COMPUTATIONAL FRACTIONS OF THE GRAIN:

MITES , DROITS , PERIODS, AND BLANKS

Philip Grierson

In the seventeenth and eighteenth centuries it was customary, in mint reck-

onings of a very precise character, to use notional subdivisions of the grain

called mites, droits, periods and blanks, each being alternately a twentieth

or a twenty-fourth of the one above it. The earliest printed listing of them

occurs in an appendix to James I ' s proclamation of his second coinage,

dated 16 November 1604,1 for a supposed earlier one of 1601 is a mistaken

inference from an eighteenth-century text.2 Their relationships are set out

by Gerard Malynes in 1622 in his Consuetudo vel Lex Mercatoria , one of the

best general handbooks of mercantile practice published in Europe during

the seventeenth century:

'the Troy we ight . . . (contains) twelue ounces, euerie ounce twentie penie

weight, euerie penie weight twentie and foure grains, and euery grain

twentie mites, euery mite twentie and foure droicts, euerie droict twentie

periods, euerie period twentie and foure b l a n k s ' . 3

The ounce, pennyweight and grain in this schedule were real weights

and their relationships to each other were traditional, but the fractions of

the grain were both imaginary and novel. They can be set out in tabular

form.

1 grain = 20 mites = 480 droits = 9600 periods = 230,400 blanks

1 mite 24 = 480 " = 11,520

1 droit 20 = 480

1 period = 24

We still use imaginary weights today. When the proclamation of 1604 gave

the weight of the penny as 7 grains 14 mites 20 droits 2 periods 12 blanks,

it was doing essentially the same thing as Schedule 1 of the Coinage Act

of 1870 did in stating the weight of the sovereign as 123.27447 grains, for

even though nineteenth-century balances could weigh much more accurately

than their seventeenth-century counterparts, such tiny fractions can only

be arrived at by long division. In King James's time the weighing of coins

and precious metals was not normally taken beneath the troy grain (0.065

grams) . This is shown by a 'Declaration of an order for the making of cer-

tain small cases for ballances and weights to weigh all manner of gold

coins'," itself reflecting the terms of a proclamation for establishing standard

weights and measures of 16 December 1587-5 It was quite exceptional for a

proclamation of 26 December 1632 on the distribution of standard weights by

the Mint6 to provide for them going as low as a half-grain.

James Murray in 1896 started a brief correspondence on the notional

fractions in Notes and Queries.7 They obviously represent an artificial

182 COMPUTATIONAL FRACTIONS OF THE GRAIN

prolongation, to 'weights' below the grain, of the alternating 20/24 multiples

in use just above it (1 ounce = 20 pennyweights, 1 pennyweight = 24 grains).

Strange as they appear to us, they were, as he pointed out, not dissimilar

to the decimal fractions that replaced them in the nineteenth century, for

decimal fractions are only the sum of tenths, hundredths, thousandths, and

so on. If the old Scottish Tron weight known as a 'drop' (l/l6th of an

ounce) can be equated with 37.588 troy grains, this means that it weighed

37 grains + 5/10ths of a grain + 8/100ths of a grain + 8/1000ths of a grain,

while expressing it in the old measures as 37 grains 11 mites 18 droits 4

periods 19f blanks meant that it weighed 37 grains + ll/20ths of a grain

+ l8/480ths of a grain, etc. Decimal fractions have the advantage of being

easier to handle, though since the last figure may be only an approximation

to the nearest integer they may be less correct. Although Murray 's corres-

pondence brought to light some early examples which he was able to use for

the entries in the Oxford English Dictionary ,8 it did nothing to account for

the terms themselves.

These in fact arose out of the need to devise specific terms for fractions

in a world that was not accustomed to expressing any but the simplest frac-

tions (three-quarters, one-eighth) numerically. The normal practice was to

employ entities whose relationships to each other was well known. People

spoke, for example, of an inch of an acre, meaning one-twelfth of an acre

(there were twelve inches in the foot), or expressed the fineness of sterling

silver (925/1000) as 11 ounces 2 pennyweights, i .e . ll/12ths (there were

twelve ounces to the Troy pound) plus 2/240ths (there were twenty penny-

weights in the ounce and so 240 in the pound) . But if fractions of the

grain were to be devised that continued downwards its pattern of alternating

twenty and twenty-four multiples, it would be necessary to find suitable

terms for them. Mite was an obvious first candidate, since it was already

used for anything very small. The others, I would suggest, were chosen

half in jest, for as written down they could be thought of as entities of

diminishing magnitude, droit as a vertical stroke, period as a full stop

(still 'period' in the United States), and blank as nothing at all. Possi-

bly, indeed, the terms were taken over from the vocabulary of type-setters

or type-cutters, for the skills of die-sinkers and type-cutters have much in

common, but' we know little of printers' technical vocabulary in this country

prior to 1683 and this can be no more than a surmise. Let us consider the

terms in order.

Mite. This word, as the citations in the OED, s . v . Mite1 '2 make plain,

was Indo-Germanic in origin and applied in Middle English to anything very

small in size (as an insect, 'mite') or value ( e . g . , the widow 's 'mite' ,

minuta in the Vulgate, of Mark xi i . 43 ) , though in the latter sense it was

influenced by the Flemish/Dutch word mijt, used for the smallest denomina-

tion of low quality billon struck in the Low Countries from the fourteenth

century onwards and worth l/24th of the Flemish groot, the equivalent of

a 'penny ' in the accounting system. This did in fact provide a notional

fraction, l/24th of a penny, unknown to the OED and sometimes used in mint

accounts: Sir Martin Bowes, for example, stated the profit on the minting

of silver between 1 June 1544 and 31 March 1545 as 8s . 8 }d . 5 mites, the sum

in fact ending 8 17 /24d . 9 It has been asserted that 'mite' was used in the

later middle ages with the meaning of a precise weight, but the texts cited

to this effect will not stand up to examination. One, Ruding 's statement

that the remedy laid down in the mint indenture of 4 December 1343 for the

striking of Edward I l l ' s gold coinage was 'a mite of a carat' is a simple

mistake, for the mytisme he quotes is a misreading for oytisme, i.e. huitieme,

and the remedy is an eighth of a carat. 1 0 The other, used in the OED ( s . v .

Mite2 2) as evidence for the application of the word to a precise weight as

COMPUTATIONAL FRACTIONS OF THE GRAIN

early as 1390, is a verse in John Gower's Confessio amantis11 (v .4412 : 'that

scarsly wolde it weie a myte ' ) , and in the context this means no more than

'something very small ' . On the other hand , the evidence in favour of its

computational use dating only from the sixteenth century is very strong, for

no fraction, whether real or notional, is mentioned in any of the late medi-

eval or early sixteenth-century treatises on weights and measures that have

survived , 1 2 and Robert Record in The Grounde of Artes, the most influential

work on mathematics published in England in the sixteenth century, asserts

firmly that no weight below the grain was in normal use. 1 3 Its introduction

presumably took place at the same time as the adoption of terms for the

other fractions, and its common meaning of 'something very small' made it

a natural choice.

Droit. This, if my suggestion is correct, would be French droit (from

Lat. directum) in the sense of 'upright ' , as in such phrases 'se tenir

droit' , 'il est droit sur ses pieds ' , 'droit comme un I ' . Although this

sense is not recorded in English, there is nothing against the hypothesis

of a borrowing from French, as occurred with blank. Whether it was also

a typographical term, as were period and probably blank, we do not know,

for there is no technical work in English on typography earlier than that

of Moxon of 1683.

Period. This appears in the sense of 'full stop' in a religious poem

published in 1609, and the way in which it is used shows that by that time

it formed part of the common speech.111 It was indeed the normal term used

in English up to the nineteenth century, when it came gradually to be re-

placed by the current 'full stop'. See OED, s . v . Period l ib .

Blank. This term was applied in English to the white circle in the

centre of a target {OED, s . v . Blank 5 b . 2 ) , and was thus something smaller

than a surrounding black circle, but in its computational sense it is more

likely to have been suggested by typography. The normal seventeenth-

century English term for what Moxon in 1683 terms the 'white between words'

was ' space ' , 1 5 as it still is today, but blank may have been used earlier,

as blanc is for such a space in French.

When and how did the use of these terms for fractions of the grain

originate? The earliest printed reference to them that I have found is in

the proclamation of 1604 already referred to. Their presence there apparent-

ly arose out of a wish to display the English system side by side with the

Scottish one, which used twenty-fourths consistently and was borrowed from

France. 1 6 But there are earlier manuscript sources, rather confusedly cited

in the OED, going back to the third quarter of the sixteenth century.

The two earliest both occur in the remarkable collection of sixteenth-

and early seventeenth-century Mint documents and memoranda which are

bound up together as Harleian MS 660 in the British L ibrary . 1 7 No.25 (fos.

76-85) in this, a 'Treatise or Discriptyone of things cheefly appertayning

to the Mintage' is by William Humfrey, a London goldsmith and assayer to

the Mint, and gives essentially the same breakdown of the grain as Malynes

was to do (fo.8lv: 'Euery subtylle grayne (doth) contayne 20 m y t e s . . . 1 ) .

The work is undated but must have been written before 1579, when Humfrey

died. 1 8 The same definitions are given in another work (No.38, fos. 107r-114r)

in the same volume, a memorandum by Sir Francis Knollys prepared shortly

after the completion of the Great Recoinage for submission to a royal com-

mission on the exchanges consisting of the Lord Treasurer (William Paulet,

Marquess of Winchester), Sir Francis Knollys, Sir Walter Mildmay, and Sir

William Cordalle. It is entitled 'A Confferrence of the waightes of Bullyone

and vallues of the syluere moneyes of England, and the syluer moneyes of

184 COMPUTATIONAL FRACTIONS OF THE GRAIN

the Lowe Contreyes, with a Comparrysone of the Exchanges used to and froe

betweene the Burse of Anwarpe and Lumbardestreete in London ' , and is dated

February 1564 of the seventh year of Elizabeth, i .e . February 1565. The

substance of this lengthy and important document was printed in 1924 by

Tawney and Power, 1 9 and it has been widely quoted by subsequent scholars,

but the list of fractions of the grain occurs in the preliminary section in-

tended to establish the mint par of exchanges between English and Flemish

currencies, and Tawney and Power omitted the detailed calculations of this

section as being too technical in character. The pattern of fractions was

thus at least well established by the 1560s, but how much further back it

goes is difficult to say. It may have been devised because the repeated

debasements of the mid-century had forced the Mint to indulge in minuter

calculations than had been required in earlier times, though on the other

hand precision, with debased coins, is a less important consideration.

How long did these fractions remain in use? It is hard to say, partly

because of their unreality, partly because they virtually represented the

'house practice' of the Royal Mint and were little used outside it - Malynes

had close relations20 with the Mint and the Royal Exchange, though his claim

that his father was a moneyer seems to be fictitious - so that they make

only very occasional appearances in printed documents. A table largely co-

inciding with that of King James's proclamation was appended to the act of

parliament of 17 July 1649 (cap.43) ordering the new coinage for the Common-

wealth, 2 1 and they are usually noted in the dictionaries and descriptive works

that began to proliferate from the mid seventeenth century onwards - Thomas

Blount's Glossographia,22 Phillips' New World of English Words," Morden's

Geography Rectified ,2" Bradley ' s Family Dictionary25 - although Samuel Johnson,

with his more literary bias, ignored them all. As late as the nineteenth

century some authors of handbooks on coinage or weights and measures still

thought it incumbent on them to explain what they were, while admitting

that in actual calculations they had long since been displaced by decimal

fractions of the g r a i n . 2 6 There was , particularly in their later stages, con-

siderable uncertainty as to how they should be spelled, period being often

periot, peryoit or perrit, and droit being often rendered doit through

confusion with the name of a Low Country copper coin (Dutch duit; English

doit) familiar in this country from the sixteenth century onwards. By the

eighteenth century they were, effectively, dead.

NOTES

1. R .Ruding , Annals of the coinage of Great Britain, third edition (1840) ,

I , 362; full text in Stuart Royal Proclamations, edited by J . F . Lark in

and P . L .Hughes (Oxford, 1973), I, no.47, pp.99-103.

2. OED, s . v . Droit, from a table headed 'Weights of Silver Coins 43 Eliz.

1601 ' , in J.Millan, Coins, weights and measures Ancient and modern,

of all nations. Reduced into English on above 100 tables (1747) , p . 7 .

Millan was giving the theoretical weights of the silver coins of his own

day , and the reference is due to the fact that these still conformed to

the standard introduced '43 Eliz, 1601 ' .

3- Consuetudo vel Lex Mercatoria, or the Ancient Law Merchant (1622) , p .292 .

4. H(umphrey) D(yson) , A Booke Containing All Such Proclamations as Were

Published During the Raigne of the late Queene Elizabeth (1618) , p . 258 .

COMPUTATIONAL FRACTIONS OF THE GRAIN

5. Tudor Royal Proclamations, ed. P . L . H u g h e s and J .F . Larkin (New Haven

and London, 1969), I I , no.695, p .547 .

6. Ruding, I, 386. The proclamation is no. 1652 in R.Steele, A Bibliography

of Royal Proclamations of the Tudor and Stuart Sovereigns, I (Biblio-

theca Lindesiana, V. Oxford, 1910).

7. J . A . H . M u r r a y , 'Subdivisions of the Troy Gra in ' , Notes and Queries 8th

ser. 10 (1896) , 255, 278-79, 338-39, the second consisting of comments

by the clerk of the Royal Mint.

8. OED, s . v . Blank ( sb . 10 ) , Droit 2, Mite 2, Perit.

9. C .E .Chall is , 'The Debasement of the Coinage, 1542-1551', EcHR 2nd ser.

20 (1967) , Table on p .463 , note. The value can be worked out on inter-

nal evidence. I am grateful to Dr Challis both for calling my attention

to this use of the word, which I had missed, and for other information

and much help generally in the final drafting of this paper.

10. Ruding, I, 217. It is correctly given as one-eighth in the summary

of the document in the Calendar of the Close Rolls, Edward III, A.D.

13k3-13k6 (1904) , pp.261-62.

11. The English works of John Gower, edited by G . C . M a c a u l a y , 2 vols. Early

English Text Society. Extra Series L X X X I . L X X X I I (Oxford, 1900-1), I I ,

67.

12. Select tracts and table books relating to English weights and measures

(1100-17^2), edited by H.Hall and F.J.Nicholas. Camden Miscellany, vol.

XV . Royal Historical Society, Camden Third Series, vol. XLI (London,

1929).

13- Robert Record, The Grounde of Artes (London, 1542) reprinted in the

series The English Experience, No.174 (Amsterdam and New York, 1969).

The correct date of the original edition should be 1543, not 1542 as on

the title-page of the reprint.

14. John Da vies (of Hereford), The Holy Roode, or Christes Crosse, p. 20,

col.2, edited by A.B.Grosart in vol.1 of Davies' Complete VJorks (Chert-

sey Worthies' Library, Blackburn, 1878): 'No Commaes but thy Stripes;

no Periods / But thy Nailes ' .

15- J .Moxon, Mechanick Exercises on the Whole Art of Printing (1683-4),

edited by H .Davis and H.Carter (Oxford, 1958), p .207 .

16. Cf. R.W.Cochran-Patrick, Records of the Coinage of Scotland (Edinburgh,

1876), I, lxxxiii, with a comparative table of the Scottish and English

systems from a Hopetoun MS of the period of Charles I. The fractions

are termed primes ( l /24th) , seconds (l /576ths), thirds (l /13,824ths) and

fourths (1 /331,776ths) .

17. A Catalogue of the Harleian Manuscripts in the British Museum (1808) ,

I, 398-400.

18. C .E .Chall is , 'Mint officials and moneyers of the Tudor period' , BNJ 45

(1975) , 62.

19. R . H . T a w n e y and Eileen Power, Tudor Economic Documents (London, 1924),

346-59. There are other copies, not used by the editors, in Rawlinson

MS D .23 in the Bodleian (Catalogi Codicum Manuscriptorum Bibliothecae

Bodleianae. Part V, fasc.3 , edited by W .D .Macray (Oxford, 1893), coll.

14-15), and in the library at Penshurst (Historical MSS Commission,

Third Report (1872), 230) . The last of these gives the name of the

author.

186 COMPUTATIONAL FRACTIONS OF THE GRAIN

20. R .de Roover, 'Gerarde de Malynes as an economic writer. From Scholas-

ticism to Mercantilism'-, in Business, Banking and Economic Thought in

Late Medieval and Early Modern Europe, edited by R.Kirshner (Chicago

and London, 1974), pp.346-66, esp. pp.346-48.

21. Ruding, I, 411. The full text is in H.Scobell, A Collection of Acts and

Ordinances of General Use made in the Parliament (London, 1658-7), I I ,

64-65.

22. T.Blount, Glossographia (1656 etc . ) , s . v . Ounce.

23. E.Phillips, The New World of English Words (1658) , s . v . Perit.

24. R .Morden, Geography Rectified, or, A Description of the World (1680) ,

p . 175 .

25. Chomel's Dictionnaire oeconomique, or The Family Dictionary, revised

by R.Bradley (1725), I I , s . v . Weights.

26. E . g . , J .Ede , A view of the gold and silver coins of all nations (1808) ,

p . 64 ; P .Kelly, Metrology; or an exposition of weights and measures,

chiefly those of Great Britain and France (1816J, p . 85 , and in his more

famous and comprehensive work, The Universal Cambist, second edition

(1835) , I, 219.