Trade. Such a Tradesman designed for a Master ought to have a pretty good Education, and a penetrating Judgment, to apprehend the Theory of the several Instruments he is obliged to make, and must be a thorough Judge of such Work as he employs others to execute. A Youth may be bound to either of these Trades any time between thirteen and fifteen Years of Age, and does not require, much Strength."}

Yet one more set of men with rules were teachers and authors of instructional texts who demonstrated the use of mathematical instruments.

John Collins himself was one of these. As an example, here is a list of his books on the use of mathematical instruments. It shows up in an "astronomical appendix" to a translation of The Sphere of Marcus Manilius by Sir Edward Sherburne, ca. 1675.

{an Account of John Collins's Mathematical Works Reprinted from the Appendix to Sir E. Sherburne's Translation of Bk. 1 of the Astronomicon of Manilius. Edited by N. Brook (Nathanael Brook: London, 1675?)}

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Some sources:

Navigation: The Mariner's Quadrant

Navigation, Smith Center for Cartographic Education, University of Southern Maine

The identity of the mathematical practitioner in 16th-century England by Stephen Johnston in the proceedings of a 1995 conference in Duisburg: Irmgarde Hantsche (ed.), Der “mathematicus”: Zur Entwicklung und Bedeutung einer neuen Berufsgruppe in der Zeit Gerhard Mercators, Duisburger Mercator-Studien, vol. 4 (Bochum: Brockmeyer, 1996), 93-120. It is closely based on material in the introduction to my thesis, and appears here by permission of Universitätsverlag Dr. N. Brockmeyer.

De republica anglorum, a discourse on the Commonwealth of England by Thomas Smith, ed. by L. Alston with a preface by F.W. Maitland (Cambridge, the University Press, 1906)

"Christs Teares over Ierusalem" by Thomas Nashe (1593) in Life in Shakespeare's England a book of Elizabethan prose comp. by John Dover Wilson (Cambridge University press, 1913) Extract: "In London, the rich disdain the poor. The courtier the citizen. The citizen the country man. One occupation disdaineth another. The merchant the retailer. The retailer the craftsman. The better sort of craftsmen the baser. The shoemaker the cobbler. The cobbler the carman. One nice dame disdains her next neighbour should have that furniture to her house, or dainty dish or device, which she wants. She will not go to church, because she disdains to mix herself with base company, and cannot have her close pew by herself. She disdains to wear that everyone wears, or hear that preacher which everyone hears. So did Jerusalem disdain God's prophets, because they came in the likeness of poor men. She disdained Amos, because he was a keeper of oxen, as also the rest, for they were of the dregs of the people. But their disdain prospered not with them. Their house, for their disdain, was left desolate unto them."

"Itinerary" by Fynes Moryson (1617) in Life in Shakespeare's England a book of Elizabethan prose comp. by John Dover Wilson (Cambridge University press, 1913)

The London tradesman; Being a compendious view of all the trades, professions, arts, both liberal and mechanic, now practised in the cities of London and Westminster. Calculated for the information of parents, and instruction of youth in their choice of business by R. Campbell, esq (London, printed by T. Gardner, 1747)

The making of the English middle class; business, society, and family life in London, 1660-1730 by Peter Earle (University of California Press, 1989)

Diary of Samuel Pepys, Tuesday 29 May 1660

The sphere of Marcus Manilius made an English poem with annotations and an astronomical appendix by Marcus Manilius, translated by Sir Edward Sherburne (London, printed for Nathanael Brooke, 1675)

"A Catalogue of Astronomers" in the work cited just above.

"The Institution of Residential Investment in Seventeenth-Century London" by William C. Baer, The Business History Review, Vol. 76, No. 3 (Autumn, 2002), pp. 515-551 (Harvard) Stable URL: http://www.jstor.org/stable/4127797

Biographies in John Aubrey's Brief Lives

The Mathematical Practitioners of Tudor and Stuart England by E.G.R. Taylor (Cambridge, 1954)

Shakespeare from the margins by Patricia A. Parker (University of Chicago Press, 1996)

Earthly Necessities: Economic Lives in Early Modern Britain by Keith Wrightson (Yale University Press, 2002)

Manilius and his intellectual background by Katharina Volk (Oxford University Press, 2009)

The English Improver Improved or the Survey of Husbandry Surveyed by Walter Blith (London, 1652)

Marcus Manilius on wikipedia

"The Search for the 'Middle Sort of People' in England, 1600-1800" by H. R. French, The Historical Journal, Vol. 43, No. 1 (Mar., 2000), pp. 277-293 (Cambridge University Press) Stable URL: http://www.jstor.org/stable/3021022

Stereographic projection in wikipedia

Hour angle in wikipedia

Azimuth in wikipedia

Solar azimuth angle in wikipedia

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Notes:

[1] Patricia Parker writes well about the disdain of gentles for their lesser bretheren. See Shakespeare from the margins by Patricia A. Parker (University of Chicago Press, 1996).

[2] The making of the English middle class; business, society, and family life in London, 1660-1730 by Peter Earle (University of California Press, 1989)

[3] Here is the relevant description: A limb is the outer edge of a sphere, in this case the earth.

Being in conference with my loving friend M. Thomas Harvie, he told me, that he had often drawn a Quadrant upon Paper pasteboard, &c. derived by himself, and never done by any man before, as to his knowledge, from the Stereographick Projection, which for a particular Latitude, would give the Hour in the equal Limb, and would also perform the Azimuth very well; and but that it was so particular, was very desirous to have one made in Brass for his own use by an Instrument Maker: whereto replying, that with the access of some other Lines to be used with Compasses, it might be rendered general for finding both the Hour and the Azimuth in the equal Limb: He thereupon intimated his desires to M. Sutton, promising within a fortnight after their conference, to draw up full directions for the making thereof. But M. Sutton having very good practise and experience in drawing Projections, speedily found out the drawing of that Projection, either in a Quadrant or a Semicircle, without the assistance of the promised directions, and accordingly, hath drawn the shape of it.
-- The sector on a quadrant, or, a treatise containing the description and use of three several quadrants by John Collins (printed by J.Macock, to be sold by George Hurlock, William Fisher and Henry Sutton mathematical instrument maker, 1658)

[4] This description comes from a book published a century after the period of which I'm writing. I couldn't find anything more closely contemporaneous. Although it does not contradict writers who published in the middle of the seventeenth century and seems to jibe with sources from the period, I can't really say it's as good a description of the one time as of the other. In the preceding chapter the author also describes the watch- and clock-making trades. My source is Chapter 55 in The London tradesman; Being a compendious view of all the trades, professions, arts, both liberal and mechanic, now practised in the cities of London and Westminster. Calculated for the information of parents, and instruction of youth in their choice of business by R. Campbell, esq (London, printed by T. Gardner, 1747)

Note on reproductions: Where not in the public domain, reproductions made in the blog post appear in accordance with fair use provisions of US copyright law. If you believe I have abused the privilege of fair use, please let me know.

mathematical practitioners

In his criticism of the universities for teaching subjects that have little practical value, John Webster asks (rhetorically) "What is Grammar, Lodgick, Rhetorick, Poesie, Politicks, Ethicks, Oeconomicks, nay Metaphysicks? if they serve to no other use than bare and fruitless speculation?" In arguing that the universities should emphasize mathematics and the empirical sciences which have some practical use he tacitly acknowledges that scholars can learn some mathematics at Oxford or Cambridge, but he says this math is the wrong kind. He asks "Can the Mathematical Sciences, the most noble, useful, and of the greatest certitude of all the rest, serve for no more profitable end, than speculatively and abstractively to be considered of?"[1]

He says, in other words, the math that's taught should be useful. Regarding this more profitable mathematics he asks, "How could the life of man be happily led, nay how could men in a manner consist without it? Truly I may justly say of it as Cicero of Philosophy, it hath taught men to build houses, to live in Cities and walled Towns; it hath taught men to measure and divide the Earth; more facilely to negotiate and trade one with another: From whence was found out and ordered the art of Navigation, the art of War, Engins, Fortifications, all mechanick operations, were not all these and innumerable others the progeny of this never-sufficiently praised Science?"

Webster was a preacher and not a particularly astute scholar. As I pointed out in my last post, he joined many of his contemporaries in believing magic, alchemy, and astrology to be subjects of equal weight with mathematics and natural philosophy (as what we call simply science was then called). In doing so he echoes a man, John Dee, who lived half a century before him and whom he calls a "myrror of manifold learning."[2] In a well-known preface to the first English translation of Euclid's Elements, Dee, like Webster, praises math and science as topics for university study and, just as much, magic, alchemy, and astrology.[3] And, like Webster, he says the application of mathematics is at least as important as is abstract speculation. In his words, "the very chief perfection (almost) of Numbers Practicall use" can be attained by the "mixtyng of speculation and practise."

In the preface Dee catalogs many of math's practical uses — from merchants' reliance on arithmetic, to the tangible uses of algebra[4], and to the many uses of geometry made by surveyors, military commanders, navigators, builders, excise men, and others. With regret Dee says he's been writing against a deadline ("the Printer, hath looked for this Præface, a day or two") and tells us his subject "is so ample and wonderfull, that, an whole yeare long, one might finde fruitfull matter therin, to speake of: and also in practise, is a Threasure endeles."

Despite the passion he shows for his subject in the preface, Dee's life was devoted more to the intangible aspects of math than the material ones. It's true he used Euclidian geometry to solve problems of navigation and trained the crews of ships so they could find their way across the Atlantic in early voyages to North America, but he believed his life's mission to be the uncovering of the spiritual forms underlying the material world. To him math was a language for use in speaking with angels. He associated its abstract beauty with mystical powers of divination which he claimed to possess.

Of the angelical beauty of mathematics he wrote: "All thinges ... do appeare to be Formed by the reason of Numbers. For this was the principall example or patterne in the minde of the Creator. ... By Numbers propertie ... we may ... ascend, and mount up (with Speculative winges) in spirit, to behold in the Glas of Creation, the Forme of Formes, the Exemplar Number of all thinges Numerable: both visible and inuisible, mortall and immortall, Corporall and Spirituall."[5]

The only son of a minor member of the royal court, he had a brilliant career at university and possessed both inclination and sufficient means to extend his education after graduation through extensive travel in Europe. Not himself wealthy, he was able to make himself useful to wealthy members of the aristocracy of England and the European continent. There appears to have been no snobbishness in him however. At a time when "gentles" treated unlettered artisans with contempt, scorn, or — at best — indifference, and when dramatists could be sure to draw laughs by poking fun at men whom they characterized as "rude mechanicals"[6], Dee was unusual in the sympathetic recognition he gave to the emerging class of "Common Artificer."

He closes the Preface by citing advantages of instruction — not in the Latin of the universities but in the English of the shop and street — made available to London tradesmen, many of whom were the first of their families to have acquired the ability to read. Of the book in which the Preface appears — Billingsley's translation of Euclid's Elements (which, as I say, was the first version to be published in English) — he writes: "[H]ow many a Common Artificer, is there, in these Realmes of England and Ireland, that dealeth with Numbers, Rule, & Cumpasse: Who, with their owne Skill and experience, already had, will be hable (by these good helpes and informations) to finde out, and devise, new workes, straunge Engines, and Instrumentes: for sundry purposes in the Common Wealth? or for private pleasure? and for the better maintayning of their owne estate?"

This title page to Billingsley's Euclid depicts some of the practical applications of mathematics to which Dee refers. (It's also, you'll notice, not prudish in depicting naked bodies.)

{The title page of Henry Billingsley's translation of Euclid's Elements (1570), with preface by John Dee; source: wikipedia}

It's generally thought that Dee's Preface and all of Billingsley's Euclid helped set in motion a gradual shift in attitudes toward mathematics and the book's readers appear to have fostered the growth of applied mathematics outside the universities. As a partial result, it's pretty clear that in the century following its appearance mathematical practitioners — the men who employed mathematics in their work as well as the printers and authors of practical math texts, the makers of technical instruments, and the technical advisors who assisted university-trained natural philosophers — became more prosperous and grew somewhat in social standing.[6]

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Some sources:

The Mathematical Practitioners of Tudor and Stuart England by E.G.R. Taylor (Cambridge, 1954)

John Dee's "Mathematicall Praeface": A Sixteenth Century Classification of the Mathematical Arts and Sciences by Charles St. Clair (pdf)

The Mathematicall Praeface to Elements of Geometrie of Euclid of Megara by John Dee from Sir Henry Billingsley's first English version of Euclid's Elements, 1570

"John Dee" by Thompson Cooper in Dictionary of national biography ed. by Leslie Stephen and Sidney Lee (Smith, Elder, & co., 1888)

"John Dee and His Supplication to Queen Mary" by P. Evans Lewin, Woolwich Public Libraries in The Library world, Vol. 5 (Library Supply Co., 1903) Extract: 'Whilst at Cambridge he only slept four hours every night, and spent eighteen hours of the day in study. So great was his knowledge, that his acquaintance was eagerly sought by such men as Gemma Frisius, Mercator, and Gaspar a Mirca, all of whom he visited in his twentyfirst year. Even at this period he was looked on askance, for he relates that in 1547 he "sett forth" at Trinity College a Greek comedy of Aristophanes, "with the performance of the Scarabaeus, his flying up to Jupiter's palace with a man and his basket of victuals on her back, whereat was great wondering and many vain reports spread about." This, probably, was only a piece of stage mechanism suitable to the crude ideas of the time and in keeping with Greene's instructions in "Tamburlaine" — "exit Venus; or if you can conveniently let a chair come down from the top of the stage and draw her up."'

"The Mistaking of 'the Mathematicks' for Magic in Tudor and Stuart England" by J. Peter Zetterberg in The Sixteenth Century Journal, Vol. 11, No. 1 (Spring, 1980), pp. 83-97. Stable URL: http://www.jstor.org/stable/2539477

"Science and Education in the Seventeenth Century: The Webster-Ward Debate" by G. Allen, reviewed by Theodore M. Brown in Isis, Vol. 64, No. 3 (Sep., 1973), pp. 422-424. (The University of Chicago Press) Stable URL: http://www.jstor.org/stable/2297

A general dictionary: historical and critical, in which a new and accurate translation of that of the celebrated Mr. Bayle, with the corrections and observations printed in the late edition at Paris, is included; and interspersed with several thousand lives never before published. The whole containing the history of the most illustrious persons of all ages and nations particularly those of Great Britain and Ireland, distinguished by their rank, actions, learning and other accomplishments. With reflections on such passages of Bayle, as seem to favor scepticism and the Manichee system, Volume 10 by Pierre Bayle, John Peter Bernard, Thomas Birch, John Lockman, George Sale, Alexis Gaudin, Anthelme Tricaud, Pierre Desmaizeaux (Printed by J. Bettenham, 1741)

Billingsley Euclid in Mathematical Treasures by Frank J. Swetz and Victor J. Katz

Shakespeare from the margins by Patricia A. Parker (University of Chicago Press, 1996)

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Notes:

[1] My quotes from John Webster come from his Academiarum Examen: Academiarum examen, or the examination of academies wherein is discussed and examined the matter, method and customes of academick and scholastick learning by John Webster (Calvert, 1654).

[2] My quotes from John Dee come from his The Mathematicall Praeface to Elements of Geometrie of Euclid of Megara by John Dee from Sir Henry Billingsley's first English version of Euclid's Elements, 1570. I have modernized Dee's use of the letter "u" where we would put "v" and given the "long s" (ſ) as "s".

[3] Dee's passion for mathematics leads him to claim (quoting Boetius) that "All thinges (which from the very first originall being of thinges, have bene framed and made) do appeare to be Formed by the reason of Numbers. For this was the principall example or patterne in the minde of the Creator." And further: "By Numbers propertie therefore, of us, by all possible meanes, (to the perfection of the Science) learned, we may both winde and draw our selves into the inward and deepe search and vew, of all creatures distinct vertues, natures, properties, and Formes: And also, farder, arise, clime, ascend, and mount up (with Speculatiue winges) in spirit, to behold in the Glas of Creation, the Forme of Formes, the Exemplar Number of all thinges Numerable: both visible and invisible, mortall and immortall, Corporall and Spirituall."

[4] Of algebra he says: "This Rule, and Arithmetike of Algiebra, is so profound, so generall and so (in maner) conteyneth the whole power of Numbers Application practicall: that mans witt, can deale with nothyng, more proffitable about numbers: nor match, with a thyng, more mete for the divine force of the Soule, (in humane Studies, affaires, or exercises) to be tryed in."

[5] Here's the full quote: "All thinges (which from the very first originall being of thinges, have bene framed and made) do appeare to be Formed by the reason of Numbers. For this was the principall example or patterne in the minde of the Creator. O comfortable allurement, O ravishing perswasion, to deale with a Science, whose Subiect, is so Auncient, so pure, so excellent, so surmounting all creatures, so used of the Almighty and incomprehensible wisdome of the Creator, in the distinct creation of all creatures: in all their distinct partes, properties, natures, and vertues, by order, and most absolute number, brought, from Nothing, to the Formalitie of their being and state. By Numbers propertie therefore, of us, by all possible meanes, (to the perfection of the Science) learned, we may both winde and draw our selves into the inward and deepe search and vew, of all creatures distinct vertues, natures, properties, and Formes: And also, farder, arise, clime, ascend, and mount up (with Speculative winges) in spirit, to behold in the Glas of Creation, the Forme of Formes, the Exemplar Number of all thinges Numerable: both visible and inuisible, mortall and immortall, Corporall and Spirituall."

[6] A Midsummer Night's Dream: Act 3, Scene 2

PUCK
6 My mistress with a monster is in love.
7 Near to her close and consecrated bower,
8 While she was in her dull and sleeping hour,
9 A crew of patches, rude mechanicals,
10 That work for bread upon Athenian stalls,
11 Were met together to rehearse a play
12 Intended for great Theseus' nuptial-day.
13 The shallowest thick-skin of that barren sort,
14 Who Pyramus presented, in their sport
15 Forsook his scene and enter'd in a brake
16 When I did him at this advantage take,
17 An ass's nole I fixed on his head:
18 Anon his Thisby must be answered,
19 And forth my mimic comes. When they him spy,
20 As wild geese that the creeping fowler eye,
21 Or russet-pated choughs, many in sort,
22 Rising and cawing at the gun's report,
23 Sever themselves and madly sweep the sky,
24 So, at his sight, away his fellows fly;
25 And, at our stamp, here o'er and o'er one falls;
26 He murder cries and help from Athens calls.

[7] Stephen Johnston makes this point. See The identity of the mathematical practitioner in 16th-century England from the proceedings of a 1995 conference in Duisburg: Irmgarde Hantsche (ed.), Der “mathematicus”: Zur Entwicklung und Bedeutung einer neuen Berufsgruppe in der Zeit Gerhard Mercators, Duisburger Mercator-Studien, vol. 4 (Bochum: Brockmeyer, 1996), 93-120. It is closely based on material in the introduction to my thesis, and appears here by permission of Universitätsverlag Dr. N. Brockmeyer. See also: The making of the English middle class; business, society, and family life in London, 1660-1730 by Peter Earle (University of California Press, 1989)

early-modern science

It's generally pretty easy to distinguish fantasy from reality. We can tell the difference between intuited knowledge and knowledge gained through observation and careful measurement. We know that magicians perform tricks without aid from (probably diabolical) higher powers. Astrology and astronomy are to us two very different things; so too alchemy and chemistry, numerology and mathematics. But a few hundred years ago these distinctions were fuzzier.

As late medieval merged into early modern times, European men (almost always just men) started to correct serious mistakes that earlier generations had made about the natural world around them and the celestial bodies above. Some of these mistakes stemmed from religious beliefs, others from the writings of the ancient Greek philosophers and their successors. By questioning received authority, carefully examining natural phenomena, making complex mathematical calculations, and faithfully recording their findings these men transformed a scholastic philosophy into a new natural philosophy. The intellectual freedom achieved by this practice of scientific demonstration (as some of them were beginning to call it) was revolutionary in its magnitude, but not in the speed with which it took place.

Just as the transition from scholasticism and faith-based cosmology was evolutionary, so too the transition from belief in astrology, alchemy, and an ability to communicate with supernatural powers as legitimate tools for interacting with the natural world. Surprisingly, this second transition — scientists' rejection of hermetic beliefs — was even more gradual than their rejection of received truth from ancient authorities and of religious superstition (the "vain religion" of the schoolmen, as one of them put it).[1]

The men whom we now call scientists would study the real world using careful observation and rigorous measurement, but they would also, for example, use astrology to cast one another's natal charts. And the men and women who paid the bills — aristocratic or even royal patrons, wealthy merchants, and large land owners — expected their scientist clients to produce marvels — things out of the ordinary — to show off to their friends. Or, just as likely, they expected predictions of future events that might be advantageous to them.

On the sheet of paper I've reproduced below Galileo Galilei sketched the beginnings of a birth chart for a patron, Cosimo II, which Galileo used to show that Cosimo's future was an auspicious one. At the bottom of the page he drew the moon in its waxing phase at it appeared on January 19, 1609.

{Galileo’s sketch of the waxing Moon, as viewed on 19th January 1609 through his x20 telescope, on the same sheet as his first draft of the Cosimo II de Medici nativity; source: The Inspiration of Astronomical Phenomena, Proc. of 4th INSAP Conference, Oxford, Ed. N. Campion, Bristol 2004}

There are other instances of this service of natural philosophers to those they wished to flatter. For example Johannes Kepler created horoscopes for the Holy Roman Emperor, Rudolf II, and Tycho Brahe made annual charts for the Danish king, Fredrik, and the royal princes. Here is one of the birthday charts that Tycho Brahe made for Prince Christian in 1577.

{source: tychobrahesverden.dk}

Early modern natural philosophers and mathematicians would also prepare genitures for themselves and their friends. Without at first recognizing what they were, I encountered these tables when working in manuscript collections containing correspondence among Isaac Newton and other prominent mathematicians of the late seventeenth century. I also noticed that a writer of brief biographies, like the gossipy John Aubrey, might inquire about the exact moment of a man's birth, not having reason to do so except the making of an accurate birth chart for him.

{Detail from the entry for John Collins in "Brief lives", chiefly of contemporaries by John Aubrey, ed. by Andrew Clark, Andrew, Volume: 1 (Oxford, Clarendon Press, 1898)}

The Elizabethan magus, John Dee, presents an extreme example of a mathematician and astronomer who was also a self-proclaimed astrologer, alchemist, and practitioner of magic arts. Dee, among many other similar works, cast a horoscope to determine a favorable day for the coronation of Queen Elizabeth.[2] Here's a chart that John Dee made for himself.

{Natal chart made for himself by John Dee; source: C.U.R.A. The International Astrology Research Center}

Here's a final example of belief in astrology, astronomy, and magic persisting alongside the new natural philosophy. In the mid-1650s a man named John Webster (not the famous author but a chaplain of Parliamentarian forces in the English Civil War) wrote a book criticising the archaic curriculum of the English universities. In it he said the subjects taught were hopelessly — indeed dangerously — out-of-date and devoid of usefulness. Rather than forcing students to learn dead languages or memorize the writings of Aristotle and other ancient and more recent scholastic authors, he says they should be taught mathematics and experimental science.[3]

Webster says "Surely natural Philosophy hath a more noble, sublime, and ultimate end, than to rest in speculation, abstractive notions, mental operations, and verball disputes: for as it should lead us to know and understand the causes, properties, operations and affections of nature..." He acclaims applied mathematics — which, he points out, benefits merchants, mariners, surveyors, mechanics and others — and he condemns theoretical mathematics as merely speculative and abstract.[4] He heaps praise on chemistry, physics, and medicine as subjects of study that are "sublime, and never sufficiently praised."

But he gives as much in the way of accolades to the esoteric subjects of magic, alchemy, and astrology. He calls magic a "noble, and almost devine Science." To him, alchemy is "the most admirable and soul-ravishing knowledge of the three great Hypostatical principles of nature." And astrology is "high, noble, excellent, and useful." As you see in this extract, he lets himself be carried away on the subject.

{transcription: "What shall I say of the Science or art of Astrology, shall the blind fury of Misotechnists, and malicious spirits deter me from giving it the commendations that it deserves? shall the Acadamies who have not only sleighted and neglected it, but also scoffed at it, terrifie me from expressing my thoughts of so noble and beneficial a Science? shall the arguments of Picus Mirandula, and others, who have bitterly inveighed against it, fright me from owning the truth? shall the thundering Pulpit men, who would have all mens faith pinned upon their sleeves, and usually condemn all things they understand not, make me be silent in so just a cause? No truly, I must needs defend that which my judgment evidences to me to be laudable, and profitable; not but that I utterly condemn the ignorance, knavery, and impostorage of many pretending Sciolists, that abuse the same; but shall the art of medicine or Chymistry be condemned, and rejected, because many ignorant Empericks and false Alcumists do profess them? Surely no, let the blame be upon the protestors, not upon the profession it self. For the art it self is high, noble, excellent and useful to all mankind, and is a study not unbeseeming the best wits, and greatest Scholars, and no way offinsive to God or true Religion. And therefore I cannot, without detracting from worth and vertue, pass without a due Eulogy in the commendation of my learned and industrious Countrymen, Mr. Ashmole, Mr. William Lilly, Mr. Booker, Mr. Sanders, Mr. Culpepper, and others, who have taken unwearied pains for the resuscitation and promotion of this noble Science, and with much patience against many unworthy scandals have laboured to propagate it to posterity, and if it were not beyond the present scope I have in hand, I should have given sufficient reasons in the vindication of Astrology." [Acad. Examen, p. 51]; source: Academiarum examen, or the examination of academies wherein is discussed and examined the matter, method and customes of academick and scholastick learning by John Webster (Calvert, 1654)}

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Some sources:

"Celestial Offerings: Astrological Motifs in the Dedicatory Letters of Kepler's Astronomia Nova and Galileo's Sidereus Nuncius" by H. Darrel Rutkin in Secrets of nature: astrology and alchemy in early modern Europe ed. by Anthony Grafton (MIT Press, 2001)

Galileo's Astrology by Nick KIollerstrom on skyscript.co.uk

How Galileo Dedicated the Moons of Jupiter to Cosimo II de Medici by Nick Kollerstrom, The Inspiration of Astronomical Phenomena, Proc. of 4th INSAP Conference, Oxford, Ed. N. Campion, Bristol 2004, pp. 165-181.

Tycho Brahe och Astrology

John Dee's "Mathematicall Praeface": A Sixteenth Century Classification of the Mathematical Arts and Sciences by Charles St. Clair, Norman

The Mathematicall Praeface to Elements of Geometrie of Euclid of Megara by John Dee from Sir Henry Billingsley's first English version of Euclid's Elements, 1570

Isaac Newton and the Transmutation of Alchemy An Alternative View of the Scientific Revolution by Philip Ashley Fanning (North Atlantic Books, 2009)

Academiarum examen, or the examination of academies, wherein is discussed and examined the matter, method and customes of academick and scholastick learning by John Webster (London, Printed for Giles Calvert, 1654)

"Education" by J.W. Adamson in The Cambridge history of English literature , in 18 Volumes (1907–21) Volume IX, From Steele and Addison to Pope and Swift ed. by Adolphus Ward and Alfred Waller (Cambridge, the University Press, 1912)

"Brief lives", chiefly of contemporaries by John Aubrey, ed. by Andrew Clark, Andrew, Volume: 1 (Oxford, Clarendon Press, 1898)

"Brief Lives" by John Aubrey, ed. by Andrew Clark (Oxford, At the Clarendon Press, 1898)

Biographies in John Aubrey's Brief Lives

Only 26 and already a professor! in Renaissance Mathematicus

"Scientific Studies in the English Universities of the Seventeenth Century" by Phyllis Allen, Journal of the History of Ideas, Vol. 10, No. 2 (Apr., 1949) Stable URL: http://www.jstor.org/stable/2707416

"John Dee" by Thompson Cooper in Dictionary of national biography ed. by Leslie Stephen and Sidney Lee (Smith, Elder, & co., 1888)

"John Dee and His Supplication to Queen Mary" by P. Evans Lewin, Woolwich Public Libraries in The Library world, Vol. 5 (Library Supply Co., 1903) Extract: 'Whilst at Cambridge he only slept four hours every night, and spent eighteen hours of the day in study. So great was his knowledge, that his acquaintance was eagerly sought by such men as Gemma Frisius, Mercator, and Gaspar a Mirca, all of whom he visited in his twentyfirst year. Even at this period he was looked on askance, for he relates that in 1547 he "sett forth" at Trinity College a Greek comedy of Aristophanes, " with the performance of the Scarabaeus, his flying up to Jupiter's palace with a man and his basket of victuals on her back, whereat was great wondering and many vain reports spread about." This, probably, was only a piece of stage mechanism suitable to the crude ideas of the time and in keeping with Greene's instructions in "Tamburlaine "—" exit Venus; or if you can conveniently let a chair come down from the top of the stage and draw her up."'

"The Mistaking of 'the Mathematicks' for Magic in Tudor and Stuart England" by J. Peter Zetterberg in The Sixteenth Century Journal, Vol. 11, No. 1 (Spring, 1980), pp. 83-97. Stable URL: http://www.jstor.org/stable/2539477

"Science and Education in the Seventeenth Century: The Webster-Ward Debate" by G. Allen; reviewed by Theodore M. Brown in Isis, Vol. 64, No. 3 (Sep., 1973), pp. 422-424. (The University of Chicago Press) Stable URL: http://www.jstor.org/stable/229755

Hermeticism in wikipedia

John Aubrey in wikipedia

Brief Lives in wikipedia

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Notes:

[1] The quote comes from Academiarum examen, or the examination of academies, wherein is discussed and examined the matter, method and customes of academick and scholastick learning by John Webster (London, Printed for Giles Calvert, 1654)

[2] "John Dee" by Thompson Cooper in Dictionary of national biography ed. by Leslie Stephen and Sidney Lee (Smith, Elder, & co., 1888)

[3] Webster's diatribe was criticized by scholars who pointed to instances where the universities were teaching the new subjects. But as Phyllis Allen and others have pointed out the chief emphasis of education at Oxford and Cambridge remained as it had been. Mathematics and natural philosophy were emphatically secondary subjects of education. "As a rule, the tutor rather than the college had the greatest influence upon the student's work. A good tutor could do much for his pupil by making wise choices in the question of reading matter. Most tutors were not interested in the new experimental sciences, and some even overlooked the work of ancient scientists. One Cambridge tutor insisted that 'Mathematics and Natural Philosophy [were] not to be hurried.' Judging by the small amount of either that the average student seems to have learned, most tutors must rarely have found time to pursue these studies in an unhurried manner. ... Aside from these classics [Aristotle, Ptolomy, Euclid, ...] there were a few modern texts available. In algebra, the more advanced undergraduate could read Thomas Hariot's Artis Analyticae Praxis (London, 1631), in which he introduced Francis Vieta's methods to England. In arithmetic, a popular text was Edmund Wingate's Arithmetique Made Easie (London, 1630). For geometry, Henry Billingsley's translation of Euclid was used, together with Christopher Clavius' commentaries upon the same author, and John Speidell's Geometrical Extraction (London, 1616), which John Aubrey says "made young men have a love to geometry." -- "Scientific Studies in the English Universities of the Seventeenth Century" by Phyllis Allen, Journal of the History of Ideas, Vol. 10, No. 2 (Apr., 1949) Stable URL: http://www.jstor.org/stable/2707416

[4] Webster cites John Dee as a main source for his comments on the value of applied mathematics and praises him as "that myrror of manifold learning." -- Academiarum examen, or the examination of academies, wherein is discussed and examined the matter, method and customes of academick and scholastick learning by John Webster (London, Printed for Giles Calvert, 1654)

Mrs. Collins

I've been studying the life and works of a man who lived in the middle half of the seventeenth century. He was sufficiently well known to have been written up by a succession of biographers, but their sources of information are paltry and all their accounts are necessarily brief. This late example can stand for all: Collins, John (1625-1683) by Agnes Mary Clerke in the Dictionary of National Biography, 1885-1900, Volume 11.

Collins rarely wrote about himself and his family. This paragraph in the draft of a lengthy letter on mathematical topics is one of only a few brief accounts.

{Extract from a letter of John Collins to Dr. John Beale, August 20, 1672. Beale was one of the earliest fellows elected to the Royal Society in the early 1660s. Transcription: "I married the younger daughter of two only children of Mr. Wm. Austin, who, being one of his Majesty's cooks, when P. of Wales, was, by Dr. Wilkins' means, made and continued master cook of Wadham college in Oxford, during the late troubles, and is now master cook, to his Majesty, of the Lord s k[itchen]. I live at my said father-in-law's house in Petty [France], W[estminster], over against the Adam and Eve. He is now in Cheshire with his other daughter, and may return, if God please, a little after Michaelmas. Whilst in Oxford he was much esteemed for his great skill in simpling, gardening, planting trees, flowers, &c. which I mention, as understanding your good knowledge and delight therein."}

He fathered seven children, about whom nothing is known. He numbered them only once, in a letter dated May 23, 1677, to a parish priest whose skill in mathematics he admired. Five years later he said that even in 1672 he had "a great family to maintain," meaning wife and children.[1]

This latter statement was a report of a request he made that the government pay him arrears in salary and pension that were owed. Here's the relevant section in the clerk's "secretary" hand.

{Source: Manuscripts of Lord Montagu of Beaulieu at Beaulieu House. Transcription: "In June 1670 Collins was employed as chief Clerke in the Councill of Plantations under Mr Slingesby as Secretary, who promised to procure the said Collins a Salary of 200£ per annum, but a Committee of the Councill would agree to allow no more than 150£, and was so ill paid that at Michaelmas 1672 there was about 300£ due to him, he having a great family to maintain, was necessitated to coame that and seeke other employments for obtaining a livelyhood, and happy it was he then lost it, in regard others so employed, have been so ill paid, and Collins hath yet owing to him on that account 150£. Moreover whilst Collins was there employed he kept most of the Bookes, which are many, his hand Writing being better liked that others."}

We don't know the date of his wedding, but if Collins had a great family to maintain in 1672 he must have been married some years before then. He can't have married while serving on shipboard in the Mediterranean (1642-49) so it's reasonable to suppose the event took place in the 1650s. Still, I think the early 1660s are a better guess.

We know for sure that the event took place before April 23, 1663, because on that date a mathematical practitioner wrote to Collins and in closing he sent his "respects to yourself and Mrs. Collins." I think it would have taken place after the summer of 1660. That was when her father was appointed a chief cook to the King. That job brought him and his family to London from Oxford and Collins was then in London and had been for some time.

Regardless of their wedding date, we can be sure that Collins and his wife were happily married because the correspondent goes on to style her as his "second self." The phrase suggests that the author, Michael Dary, perceived an unusually close relationship between man and wife. It was used by others in Collins' time (and later) but as between friends not marriage partners. You can see this in the examples given in the Oxford English Dictionary. And you guess how infrequently such closeness was apparent between man and wife in reading the forceful admonition of William Penn, speaking out against the usual practices of his time: "But in Marriage do thou be wise; prefer the Person before Money, Vertue before Beauty, the Mind before the Body: Then thou hast a Wife, a Friend, a Companion, a Second Self; one that bears an equal Share with thee in all thy Toyls and Troubles."[2]

At the time Collins married, both he and his fiancée were modestly well off, "middling" in the terminology of the time. Afterwards his personal finances advanced and declined in a pattern similar to the fluctuations of the finances of the royal court and, at the time of his death in 1683, he was owed quite a bit in suspended pension and other deferred government payments.[3]

His wife's name was Bellona. As he says in the letter quoted above, she was the younger of two daughters, born into a small family that was headed by a master chef, William Austin. During her youth William Austin was, first, the chief cook in the kitchen of the Prince of Wales — Charles, eldest son of king Charles I — and then, during the years of the Civil War and Commonwealth, chief cook in the kitchen at Oxford's Wadham College.[4] When Charles became King Charles II, Austin was appointed his chief cook of the "household" kitchen. The household kitchen was "below stairs" and it fed not the King and those who dined at his table, but rather all others who ate at the king's expense: staff, courtiers, hangers-on, and even members of the House of Lords when they gathered in Parliament.[5]

By the time of her father's appointment to serve the king Bellona was probably of an age at which she have been expected to seek a husband and start a family. We don't know when she met John Collins. It's likely they encountered one another in the late 1630s, during her father's service to the Prince of Wales. Then in his teens, Collins was employed as a "servant's servant" to help John Marr, who was clerk in the kitchen where Bellona's father was master cook. If not Bellona herself, Collins certainly was acquainted with William Austin at that time. Whether or not they met when young, they're likely, as I say, to have bonded sometime after August 1660 when Austin returned from Oxford to London on his appointment as head of the new King's household kitchen.[6]

Not long after the time I suppose the two to have begun courting, Bellona sought and received appointment as a laundress for the intended wife of King Charles. The treaty of marriage was signed June 23, 1661, but the royal wedding did not take place (in three ceremonies) until the following spring. Bellona received her appointment in between, on November 14, 1661. It was no menial position. She was "laundress of the board" and her job was both to supervise and to some degree carry out the cleaning and pressing of the queen's table linen. There were two other laundresses of the board: one of the king's "privy" table and another of the household. The three had help from at least four pages, probably more, as well as a yeoman and a couple of grooms. Since meals consumed at the queen's table were smaller than at the household table and both smaller and less elaborate than at the king's table, Bellona would have needed less of this help than the other two.[7]

Not surprisingly, the salary of the laundress of the queen's board was a few pounds lower than that of the two others. It does not seem like very much money at all — £18 5s a year — but it was supplemented by "board wages," or money paid out in lieu of room and board and these board wages may have enhanced her income quite a bit. The amount of her board wages isn't recorded, but when in 1685 the board wages of the laundress to the household table were stopped, her salary was increased to £120. If Bellona's total income from her job was even approaching £100 a year she was doing quite well by standards of the time. In fact she would be doing very well whether she was then a single woman living at home or a newly married one setting up her own household.[8]

Competition for the position was intense. After Charles was crowned he and his court officers were inundated with requests from people who had suffered by their adherence to the royal cause during the Civil War and Commonwealth period. This extract from the Calendar of State Papers, Domestic, for May 1662, shows three formal requests for the job.[9]


The three were occasioned by the wedding of Charles and Catherine in Lisbon by proxy in April 1662. The petitioners evidently did not know (or did not care) that Bellona had received her appointment half a year before. The record of her appointment is laconic.[10]


As a child of the royal household Bellona would have grown up with many of the people with whom she now served. However she would not have been personally known to any of the high officers of the court, and their reference to her as "Mary, jun." shows that they did not know her given name (presumably in their ignorance they used her mother's name — hence the "jun.").

Although most single women were in the workforce, few had jobs as well paying as Bellona's. No matter how much her family connection may have helped her, she herself must have both vigorously pursued the job and shown herself worthy of holding it.[11]

We don't know what Bellona looked like, but this Dutch painting probably gives a reasonably good idea of her clothing and the work she performed.

{Washerwoman by Gabriel Metsu, ca. 1660s; source: wikipedia (National Museum, Warsaw)}

In Bellona's time one laundered table linen by boiling and washing with soap. The laundresses used lye to remove stains and sunlight or bluing to whiten. They hung or spread linens to dry and then used either "smoothers" or heated irons to flatten the fabric and give it a pleasant sheen. Once smoothed, the linens would be placed in a press such as the one shown below. The press would impart attractive folds.

{This press is in collections of the Wawel Royal Castle, Cracow.}

Not an ordinary meal, this shows the coronation banquet for James II, the successor of Charles II. You can see the folds in the linen at table ends.

{source: The history of the coronation of James II and of his royal consort Queen Mary: solemnized in the Collegiate church of St. Peter in the city of Westminster, on Thursday the 23 of April 1685 by Francis Sandford (London: In the Savoy: printed by T. Newcomb, 1687)}

This enlarged detail shows the folds more plainly.


Here are, at left, a glass English linen smoother and, at right, a detail from a medieval painting showing linen folds in a more ordinary meal at the king's table.[12]

{The right hand image is a detail from a medieval painting (Histoire d'Olivier de Castille et d'Artus d'Algarbe, Paris, BnF). I couldn't find an example from Bellona's time. Source of both images: oldandinteresting.com}

These two images also give a general idea of Bellona's appearance. The first shows an English housewife in the time of Bellona's childhood and the second shows a Dutch servant of the time when she'd become an adult. She may have looked something like the first when she dressed at her best and something like the second when at work.

{On the left: Drawing of an Englishwoman by Wenceslaus Hollar, circa 1645; source: English Costume Painted & Described by Dion Clayton Calthrop (Adam & Charles, London, 1907). On the right: Detail from A Woman Reading a Letter by Gabriel Metsu, ca. 1662 (Dutch); source: Nicole Kipar's Late 17th Century Clothing History}

Of the clothes worn by working women in the reign of Charles II, one source says: "The poorer classes were not, of course, dressed in hooped skirts, but the bodice and gown over the petticoat, the apron, and the turned back cuff to the short sleeve were worn by all. The orange wench laced her gown neatly, and wore a white cloth tied over her head; about her shoulders she wore a kerchief of white, and often a plain frill of linen at her elbows."

--------

Some sources:

An introduction to merchants accounts : containing five distinct questions or accounts by John Collins (London, Printed by James Flesher for Nicholas Bourn, 1653, 2d ed 1664)

Report on the manuscripts of Lord Montagu of Beaulieu, Great Britain. Royal Commission on Historical Manuscripts (Printed for H. M. Stationary off., by Mackie & co. ld., 1900) and the MSS original from Beaulieu

The Personal Rule of Charles I by Kevin Sharpe (Yale University Press, 1996)

The Later Stuart Royal Household 1660–1714 in 'Chronological Survey 1660-1837: The Later Stuart Household, 1660-1714', Office-Holders in Modern Britain: Volume 11 (revised): Court Officers, 1660-1837 (2006), pp. LXXVI-XCVIII. URL: http://www.british-history.ac.uk/report.aspx?compid=43757 Date accessed: 09 December 2011

'Introduction: Administrative structure and work', Office-Holders in Modern Britain: Volume 11 (revised): Court Officers, 1660-1837 (2006), pp. XX-XXXVII. URL: http://www.british-history.ac.uk/report.aspx?compid=43751 Date accessed: 09 December 2011.

The King's Servants: the Civil Service of Charles I, 1625–1642, by G.E. Aylmer (London, 1961)

The Database of Court Officers 1660-1837 R. O. Bucholz, Project Director. The Database of Court Officers is an online computer database providing the career histories of every remunerated officer and servant of the English royal household from the Restoration of the monarchy in 1660 to the accession of Queen Victoria in 1837.

Calendar of state papers / Domestic series / Reign of Charles II, 1661-1662 ed. by Mary Anne Everett Green (Longman, Green, Longman, & Roberts, 1861)

Some fruits of solitude by William Penn (London, Printed for Thomas Northcott, 1693, reprinted: S. T. Freemantle, 1900)

The Life and Times of John Wilkins Warden of Wadham College, Oxford; Master of Trinity College, Cambridge; and Bishop of Chester by P. A. Wright Henderson (William Blackwood and Sons
Edinburgh and London, 1910)

Calendar of State Papers, domestic series, of the reign of Charles II 1660-1685 (Longman, Green, Longman, & Roberts, 1861)

Calendar of state papers, domestic series, of the reign of Charles II: preserved in the state paper department of Her Majesty's Public Record Office, Volume 1 (Longman, Green, Longman & Roberts, 1860)

Correspondence of scientific men of the seventeenth century: including letters of Barrow, Flamsteed, Wallis, and Newton, printed from the originals in the collection of the Right Honourable the Earl of Macclesfield, Vol. 1, compiled by Stephen Jordan Rigaud (Oxford, the University Press, 1841)

Correspondence of scientific men of the seventeenth century, including letters of Barrow [&c.] in the collection of the earl of Macclesfield, Vol. 2, compiled by Stephen Jordan Rigaud (Oxford, the University Press, 1841)

Some fruits of solitude by William Penn (London, Printed for Thomas Northcott, 1693, reprinted: S. T. Freemantle, 1900)

English Costume Painted & Described by Dion Clayton Calthrop (Adam & Charles, London, 1907)

History of laundry on oldandinteresting.com

Prospects and preliminary work on female occupational structure in England from
1500 to the national census by Jacob Field and Amy Erickson (University of Cambridge). Extract: "The assessments for the 1666 Hearth Tax for the City of London, abstracted by Jacob Field for his doctoral thesis on the Great Fire, illustrates this approach but also show its difficulties. This listing was drawn up by a number of different assessors, not all of whom recorded occupations. The total sample of householders was 11,195, 1,661 of whom were female. Around ten per cent of females had their occupation recorded, representing 177 individuals, compared to around 20 per cent of males, representing 1,888 individuals. As table 1 shows, the data is slightly skewed towards the upper end of the socio-economic spectrum – particularly vastly underestimating the proportion of females engaged in service." (See table p.6)

Identifying women's occupations in early modern London by Amy Erickson. Abstract: "This paper is a preliminary survey of three sources for women's occupations in eighteenth-century London: apprenticeships in the city livery companies; the registers of Christ's Hospital showing apprenticeships; and the records of testimony in the Old Bailey. There is currently only one article in print on the female occupational geography of London in this period (P. Earle, 1989), based on testimony in church court records. In the sources examined here, women worked largely in public, trading and production occupations. This profile is substantially different from the preponderance of domestic service and making/mending textiles which appears in the church court records."

"Never Married: Singlewomen in Early Modern England Never Married: Singlewomen in Early Modern England by Amy M Froide; review by: Retha M Warnicke" Renaissance Quarterly, Vol. 59, No. 2 (Summer 2006), pp. 622-623 Published by: The University of Chicago Press on behalf of the Renaissance Society of America; Stable URL: http://www.jstor.org/stable/10.1353/ren.2008.0342
Froide says that about a third of English women were single during the middle years of the seventeenth century. Many stayed unmarried, but most eventually, like Bellona Austin, did marry. Social norms made it difficult for them to support themselves, but many did nonetheless. Excerpt: "singlewomen, like all women at this time, were considered physically and emotionally inferior to men in a patriarchal society that disadvantaged them in comparison to men of their class or status, especially in regard to wealth, earning power and access to high status public office."

"Singlewomen in the European past, 1250-1800 by Judith Bennett; Amy Froide; review by June Purvis" The English Historical Review, Vol. 115, No. 461 (Apr., 2000), pp. 443-444Published by: Oxford University Press; Stable URL: http://www.jstor.org/stable/579115

"Hilda L. Smith. All Men and Both Sexes: Gender, Politics, and the False Universal in England, 1640-1832, review by: Deborah Valenze" The American Historical Review, Vol. 109, No. 1 (February 2004), pp. 251-252 Published by: The University of Chicago Press on behalf of the American Historical Association; Stable URL: http://www.jstor.org/stable/10.1086/530280

Catherine of Braganza (Queen) in the Diary of Samuel Pepys

Catherine of Braganza

Catherine of Braganca (1638 - 1705) on h2g2 by Not Panicking Ltd

Catherine of Braganza, in Wikipedia

Queen Catherine of Braganza Website of the Queen's Royal Surrey Regiment

C17th England: Catherine of Braganza on themakeupgallery

Portrait of Catherine of Braganza by Mary Ellyn Kunz on the web site of Pennsbury Manor Volunteers

Catherine of Braganza on Tea at Trianon by Elena Maria Vidal.

Catherine of Braganza (1638-1705) by Heidi Murphy on Britannia.com

Catherine of Braganza by Thomas Frederick Tout in the Dictionary of National Biography, 1885-1900, Volume 09
Catherine of Braganza

Early modern England 1485-1714 by R. O. Bucholz and Newton Key (John Wiley and Sons, 2009)

---------

Notes:

[1] The priest was Thomas Baker who held the living at Bishop's Nympton, Devon, and, as an avocation of course, was an excellent mathematician. On May 23 1677 Collins wrote him this. "I have yours of the 23d of April, and have been dilatory in answering. The truth of it is, it hath been my misfortune to be concerned in public employments, as in the Council of Plantations, &c., wherein I have not been paid, and have great arrears due to me, for want whereof I am almost ruined; and having a numerous family to maintain, to wit, a wife, and seven small children, I am forced to undertake such occasional business as offers, and by consequence to neglect a correspondence with the learned, which, though unworthy, I much covet. Sir Jonas Moore being a surveyor of the Stores and Ordnance, and now naval preparations going on, he is much in journeys and absent, so that I can give you no account as yet of your labours going to the press, though I much wish I could, and shall omit no endeavours to hasten." -- Correspondence of scientific men of the seventeenth century: including letters of Barrow, Flamsteed, Wallis, and Newton, printed from the originals in the collection of the right honourable the Earl of Macclesfield : In two volumes, Volume 2 compiled by Stephen Jordan Rigaud (Oxford, at the University Press, 1841)

[2] Christoph J. Scriba's article on Collins in the DNB says "About 1670 he married Bellona, laundress of the table linen to the queen, and the younger daughter of William Austen, head cook to Charles II; they had seven children." It's strange he gets the wedding date wrong, though all else right. Regarding second self, here is what the OED says:

second self n. a friend who agrees absolutely with one's tastes and opinions, or for whose welfare one cares as much as for one's own.
1586 T. Bowes tr. P. de la Primaudaye French Acad. I. 150 The mightie and inuiolable bond of friendship, as of a second-selfe did constraine him to lend his eare to his friend.
1665 R. Brathwait Comment Two Tales Chaucer (1901) 93, I will offer to your choice two things, wherein please your self, and you shall please me who am your second self.
1778 F. Burney Evelina I. xxvi. 215 As to Miss Mirvan, she is my second self, and neither hopes nor fears but as I do.
1851 E. Bulwer-Lytton Not so Bad i. i. 6 Ha, Softhead! my Pylades—my second self!
transf.
1609 Shakespeare Sonnets lxxiii. sig. E4, Blacke night..Deaths second selfe that seals vp all in rest.

Penn's admonition comes from Some fruits of solitude by William Penn (London, Printed for Thomas Northcott, 1693, reprinted: S. T. Freemantle, 1900). Here is the closing sentence of the letter to Collins by his mathematical practitioner friend, in full:

Not to trouble you further, but my respects to yourself and Mrs. Collins, your second self, I shall only tell you, that if there be any thing wherein I may serve you at Bristol, it shall be endeavoured by

Your engaged friend, Mich. Dary

Bristol, the 23rd
April, 1663.
-- Correspondence of scientific men of the seventeenth century compiled by Correspondence of scientific men of the seventeenth century (Oxford, the University Press, 1841)

[3] Regarding his status as someone "middling" Collins wrote of himself that he was "but a mean person," mean and middling connoting the same standard of living. Regarding money owed him, he was not alone in being stiffed by the government. The court always paid out more than it took in, but periodically the imbalance became so great that economies were necessary and it was these bouts of financial retrenchment that made government employment perilous. Collins did eventually receive some payments that the government owed him but not nearly what was owed. The phrase "but a mean person" appears in: "Narrative of John Collins, 1682," Report on the manuscripts of Lord Montagu of Beaulieu, Great Britain. Royal Commission on Historical Manuscripts (Printed for H. M. Stationary off., by Mackie & co. ld., 1900)

[4] William Austin's association with John Wilkins is an interesting one. I suspect they were linked by friendship with John Marr. Wilkins was a scholar at Oxford. Marr was clerk, that is accountant and purchasing officer, in the same royal kitchen where Austin was chief chef. Wilkins and Marr were both eminent mathematicians and, when the royal court was in Oxford they very likely formed an acquaintance. When the position of chef at Wadham College became vacant, it's reasonable to suppose Marr proposed that Wilkens, then head of Wadham, hire the man for the job. It's interesting that Marr had employed Collins as "servant's servant," in this case clerk's assistant, because, though still in his teens, Collins may have met both Bellona Austin as well as John Wilkins at this time. He later wrote: "In my Youth-hood I was employed in Clerk-ship under, and received some Mathematical Knowledge from Mr. John Marr, one of the Clerks of the Kitchin to His Present MAJESTY, when Prince of Wales, the said Mr. Marr being very Eminent for his Mathematical Knowledge, some testimony whereof' may be evinced, from those excellent Dyals, wherewith the Gardens of our Late SOVEREIGN were adorned." -- An introduction to merchants accounts: containing five distinct questions or accounts by John Collins (London, Printed by James Flesher for Nicholas Bourn, 1653, 2d ed 1664)

[5] 'The household below stairs: Household Kitchen', Office-Holders in Modern Britain: Volume 11 (revised): Court Officers, 1660-1837 (2006), pp. 502-509. URL: http://www.british-history.ac.uk/report.aspx?compid=43871 Date accessed: 25 November 2011.

[6] Here's a record of William Austin's appointment as master cook to King Charles II. The date of appointment is only a few weeks after Charles' return from exile.

{source: The Database of Court Officers 1660-1837 R. O. Bucholz, Project Director, an online computer database providing the career histories of every remunerated officer and servant of the English royal household from the Restoration of the monarchy in 1660 to the accession of Queen Victoria in 1837}

This table gives some idea of the extent and varied functions of the ca. 300 staff members "below stairs":

{source: The King's Servants: the Civil Service of Charles I, 1625–1642, by G.E. Aylmer (London, 1961)}

[7] See my list of sources for information about Catherine of Braganza, the royal laundry, and related topics. Bucholz provides a succinct description of the laundry's functions: The Database of Court Officers 1660-1837 R. O. Bucholz, Project Director, an online computer database providing the career histories of every remunerated officer and servant of the English royal household from the Restoration of the monarchy in 1660 to the accession of Queen Victoria in 1837

[8] See the Bucholz database for amounts paid laundry staff members.

[9] Calendar of state papers, domestic series, of the reign of Charles II: preserved in the state paper department of Her Majesty's Public Record Office, Volume 1 (Longman, Green, Longman & Roberts, 1860)

[10] Calendar of state papers, domestic series, of the reign of Charles II: preserved in the state paper department of Her Majesty's Public Record Office, Volume 1 (Longman, Green, Longman & Roberts, 1860)

[11] On single women in the workforce, see entries for Amy Ericson and Amy Froide in the sources list.

[12] Here is this interesting painting in full.

The BnF's caption reads: "Festin d'apparat. Histoire d'Olivier de Castille et d'Artus d'Algarbe, Paris, BnF, Département des manuscrits, Français 12574 fol. 181v. La table d'honneur est isolée sous un dais, tandis que le gros des convives se répartit le long d'une table, dont ils n'occupent qu'un côté. Le ballet des serviteurs est mené par le maître d'hôtel, tandis qu'au buffet et près du prince veillent d'autres officiers de bouche, prêts à répondre à ses moindres désirs. Des musicicens égayent le repas."