Proc Soc Antiq Scot, 123 (1993), 395-418

The in medieval and early modern Scotland Julian Goodare*

ABSTRACT The 'long hundred' of 6 score was the norm in Scotland for non-monetary sums from the early middle middle17thagesthe the to of century. existedIt together with a 'long thousand': where c = 120, m = 1200. It originated with the Germanic practice of counting in tens up to 120 ('twelvety'), that amount being roman c; but it later came to be regarded as 6 score, occasionally as 10 dozen. It was not part of a ' system', rather of a mixed-base system in which decimals predominated. foundItis accountsin produceof variousof kinds,all used not for though was it commodities; wool, in particular, was reckoned by the short hundred until the early 16th century. appendixAn listscommoditiesthe longwhichof for use (and/or short) hundredshas been identified between 1200 1650.and Calculations thisin period were counting-board,the carriedon out medievalthe version of the abacus. It was easy to use this for non-decimal bases, and it is shown by diagrams how the long hundred could have been handled. The long hundred disappeared when counting-boardthe replacedwas paperby calculation using arabic numerals.

INTRODUCTION During an earthquake in northern Scotland in 1597, 'a man in St Johnstoun laying compts with his compters, the compts lappe off the boord'.1 The purpose of this article is to investigat doings e whawa e , h tfocusin characteristie on n go c aspec earlf o t y accountine th g- long hundred. s lonha g t I been recognized thar non-monetarfo t y sum medievan i s earld an ly modern accounts romae th , n numeral 'c' usually (thoug t invariablyhno t 120) bu represent . 0 10 t no s Peter Gouldesbrough has demonstrated this with admirable succinctness in connection with the Exchequer Rolls f Scotland.o s alsha o e drawH 2 n attentio unfortunate th o nt e fact thae th t editors of the volumes covering the years 1379 to 1600 converted to arabic taking 'c' erroneousl s 100.ya 3shoo t Wha s wi o hopI mortd lone o et eth gfull w hundreho y d originated ,s use calculationw whawa dho t i ford t an ,auditd an s s were actually carriet ou d wit . Finallhit yshalI l demises looit t ka . The long hundred was part of a system which also included a long thousand. Where 'c' meant 120, 'm' meant 1200 illustrato T . taky ecomptroller'e themth ema e w , s accountr fo s

Departmen* f Scottiso t h History, Universit f Edinburgyo h | SOCIET 6 39 ANTIQUARIEF YO SCOTLANDF SO , 1993

1600-1, which give a figure for the charge of poultry, a slightly smaller figure for the discharge e 'reststh balancer d o ' an , roman i , n numeral followss sa givI . e arabic figuresr fo , comparison, beside them:4

Charge iim iic liiii 2694 Discharge im ixc vxx v 2385

Rests iic Ixix 309

A further example, the addition of the charge of capons in the following year, will underline the point:5

vc xlii 642 ic xlii 162 xvi 16 Iv 55 ic Ixx 190 ic xx 140

Total i mv 1205

Evidence thae lonth t g hundre d lonan dg thousand were usage f speecho s t merelno , y peculiarities in the notation of roman numerals, comes from the Privy Council records of 1614. The customer depute of Leith held a licence to export 'three thowsand stane weght' of wool, and had exported 'ane thowsand eyght hundreth and three stanes' at the point when an order bannin l exporgal f woo o s issuedt wa l ; there 'resti stransportie b yit o t t thowsane an t d

ane hundreth fyvescoir xvii stanes'. arithmetie Th c her corrects ei . 6

DEVELOPMENE TH LONE TH GF THUNDREO D e mosTh t detailed accoun e lonth gf o thundre e medievath n di lStevenson H period W y b , , sees its genesis in a specific habit of Germanic cultures, firstly, to count in decades (20 was ) andon , o s secondly d (fo2 1 an r, d regaro thit 10 ,an sx 1 1 d3 s wa 0 essentiall3 , 10 x y2 purpose thid an s, purpose only s additionaa ) l primary numbers. Hund- prefia s a Anglon i x - Saxon meant 'decade', added to the decades from 70 (hund-seofontig) onwards, so that the firse th en tf do decada l sequence went hund-eahtatig x 10 8 , ( 'eighty') , hund-nlgontigx 9 ( 10, 'ninety'), hund-teontig (10 x 10, 'tenty'), hund-endlefontig (11 x 10, 'eleventy') and finally hund-twelftig , 'twelvety')10 x 2 (1 . This number coul e equatedb d with hund (Latin centum), whic noua s ha n meant 'hundred'. Sinc shore eth t hundred never disappeared, we find hund-twelftig hund-twentigd an ('a hundre twenty'd an d ) both meaning whae w t would call 120, while hund-teontig was also sometimes equated with centum. For higher numbers lone th , g hundre turmultiplies n di nwa primariey db only0 s1 froo ,t producinm1 ga 'thousand' of 1200.7 This system was never used for money or dates, and thus always had to coexist with a stricter decimal system of counting. e Anglo-SaxoTh n e lonorigith gf o nhundre d might e confirmeseeb o me t th y b d appearanc Domesdan ei y followine Boo th s figures it f ko f o ge : gloson 'hi n eo s numerus Anglice computatur t centues d o cxx'.i ,m pr 8 However RounH J , d pointe t thadou t this GOODARE: THE LONG HUNDRED IN SCOTLAND | 397

passage related to Lincoln, and adduced other evidence to suggest that this long hundred existed in parallel with (though was not identical to) a 'six-carucate unit' in the Danelaw, while the rest of England was assessed in Domesday on a system of five hides: 'we may fairly hold the Anglicus numerus, or long hundred, to have specially prevailed in the "Danish" districts, which were also assessed shale w , twelve'.d l findan x sumn i si , f 9so The development of the long hundred in England is of interest to us in that it may provide clues as to when and how it arrived in Scotland. If it was favoured by the Danes and reached Scotland through them, this would imply a terminus a quo of the ninth century - and knoe w we earl th tha yn i t 10th century ther mucs ewa h interaction betwee e kingdonth f mo

the Scots and the Viking kingdom of York. If, however, Danish influence were discounted, 0

we might be allowed - or obliged - to look 1 further back. Since there seems to have been little southern influence on the Pictish or Scottish lands in the eighth century, we might have to consider the impact of the Anglian expansion that took place in the century or so before the battle of Nechtansmere in 685." But since the Scottish long hundred was, as we shall see, primarily a unit of reckoning of traded commodities, it would be unwise to push its origins r bacfa ko withouto t direct evidence relatin tradeo gt s enoug i t I . concludo ht a s e thawa t i t Germanic method of reckoning which reached Scotland from the south. It has, however, been suggested thae lonth t g hundre n Scotlandi havy dma e derived from Celtic systems of land assessment. In an impressive study of land assessments in medieval Scotland, Alexis Easso s arguenha d convincingl lane y th thad l unital t s outside eth south-east - particularly the western ounceland and the north-eastern davach - originated in the 20-'house' unit of the Scots of Dalriada. She cites examples of groups of six davachs and of six ouncelands, and an example of a group of 120 'houses' in Dalriada, and continues: e significancTh twente th f o ey hous systee unith n f i assessmentm o kingdoe th n i t f Dalriadmo a cannot be denied and the appearance of the 120 house grouping (six times the twenty houses) is a strong indication thaframewore th t organisatioe th r fo ke late th rf no davac ouncelandd han s into larger territorial units was already present in the seventh century in Dalriada. Was this framework base duodecimaa n do l syste f countingmo precursoe th , f wharo t later became knowlone th gs na hundred (12 x 10 or 120)?12 The answer, regretfully, must be no. It is not a long hundred, or indeed a hundred of any kind, unless it is called a hundred. The '120 house grouping' that Dr Easson cites is from a list in the seventh-century Senchus Per nAlban of the numbers of tech (houses) held by branches of the Cenel nOengusa, the Islay kindred of the kingdom of Dalriada: 'Odeich xx tech Freg cxx tech Cladrois Ix tech Rois deorand xxx tech airdhes xxx tech loich rois xxx tech Aith ceniun si a n cassii l x oengusxx l tech'. x Senchuse a xx th lis e n 1i t 3Th f houseo s held by the Cenel Loairn, the Lorn kindred, contains a number of 20-house groupings but none of 120; a single example of 'cxx tech' is not much on which to construct a general theory, however tentative t howeveBu . r many case f 'cxxo sfounde w ' ' woul'c , d stil e 100b l t i ; lona woule gb t hundreddno .

THE CONCEPT OF THE LONG HUNDRED The general concept of the long hundred has provoked much confusion. On first discovering it, historians are liable to set off excitedly in pursuit of an early medieval 'duodecimal system', which (accordin writere on s supersede o gt wa ) dallegedle onlth y yb y revolutionary introductio abacue e lltth th f hno n s i century. temptatioe 14Th fino nt 'duodecimada l system' 398 SOCIETY OF ANTIQUARIES OF SCOTLAND, 1993

in every example of reckoning in groups of 12 is so strong that it is as well to be clear about what it would involve. In the duodecimal system, the 'hundred' is not 120 but 144 (notated '100 arable)n i ' e 'thousandth ; t 120 t 172no 0s bu i '8 (notated '1000 arable)n i ' r efficienFo . t duodecimal calculation, two additional arable numerals are needed to represent decimal 10

and II. An 18th-century textbook did give a method for duodecimal calculation without 5

such numerals1 , observing that 'this method is chiefly in use among workmen; by it they cast up the contents of their superficial and solid works'. Their arithmetic had to cope, for instance, wit cubiha c ofl2xl2x!2 cubic . Using only decimal numerals, this duodecimal metho cumbersomes dwa e authorth d an s, bleakly observed that 'we would recommend the decimal calculation, as greatly preferable both for facility and dispatch'.16 Many things were indeed reckone twelvesn di , partly becauss convenientlwa 2 1 e y divisible by a larger number of integers than 10, partly because (as a result) some goods were easier to pack in dozens, and partly because the twelve apostles had symbolic significance. Many burgh councils consisted of 'xii of the lelest burges and of the wysast of the burgh', or at least were though thao s doine ters a th , tf m o gtso 'the dusane' coul e use db r burg dfo h councils of any size.17 The convention of royal burghs as late as 1552 tried to rectify the 'grete variance' in elections and to get all burghs to adopt 'ane new counsale to the nowmer of twelf personis'.18 Many things (though not, presumably, councillors) were even reckoned by the gross. Gloves were counted in a 'groce conteining tuelff dusane' by the committee

revising the customs rates in 1612. But roman numerals precluded a full-blown duodecimal 9

immediatele b t no system.y ma yt I obviou s thae 'vii th t iiii' ashlar stones1 purchasee th y db

0 x x

maste f worko r 2 n 15,29-3i s facn 0i t totalle t dgrossa ente e accountinno e ter th rd th :m di g system.21 Wha have w t medievan ei l arithmetic, therefore interlockinn a s i , g serie f mixed-basso e systems, using mainly base 10 (decimals) but incorporating a rich variety of other bases of which 12 was merely the most common. This was quite normal until the rise of metrication in modern times, while time, for instance, is still reckoned in a mixed-base system. One only has to think of the large variety of bases for computation in the standard Scottish weights and measures; thus the grain measures were largely in base 4.22 The decimal system nevertheless remaine basie dr mosth sfo t people's counting systems traditionae On . l reckoning methos dwa strictly limitee decimalsth o dt : finger reckoning, which could a deasophisticate n i l y dwa with number o thousands.t least a s p u t 23 Even when people started with non-decimal quantities, they would sooner or later end up multiplying them by tens, as with the 144,000 souls (12 x 12 x 10 x 10 x 10) redeemed from the earth in Revelation xiv:l-3, who would no doubt have been familiar to all numerate people in this period. The long thousand (10 long hundreds) exemplifies this well. Once established, the long hundred became an independent unit of reckoning, and its original structure as a unit based on the 12th decade was forgotten. The long hundred in Scotland could occasionall regardee yb doze0 12)x 1 0 s , dna (1 whic s onlhi y coincidentally the same as 12 decades (12 x 10). The master of works in 1535-6 paid 27s 6d for 'ic vi dosan i ladiev s sand, pric dosank eil d.'x arabie ex 2Th 4 c loads8 figur19 s ,i e which seemo st have been though s 16'/a f 2o t dozen. Normally, however e Scotth , s whe t reckonin nno scoresn i o e lons tenn Th gi .d g di s hundred thus came to be thought of as 6 score. The primacy of scores occasionally gives rise to what appear at first sight to be inconsistencies, as in the figure of 'vixx ix' (129) chalders of oatmea comptroller'e th n i l s account f 1601-2.so 25 Ther evee ear n 'viiixx xii' (172) poultry augmentationw recordene e th n di s account f 1593-4o s stild an ,l larger number f scoreo s s GOODARE LONE TH : G HUNDRE SCOTLANN DI D 399

may be found.26 We shall see shortly how these may have arisen. We also find curiosities like 'Ixxxxxxvi', which would normally have been thought of as 5 score 16 and written 'v™

e lonxvi'.Th g hundred, however s morwa , e than merel convenienya f denotino y wa t g6 7

score lone 2 th : g thousand, clearly reckone 'hundreds'0 1 s da , proves this. If the long hundred was early detached from its Germanic roots, did it have some other function enablin continuo t t longgo i s t r thi?A efo s poin shoule w t d conside generae th r l pre- industrial approac systemo ht f measurementso statutA . f 158eo 1 ordere dtabla f goodeo o st e issueb customerso dt , 'ordaning that f woleverio k l se esai l conten t twentiebo e foure

stanes, everie hundreth skynni scoirx everid sse an , e dosan f claytdo h twelf ellis allanerlie'. 8

Over time, many unit f reckoninso g (not just hundreds t sacksbu , , dozen othersd san ) tende2 d to inflate themselves in a slightly surreptitious way, which the statute aimed to restrain. This gave those familiar with the system an advantage; moreover, those with political power could demand rent othed an s r fixed duties from their tenants using larger units .statute Andth s a ,e suggests, customs duties (which were levied pro rata, so much per 'hundred' skins, rather than ad valorem) would fall if merchants could convince the customers that a larger unit should be used to assess them. The 'hundred' of 6 score may owe its popularity in the 14th century, when customs duties bega beao nt r heavil traden yo thio t , s factor.29 Keith Thomas approache e concepth s t differently, seein e Englisgth h long hundres da e 'styliseth f o e d quantitieson , likbaker'e eth s dozen, into which there entere elemenn da f o t gift exchang r "complimentareo y excess", likmodere eth n tradesman's discount' citee H . s examples of 'hundreds' of 104, 112 (the hundredweight), 120, 124 and ISO. However, Sir 30 e wronb Keit y conflato gt hma s 'hundred hi e4 (th 10 e f Londoo ' n syste f m'trett'o n a , allowance of 4 on top of the short hundred) with the other examples which were all units of reckonin e whol thein rightn th gi e relate n ow rth e O t .distinc dbu t concep f inflatioo t n i n units of reckoning seems more useful. It would be misleading to regard the Scottish long hundre s 'complimentara d y excess' r thifo ,s woul e analogoudb modern (i s n supermarket jargon) to an 'extra 20% free' added to the ordinary hundred - which, of course, it was not. e choic a 'hundredTh f eo rathe6 f o ' r tha scorn5 initially ema y have been made througha preference for larger units, but it never grew any larger. The English long hundred may have develope mano dto y complex variation workablee b o sScotlant n i t always bu ,wa t di s clearly singla e uni resultf a 120 o ts A . t workei , d wellasted an l londa g time.

LONE TH G HUNDREE US N DI What, then, was the long hundred used for - and in which periods? We may look for it in assessments of land, and in reckonings of traded commodities, both in domestic and overseas trade. In trade, we shall find the long hundred universally in operation, so much so that the search for it becomes rather a search for exceptions to it. The point to make at the outset is that long and short hundreds operated in parallel, but like parallel lines they did not meet. Each individual category of produce was reckoned either in long hundreds or in short hundreds, but not in both - otherwise the term 'hundred' would have become meaningless. (At leas theorye th t s tha;wa t there were exceptions.) Althoug investigationy hm s cannot claimo t be exhaustive, they may serve as a model to show other researchers what kind of environment the long hundred inhabited, so that they will recognize it when they come across it. Lon r shortgo , 'hundreds Scottisn i ' h chartert commonno e e usuaar s Th . l Scottish ploughgate was 104 , and a 12th-century charter granting a ploughgate in Heton (Roxburghshire) enumerated this as 'quinquies viginta acris et quatuor'.31 Why not 'centum 400 | SOCIETY OF ANTIQUARIES OF SCOTLAND, 1993

et quatuor - woul' tere dth m 'centum' have been understoo lona s dga hundre contexe th n di t of reckoning clere th ks f acreso ssimplwa r ?O ytere reluctanr lesth m fo e s us tha o o t tntw hundreds same thae shilliny th on tewa n s alwayi , gwa s 'xi fino id dd.'e 'centum?W a r fo ' single hundre a gran n i d t including pastur n Dalgarnoci e k (Dumfriesshire r 'centufo ) m

cues'. On the other hand, there is an example of a grant by the Scottish crown of 'vii viginti 2

acras' 3 in Tottenham, which could have been notated as 'cxl' (short hundred) or 'cxx' (long hundred). e existenc3Th 3 a lon f o ge hundre n reckonini d g acres mus e regardeb t s a d unproven. What we have in land assessments, it seems, is a system including some groups of 120 t thesbu , e were understoo s 'ada (longhundrea s a t twentyd ) no 'hundred'dan d an ' . Later assessments of land tended to use monetary terms - 'poundlands', 'merklands' and so on. At the outset at least, these terms were regarded as denoting actual sums of money, as appear reference th n i s n 132i monea e o 8t y incom r Princesefo s Johann f 'deuao x mille liuereez de terre et de rente par an par resnable extente'.34 As a result no tradition of using lone th g hundre r thedfo m developed. In counting sheep royae th , l clerks must have been awak whao et t kin f hundredo s dwa current, since therhino n f definitio o ts e i frequene th n ni t enumeratio f 'ducentano s matrices oues', 'mille ouium' and so on.35 That these numbers meant something more precise than 'a lot'thad an ,t there were other way f reckoninso g them, appear lata n esi 12th-century grann i t Mow (Roxburghshire) including 'pasturam quingentis ovibus, et aisiamenta pasture ceteris animalibus quantum pertine unad a t m carucatam terre (pastur r fivfo e e hundred cowsd an ,

easement of pasture for as many other animals as pertain to one ploughgate of land)'. What 6

kind of hundreds these were does not appear, but it seems likely that long hundred3 s were

meant r ther earlsheee fo fo ,th y ye n pi wer us 14t n ei h century.problea s i t I m that recurs. 7

Only when an arithmetica3 l sum is given (typically 'x hundreds, price of each y, total z'), or whe clera n k explicitly record e telw l e fact n whath s meant ca , wa t .good w Whefe o sns were reckone sucn di h large quantities have w , regrettablea informationr ou n i p ega . But althoug medievae hth l lon gslippera hundree b y y d ma fisfinall n catcho ht ca e yw , lanaccounte 1260n i th t keeped e i bishoprie n i ,th th f f so ro f Glasgowco :

Summa ... xic anguille. Expense in servicio regis, viic anguille. Item, in servicio regine, ixxx anguille. Summa expense, viii t Ixe c anguille t debet IE .xe anguillasc c t .

Tota f charge[o l . eleve.. ] n hundred eels. Expende service kinge th th n di f , eo seven hundred eels. service Item queene th th n i ,f eo , nine score eels. Tota f dischargeo l , eight hundre sixtd dan y eels. And ther owine ear hundreo gtw sixtd dan y eels.38

After this whicn i , lone hth g hundre manifess di arithmetice th nexn n i t ca t e identifw , n i t i y use for marts in 1266, which the clerk has kindly explained: 'ccc carcosiis vaccarum, scilicet, xviiixx (three hundred carcasse f cowso s , sayo that s ,i t eighteen score)'. e samth en 3I 9 year, durin e establishmength pare th f Kincardine ko f o t , 'perticatarum' (perches measuremena , t

of length) were counte e lonth gy db hundred. n 1290I , ther s mentioei f cheesno n 'viei

0 x x

tonegall [casks] pro quolibet4 centum'. Between 1328 and 1331 the unusually full 1

chamberlain's and sheriffs' accounts show 4 the long hundred used for salmon, oatmeal, sheep,

dried fish, herring, sheep carcasses, stones of wax, pounds of dates, and ells of linen cloth. 2

e centurLateth n e loni r th y g hundre recorn o r s chickensi d dfo , f aleo s , gallonf o s 4 wine chalderd an , e 15tf buildind coalth o s had n i ;centurn ca g e stonew y , white d fisan h

chalder f salt.so Although dried fish also were usually counte lonn di g hundreds 133n i , e 0w 3

find: 'et d4 e viiim, ... quorum quodlibet mille faciunt per centenam, sexies viginti, mille et GOODARE LONE TH : G HUNDRE SCOTLANDN I D 401

ducentos pisces. Et sic est numerus ixm vic. (And of eight thousand, of which each thousand, wit hhundrea e thousan scorex on si s hundref o dha o ,numbee dtw th o ds s nin i rfishd eAn . thousan hundred.)'x dsi 44 Evidentl t leas service ya clere th on t n kunhapps i f Davi eo wa I dI y with the long hundred and was determined to translate it. Wit growte hth f overseaho s trade must have com greateea r familiarity wit unite hth f o s reckoning familiar on the Continent - at least for Continental commodities imported to Scotland. As a result there was a falling-off in the use of the long hundred for commodities such as ginger, and the beginnings of a divergence between Scottish and Continental practice. Scottish merchants seem to have been as happy to buy goods reckoned by the short hundred as their counterparts were to buy Scottish goods in long hundreds - so long as the price was right doubto n , . e wardrobe clerth Th f ko e bought linen clot canvad e lonhth an gy b shundre n 136di 4 and 1374, as appears from the enumeration of 'trescentarum quinquies viginti et decem ulnarum tele linee stricte (three hundred, five score and ten ells of narrow linen)' and 'vc vxx

iiii vlnis canubii'. handbooa t Bu r merchantkfo s tradin Flandero gt s about 1400 gavea 5

table of unspecified4 cloth or canvas prices at which 'v of eln makis the C'. This cloth may

x 6 4

well have been for import to Scotland. Andrew Halyburtox n was often buying canvas in e 15tshore th th sols h f y to century dwa b hundred t d i Flander en d e an , th :t a s'Ite m boch. .. t in Handwerp 220 ell canvas, price of the C. 23 s. 6 g. Som of this canvas, 2 li. 11 s. 8.' His 47 imports were man variedd an ywherd s possiblan i , t i e tello t e , they were also reckoned thus. t 4seemI 8 s that people cease recalculato dt e goodth e s they importe termn i d f o s domestic units. Thus ricalmondd ean s were still accounte lonn i r g dfo hundred 1375n si t bu ;

saltpetr sulphurd ean , importe Jamey db 1457n i I sI , arrive shorn di t hundreds. 9

Turning to Scottish exports, we can see tha4 t the long hundred continued. The earliest

customs accounts, in 1327, show woolfells reckoned by the long hundred. But the 0

merchants' handboo f 140ko 0 gave table r 'Thsfo e reknyn skyne th f gso that vxx , makiC e sth 5 woly sa l o t thaskyns s i t , schorlingi hogrell'& s d 'Than , e C reknyn e e skynth th t f a sgo

makis vi'; these latter were unspecified. This distinction must remain mysterious; the

1 5

handbookxx may also relate to imports, but it is unlikely that commodities such as woolfells e importewerb o et o Scotlanddt , whil custome th e s accounts show woolfell l otheal d r an s skins invariably exported by the long hundred. Andrew Halyburton also recorded export f skinso s , thus: 'Ite mApryln i l ann, o94 rasauif Jameo t ou st Makisso sekin2 f skyniso s 3 skyns, contenan44 d . an Ite 2 md46 rasauit

out off Wyllyem Peterson at that samyn tym a sek contenand 469 skyns, in al 1354 skyns.' 2

Not only did he receive skins by the long hundred, as the arithmetic here shows despite it5 s unusual arabic notation (he had 1614 skins by our reckoning), but he sold them to Flemish merchants thus . n 1588 i Lateimpost w , ne on ,r n Scottiso s h goods imported into France included 'fyv hundretek il sol r zfo h skynnis 'fourtd an ' y fyv hundretk e il sol r zfo h cairsy'n i ; the circumstances the French authorities must have meant the Scottish long hundred.53 Skins were enumerated individually t hidebu , s were packe thue w lastsn d i s d havan , o et look for hundreds of lasts. Even the customers of Edinburgh were not handling such large quantities until 1498, when '5 score 18' lasts were exported formula , a usually (thougt hno always) signalling that the 'hundred' was regarded as 6 score. In 1523 we have confirmation: custo f £32m o s pai n 'centu1wa do m lastaru t mundecie m dacraru dimedim mcu o corriorum (a hundred lasts, eleven and a half dakers of hides)'.54 Andrew Halyburton mentioned 'Pabyllis quhit' (Peebles white cloth) measured in ells by the short hundred.55 However, ells of cloth were reckoned by the long hundred in Dundee 402 | SOCIETY OF ANTIQUARIES OF SCOTLAND, 1993

in 1592.56 According to Sir John Skene's memorandum on the customs, drawn up in 1597, 'sex scoir of skynnis ar reknit to be the hunder ... Sex scoir elnis wollin claith is lykvayis reknit for the hunder'.57 The customs book of Dumfries in 1621 also shows ells of linen cloth in long hundreds, as well as sheep, lambs, cattle and woolfells.58 e 16tBth y h century, domestic trad d accountan e f monasterieo s landlordd an s n ca s broaden the picture. It should be remembered that for many goods there was no unified market syste n pre-industriami l times y explaid thian ma s, n e apparentlsomth f o e y contradictory domestic evidence f therI . e were local weight measuresd an s , there could equally well have been local customs on numerical reckoning. Further local research might shed ligh this.n o t 59 The monks of Dunkeld seem to have been reluctant to use the long hundred, but their accounts sho wy whe thasa no tt thethed yha y e editower t doinTh f Rentaleno e. o r so g Dunkeldense has translated the roman numerals into arable, but we can see that the purchase of d indicate'7204 s 3 ' e lonload7 th £ seac d gf pear 2 o s hundred.t hfo a t 60 Howevere th , summation e abbey'th f o s s receipt f poultryo s , chickens, capon salmod an s n show thae th t short hundre s beindwa gfacn i used td s notethian , wa ss 'computand da o nonaginta decem centuo pr m (countin e hundred)'.th g r ninetfo n te y6 1 Bere, oatmea sheed an l p were also enumerate shore th y t db hundred. 62 Candles, however, were purchase lone th gy dhundred.b 63 In paying a workman's wages for '28814' days, the enumeration of days was specified as 'computando nonaginta deci centum'o mpr , whereas load f peao s t were again 'computando centum vigint o centupr i m (countin ghundrea e hundred)'.twentd th an d r yfo e unusua6Th 4 l language of this formula - not 'six score for the hundred' - indicates a strong commitment to the short hundred but also perhaps an awareness that this was not universal. Later accounts were confused, with examples of both long and short hundreds for loads of peat,65 loads of clay, loadd 6 an 6f sand. so 67 It was perhaps to avoid this kind of confusion that the priory of St Andrews eschewed the term 'hundred' altogether, accounting for example for 'xiixx xiiii' chalders of oats.68 Another possible reason is that their clerks recorded receipts of grain using 'c.' as an abbreviatio e thase t n confusio ca r 'chalder' e fo n on nd an migh, t have arisen ove entrn a r y like, for instance, 'xx c. ii b. i p. ordei'.69 In the 1590s the household books of the Campbells of Glenorchy show salmon and cheese, and (in 1621) bread, being reckoned by the long hundred.70 Weight f bullioo s othed an n r meta e complicatedar l . Iros reckone e lonnwa th gy db hundred in 1329.7I In 1593, accounts of lead ore were given 'comptand sex scoir to the hundreth'.72 But in the early seventeenth century, both iron and lead were reckoned in short hundreds: '1194 stan libe4 . wech f Scottio t s iron i meri t ea k stane: im vc Ixxxxi i. vii s lib i iv . d.'; 'iic xviii stain f gadeo e leid t xxvstainee ea th . vii s . i d i : iic iiii xlibx x . xii . iiis i i d.'s 7A 3 for bullion, of silver in 1438 were reckoned 'centenario computato quinquies viginti (counting"fiv ehundred)'e scorth e accountr th efo e maste e mint th th bu , f f to so r generall y use e londth g hundre r bullio e 15tdfo th hn ni century. t golsilved 7Bu contraca 4dan n i r f o t 1568 were specified as 'comptand fyve scoir to everie hundrith'.75 The mint account for 1582-3 give a charge of silver in both roman and arable: 'vic vii st. vii p.: 607 st. 7 p.'76 The most likely explanatio e earlth yr fo nlon g hundre r iro dfo s thani t derivei t s fro mperioa d when people still recalculated import termn si f domestiso cdivergene unitsth t bu , t usager sfo lead must remain a mystery. With the advent of printing, books were reckoned by the short hundred. Perhaps the long hundred could onl usee yb r commoditie dfo r whicsfo h medievaa ther s ewa l traditiof no GOODARE: THE LONG HUNDRED IN SCOTLAND | 403

t mighi r doinO t. simplso g e thae shoryb th t t hundre s usewa dd because most books were

imported. The position here is analogous to that for the metals. One notary, Robert Lauder 7

in North Berwick, paginated his first two protocol books (coverin7 g the periods 1540-62 and 1563-9) in long hundreds, but his third book (1569-73) used short hundreds for this purpose. This is the only known pagination in long hundreds. Lauder may have been a nonconformist, sinc fors r numberehi m fo s suc s 'xcixs '99ha wa ' - conventiona' lt then s todayno Hi t . bu , '199' followed the usual form, 'c iiiixx xix'.78 It will not have escaped notice that I have not yet mentioned wool, the chief export of medieval Scotland importan.n a Woo s wa l t exceptio lone reige th th gf no o hundrednt . Lasts of wool were explicitly enumerated 'computando centenari d quinquiea o s vigintie th n i ' Edinburgh customer's account f 1375o s thesd an , e accounts sho wpattera f exclusivno e eus shore oth f t hundred bac o 1362.kt 79 Lik lase f hideseth o t enormoun lase a f woo th ,o s t wa l s quantity, and the Edinburgh customs administration was virtually the only institution ever to hav0 lasts s e earliesman10 a e Th .s a y t surviving customs accounts e latth e r 1320fo , d an s early 1330s, show no actual 'hundreds' of lasts of wool; instead we get 'quinquies viginti octo lastarum' (Edinburgh, 1327) and 'septies viginti et quinque lastarum' (Berwick, 1330). occasione Oon n , 1329 Berwice ,th k wool customs were accounte sackn i r - sdfo 'milliu m quingentorum trium saccorumaccoune t detaileth t no s bu i t d- ' enougwhae se to ht kin f do hundre beins dwa g used.80 In the next century there were occasional deviations from the rule: 117 lasts were notated as 'quinquies viginti septemdecim lastarum' in 1410, and in 1413 an example of a long hundred occurred. However, with some exceptions the short hundred remained the norm for the rest of the century. In the early sixteenth century there were more examples of the '5 score' formul custome th n i a s accounts lase th t d customean , f Edinburgo r accouno ht r he r fo t wool usin e shorgth t hundred appear o havt s e been Janet Paterso n 1515i n . Thereaftee th r long hundred took over.81 Because custom was payable per sack, not per hundred, this had no e lone customeffecth th t gcleay n no hundreo t wh s ri dutiess t adoptei dwa d an t ,thi a d s point.82 But ther s nothinwa e g obviously perverse abou e adoptio th te lon th gf no hundre r dfo earle wooth yn i l 16th century contrarye th n o ;change th , e brought wool into line with most other commodities. Enough has been said to show that the long hundred of 120 (never any other amount, unlike in England) was a well-understood and well-nigh universal unit of reckonin r tradegfo d commodities, bot domestin hi internationad can l tradelate th e n middli , e ages. What may seem perverse is that people persisted in an arithmetical system that appears unnecessarilo s y complicate useo d t nex y objece m th t ;wili tf e o sectiotb l shoo nt w that i t wa goosa d deal simple seemy r thama t .ni

COUNTINE TH G BOARD e primarTh y purpos e accounte larg th th e crown f f eth o e o institutionf r o so , s sucs a h monasteries, that we have been considering, was to demonstrate to the auditors that the correct amounts of money or produce had been received and spent. The auditing process consisted largel f addine figureyo th checkingd p gu an s r sometimeo , s inserting e totalsth , . Roman numerals could not be used for calculation; the process of recording numbers on procese paperth d f calculationan so , , wer separato etw e things merchane Th . t with whoe mw began used a counting-board for working out his accounts; how did it operate, and how were calculations usin lone gth g hundred carried out? 404 SOCIETY OF ANTIQUARIES OF SCOTLAND, 1993

§ ————————— 10000 (100) 10 0x t ————— ft —————— t ————————— 1000 ) (1010 0x t § —————————————————— 100 (10 x 10) t ) 10 x 11 0( t §• ———— •••• ——— t ——————1

ILLU 1 S Decimals

r understandinou r Fo f calculationgo counting-boare th n so indebtee ar e dw Robero dt t Recorde's Ground of Arts, the first popular English arithmetic treatise in the vernacular, first

published between 1540 and 1542 and frequently reissued for the next century and a half. 3

Before considering the counting-board's use for monetary calculations or long hundreds, it is8 best to begin by establishing the basic system of calculating in tens (illus 1). For this, the first five lines of the board represented (counting from the bottom) units, tens, hundreds, thousand thousandsn te d fouo t an s p r U .counter s coul linee placee db on furthe a ; n do e on r was then placed abov line s thurepreseneth o et wa s t likI abacun . ea 5 t s turnes sideit n .do Recorde gives as an example the addition of 8342 and 2659, to produce the answer 11001; her egivI e justhree th t e figures, though Recorde illustrate l intermediatsal e stages. More lines could be added for larger numbers, although in fact numbers with more than five figure f pounds(o s , unit f produco s r anythineo g else) were rare, indeed practically non- existent before the 17th century. The Roman-derived tradition of numeration did not envisage numbers as large as a million, and had no way of notating them on paper.84 I have not seen any million Scottisn i s h accounts befor greae th e t switc arablo ht e numeral mid-17te th n i s h century. r poundsFo , shilling pencd an e ssyste th es mor mwa e complicate e dfirs (illuTh t . 2) s line represented pence, followed by shillings, pounds, scores of pounds, and hundreds of pounds. Again no more than four counters were allowed on the line, except for the pence where five were permitted; a single counter above the line for all columns but the first represented 10 (for the first it represented 6 pence), while 5 (except for the pence) was represented by a single counter placed on the line a little to the left. Recorde gives as an example £19 s lidcountere 8 19 lefTh e . th t o representet s e seconth e n th o d n s lineo d5 5 £ , third and £100 (ie £20 x 5) on the fourth. The basic counting-board, when calibrated in tens like its close relative the abacus,

could add, subtract, multiply, divide and extract roots. It must have been slower than an 5

abacus with beads strung on wires, but had the advantag8 e of an unlimited supply of counters for layin t mangou y number t oncea s . Recorde (who preferre emergene dth t metho f papedo r calculation) recommended only addition and subtraction in the monetary version. It ought to have been possible to multiply using the method of 'duplation and mediation', repeatedly halvin e firsth g t numbe d doublinan r e secondgth t whethe t s donethiBu . no e wa s r th ,o r auditor's overwhelmin a syste r gfo m nees whicdwa h accuratelp woulu d dad clearlyd yan , and the counting-board was well suited to this. GOODARE LONE TH : G HUNDRE SCOTLANDN I 5 40 I D

-t—tttt——————————————————————) 20 x 1 (£ 0 £2 — •--•§•————————————————————————— £1 (Isx20) t •—••••———————————————————————— ls(ld) x12 t •ttttt——————————————————————— Id

ILLU S2 Money ————ft——————————t——————————————— 1200 (120 x 10) ————1§———————t—ttM————————••——— 120 (20 x 6) ————•«———————t—————————————•••—— 20 (1 x 20) t ————••§§——————•———————————t—fiti— 1

ILLUS 3 The long hundred as 6 score

Recordt mentiono d edi n reckonin lone th gy ghundredb doubo n , t becaus they eb t ni was not so prominent in English usage. But Scottish clerks certainly used it on their counting-boards, and it is possible to reconstruct how they must have done so. Knowing that they tended to reckon the long hundred as 6 score, and seeing from the above monetary exampl scorew ho e s wer e thae se handledt n theca ye musw , t have take e firsth n t lins a e units e seconth , s scoresda thire th ,s (long da ) hundreds fourte th s (longd a h an , ) thousands. Illus 3 returns to the example with which this article began, and reconstructs how the comptroller reckone s poultrydhi : iim iic liiii (2694) less im ixc v x(2385v x ) equals iic Ixix (309)middle th n I . e figure (the discharge) countere th ,lefe th t o represent s scor5 5 , d 5 t ean hundred firste th ,n so secon third dan d lines respectively. Apart from the minor inconvenience of having to represent the 'liiii' as 2 score 14 and 'Ixix' as 3 score 9 (as had also to be done with money), we can see that the counters followed the roman numerals closely - and unlike roman numerals, they could be used for computation e comptrolleTh . r woul difficultdo n hav d ha e convincinn i y e exchequegth r auditors thas figurehi t s were correct. Thos wiso checo wh et h k this should note that subtractio counting-boare th n no d began wit higheste hth numbers. Three score4 scor d ean , though reckone e counting-boardd th thu n o s , were usually written d 'Ixxx''lxan ' minoritA . f clerko y s see preferenca havmo t d ha e r 'iiifo d e xxan ' 'iiii havthey d xx'an ,yma e bee e onecontinueo nth swh e o 'xiit th p r xxmoren du o '(i r o , hundreds , sayto ,p u 'xii) c mora lx'. t 8eBu 6 likely explanatio s thani t they were reluctano t t create an extra group on the counting-board, preferring to add extra counters to the highest one. What of the fact, noted above, that a few clerks seem to have regarded the long hundred as 10 dozen? Probably this arose because they took the second line of the board to represent 6 40 SOCIET ANTIQUARIEF YO SCOTLANDF SO , 1993

1200 ) (1210 0x 120 (12 x 10)

t -t ) 12 x 11 2( t 1 ILLUS 4 The long hundred as 10 dozen t

t t it

ILLU S5 Mone 'Auditor'n yi s accompt'

not score t dozensbu s , whic s actuallhwa y simpler than using scores. Each s linonl0 ewa 1 y times the one above it (12 in the case of the second), so that the intermediate counter could be regarded as 5 (6 in the case of that between the first and second). The extra counters at the left coul e dispensedb d i withdosan v e 'i Th .i ladiv e s sand' mentioned above would have

appeared on the counting-boarc d as in illus 4. I have give l thesnal e example whan si t Recorde calls 'merchants use', becaus systes eit m of linecounting-boara n o s d approximates more closel whao yt understan e w t abacuse th y db . However e describeh , alternativn a s e system, 'auditors accompt', whic s probablhi e on e yth exchequere useth n di . Account exchequee th n i s r wergreea n eo n lait cloth;dou 87 lines were foro t t rulemi seriea n df o boxes o s this n reckonine O . th , s mad a fashio gwa n ei n which, although it looked quite different from the counting-board, employed identical principles. Instead of a series of lines, there was a series of boxes or groups, the right-hand one representin unitse gth . Counters coul placee db thren do e lines within each middle boxth n ;o e lowed an r lines the righp countea y to t lef p countet 5 t a bu to t , t e represente1 a r on s da d an , d10 (6 wit pence)e hth . Illu give5 s s Recorde's explanatio notato t w eho £19 f no s lide 819 Th . groups represent (reading from righ lefto t ) pence, shillings, scored san poundsf so . How this worked in practice may be gathered from the classic account of the medieval English exchequer, the Dialogus de Scaccario: A cloth is laid on the Exchequer table ruled with lines, and ... the coins used as counters are placed in the spaces between them. The Accountant [ie the sheriff or other officer presenting his account to the auditors] sits in the middle of his side of the table, so that everybody can see him, an thao s hands movn hi t dca e freellowese s workit th t n a yI . t righte spaceth placee n h , o , e sth hea f pencepo , eleve r fewersecone no th shillingse n I .dth nineteeno t p thire u , th pute dh e n I .sth pounds thid an s; colume fourte heae nth th th f shoul po s n i hI . directle .. db m fronn hi yi f o t scores of pounds. In the fifth, hundreds, in the sixth, thousands, in the seventh, but rarely, tens of thousands muse H . t.. . take care tha hans hi t d doe t outrusno s tongunhi r viceeo e h versa;s a t bu reckons, he must put out the counters and state the number simultaneously, lest there should be a mistake in the number.88 GOODARE: THE LONG HUNDRE SCOTLANN DI 7 40 | D

The Dialogus describes actual coins being used as counters, but soon special brass counters or jetons were being produced in great numbers, mainly in Nuremberg, for a European market. Many governments also had special silver tokens struck, possibly for use in central government accounting, and (sometimes in sets of 100) for presentation purposes. One such Scottish token, issued in 1588, is in the National Museum of Scotland.89 The master of works' accounts recor e purchas x standth d se f counteran do d f 'papey o ean la k o t in sr mak thir comptis with' in 1619, and 'twa stand of counteres for laying of the comptis in exchaker 1633.n i ' fine Bishoe W dth f Orknepo y checkin rentas ghi l with counter 1614n si : 90 I have spent almos perusinn i t thiy layind da s gan g this rentall, wretti e Davinb d Hart, according takismee th o t n comptis countersfindisy d m an , e b , f thei , y hav t deceaveeno , thawhole dme th t l ren . wilt excei.. t no l d eight thowsand merkis beyon e thriddisth d . Youy rm lordshiy tr y pma compt, and teach me if I have erred.91

DECLINE e declin lone Th th gf eo hundre bees dha n linked erroneousl influence th o yt f 'tho e e abacus, whic s base hwa tenn hundreds'.d do an s have w es 9A 2seen , e counting-boaruserth f o s e d(i abacuse th ) were jus s muca t t homha e with dozen scoresd an scoul d an , dlone easilth ge yus hundred. What really encouraged the shift to reckoning by the short hundred was the rise of paper calculations using arabic numerals, thus combinin e hithertgth o separate functionf o s calculation and writing accounts. When deployed properly, arabic numerals never used the long hundred althougd an , t tak hattempn no e a ther d roots di somy et wa i b t . , eso clerk o d o st e demis e lone storth th Th f gf yo o e hundre e tolb ddo t withi thus e contexha se th n th f o t replacement of roman numerals by arabic. By 1600, arabic numerals had been known in western Europe for over four centuries, but they had never achieved the respectability of the roman system. Their earliest use in Scotland seems to have been for 15th-century monumental inscriptions.93 Central government, with well-established bureaucratic traditions, adhere dsystemd stronglol e th . o yt rarOe nth e occasions when arabic numerals appeare accountn di crowe th f nso before about 1600 they were always in subordinate positions, for example in dates within the text (not the more importan e account)t heae th date th f do t a s , 'upoun Mononda f Augus o xxvie y th da i t 159 valuee 9th ...'n f penci so r ,o e only, 'xvii d.'i8 . libs 9 4i . Related to the rise of the new numerals, there grew up two modes of thought in connection wit specializea hs a arithmetic t i w dsa e olde skile Th . on r l handed dow oray nb l tradition within closed bureaucracies; the other, as part of a movement of scientific enquiry and popularization. Christopher Hill has noted that the two were often in conflict, and locates the vernacular arithmetics published by the likes of Recorde (who was a London physician, crowa t no n bureaucra r universito t y teacher) withi lattee nth r model. t 9begaI 5realisee b o nt d that arabic numerals and decimal calculation were powerful tools. This is not the place to discuss John Napie f Merchistono r t logarithmbu , s coul t havdno e been inventee th n o d counting-board. Reckonin countery gb s thus bega seeo nt m old-fashioned t requirno usee d eth di o t rt I . e literate begab o e despises b e illiterate'd o nt th an , s da s metho f reckoningdo . Thoso ewh were literate (an increasing number) wanted to use paper calculation.96 Not that they could advancen necessarila n i o s d o way.yd 97 Alexander Hunter, whose 1624 treatis measuren eo s was aime t landlorda d s wantin conduco t g t survey f theio s r property, remarked: 'Thers ei 408 | SOCIETY OF ANTIQUARIES OF SCOTLAND, 1993

none so ignorant, but they doe, or may easilie know, the names of these ten figures, 1.2.3.4.5.6.7.8.9.0. with their strengt firse second th an t n hi d place.' However, because 'there is not many that can multiplie and divide numbers', he provided lengthy tables allowing peopl woro t et areakou s without havin o so.d 9o 8gt Thus bor reade wa snth y reckonera , genr f aideo computatioo t s n that would continue unti e advene pocketh lth f o tt calculator. counting-boarda f o t suggesHunte e mentioe no h us d e d di rth di t nr romano , n numerale th r so long hundred s arguabli t I . e thae counting-boardth t t least a s ,bein wa , g discarded prematurely. The spread of paper calculation was linked to the spread of basic arithmetic treatises in the vernacular, notably that of Recorde. This was known in 16th-century Scotland, but it had not reached the elite. The only mathematical book in James VI's early library seems to have been the Scholarum Mathematicarum by Peter Ramus, a philosophical work which was not primarily designe arithmetin a s da c textbook. havy ma e t "I bee copna f Ramuo y s thae th t poet William Drummond of Hawthornden presented to Edinburgh University library in 1605.10° Meanwhil Edinburgn a e h bookselle s sellinwa r g Recorde's worko s weltw a ,s a l other unidentified (but cheaper) vernacular arithmetics, in 1580.l01 The Dundee merchant David Wedderburn lent 'ane Inglis bui f Arithmetikko colleagua o t ' 1607.n ei 102 earliese Th t systemati f arabio e cus numeral accounte th Scottise n si th f so h crown seems to have been in a new and minor branch of the records, created in 1614: the accounts of bullion received in the mint.103 (The receiver of bullion was Alexander Hunter, author of the treatise referre above.o t d ) Figures were writte rulen i n d column r stonesfo s , pounds, ounced an s deniers dashA . , rather tha nzeroa places columy an wa , n di n l figurewitni ha . Eve thesn ni e accounts, the final, formal totals for the charge, and all the figures for the discharge, were in roman. These accounts exhibi exampln a t clera f eo k still countin scoresn gi , wher figure eth e of 'sax scoir fyve stane' is given.104 But another new branch of the accounts, for the lordship of Dunfermline and other lands assigned to Prince Charles in 1619, was launched completely in e traditionath l form, with exclusively roman numerals and f courseo , , long hundredr fo s produce. 10furtheA 5 r example accounte th , f expenditurso Hilderstone th n eo e silver minesd ha , long hundred r nailfo s s ('ane thowsand grea peicee t th nailli bellowee . d th : i Io xt sxi li.'t a s )

but short hundreds for goods (melting pots) bought in London. 6

Meanwhile, somethin happenins wa accounte d th god maste e n gi th f f worksso e o r th n I . 10 16th century these had been kept in the conventional way. However, in 1616 we find the following: Ite mCuthbero t t Wilsoun ic xliii laidi f lymso t eou of Kirklistoun to the castell of Edinburgh at xii s. the laid inde Ixxxv lib. ...l07 The final total is mutilated but it must have been £85 16s, making the 'c' a short hundred. earliese Thith s si t exampl shora f eo t hundre sucn di contexha t tha I havt e seen. Perhapt si was just a mistake, since the same accounts offer an example of the long hundred and another

of the long thousand. But one later entry looks as though the clerk may actually have 8

translated three long hundred10 s into 360. In another volume of accounts, covering 1616-19, 9

one early entry ran as follows: 10

Item to the querriers of Innerleith craig for winin f icgo Ix futte f heweo s n warr kfo r awie ou th ncastel. e e d cairteb th i d xv le l t sa futte inde x lib. xiii s. iiii d."° GOODARE LONE TH : G HUNDRE SCOTLANDN I D 409

One would normally expect 'ic lx' to be VA long hundreds, but here the arithmetic shows that once again the short hundred was in use. The quarriers of Inverleith supplied hewn stones by the short hundred again the following week, but on the same day we also find flooring nails purchased by the long hundred.111 This may have had something to do with contracts concluded with different suppliers, but even the quarriers of Inverleith were paid by the long hundred two weeks later.112 Thereupon the long hundred was used on every occasion, clerkbue th t t thisa s time were using arabiquitw fe ea c numerals t entrie ge tha o e s , w st like this (in 1619): Item for scharping of 520 maisone irones at viii s. the hundreth xli s. iiii d.113 After that eve e arabinth c numerals disappeare whilea r dfo , returnin e accountgth theio t s r 16th-century appearance. When they came back, in the accounts for the repair of Stirling Castle in 1628-9, they were recorded by an incompetent clerk - something almost unheard of in earlier centuries e staf t f th centraleasa o ,fr fo t l government. Tak followine eth g serief o s entries, for example: Ite Johna mfr f Julio e cas 0 2 Smiti2 2 t10d e 0han th fluiring naill at 16s. the 100 inde xxiiii s. Item 1700 and 30 cast lang sklait naill at 12 s. the 100 libx . xii. s i inde Item 100 and 30 cast plainscheour naill at x s. the 100 inde d.i xviv 11 . 4s i arithmetie Th l thesal wrongs n cei i , whichever hundre beins dwa g used. Thi conceivabls si y an early case of the 'administrative decay' of the mid-1630s, noted by David Stevenson.115 Or a sympto e e transitiob th y f mo ima t n fro counting-boare mth papeo dt r calculations, with some people not fully understanding either. All the sums above would come out correctly if the 'hundred' were regarded as 40; perhaps the clerk somehow confused the 'hundred' with 2 score. (The error benefite e supplierth d s rather tha e mastenth f works.o r ) Another peculiar entry, also producing the wrong answer, illustrates the pitfalls of arabic numerals to those who were more familiar with roman ones: Item come fra Johne Grahame the 18 of October 100 . 80 . 16 skailyie at Iiii s. iiii d. the 100 inde iii i d."iv lib. 6s i .v Six months later, the short hundred was once more in use for purchases of loads of and of sand.117 A parallel account book for works at Falkland Palace used few arabic numerals, and also mixed lonshord an g t hundred - s onl lase f thesth yo t e entries use shore th s t hundred: Ite r caryin mhundrete fo an f go h xlii kairtfull f walkairtfulo k il l. s stane i ii l t indsa e xxiiii . libs i v . Ite r leadinmfo f 16go 6 kairtful f walo l l stanes and paithement at iii s. ilk kairtfull inde xxvii lib. xviii s. Item mair to the said David [Masterton] for xic Ixxiiii fute of glass at v s. ilk fute wrocht be him in the pallace of Falkland inde iic iiiixx xiii lib. x s.118 The parallel accounts for Dumbarton Castle, however, used only the long hundred, as 410 | SOCIETY OF ANTIQUARIES OF SCOTLAND, 1993

did all the copious 1633 accounts for all the royal buildings, which again used hardly any arabic numerals: Item to Alexander Flabairne for ane hundereth huikes at ii s. the peice xii lib.119 But these wer e lasth et identifiable long hundred thin i s s brance accountsth f ho e nex Th .t serie f accountso s relate 1639o st , afte Covenantere th r taked sha n findpowere w :d an , Item to James Stewinsone for a hunderth stane weyght of iroun being five schoir ... Ite Robermo t t Huntahundee an r rfo four schoir xiiilaie s th di i. s lai i f lymdo xi t e a i lib icxv . viii s.120 t entirelno s i firse yt I th cleat y entrwh r y neede e qualifieb e phraso dt th y b de 'being five schoir', since s ironormallwa n y reckone e shorth y t b dhundre n thii d s period; presumably the clerks had not yet shaken off the legacy of the past. But in the 1649 accounts the arabic numerals, arranged neatly in columns, using exclusively the short hundred, testified to the fact that a revolution had taken place.121 e masteTh f workso r ' account e instructivar s illustratinn ei e lone decath gth g f yo hundred t thebu ,y wer eminoa r branccrown'e th f ho s fiscal records. More important were eth comptroller's accounts, and these continued in their traditional course, new ideas on arithmetic notwithstanding. They did, however, begi betrao nt a slighy t self-consciousness abou lone th t g hundred. From 1624-5, although summation f produco s e still usenota , deit

'compting sex scoir to the hundreth' was usually added. All the major accounts of the 2

crown continued to use the long hundred, and roman numerals12 , up to the Covenanting revolution drafe Th . t discharg e 1636- parth f o t 7 treasury account arabie us d c di snumerals , but it was not compiled until 1658.123 e CovenanterTh t changroyae no th l d l al edi saccount s overnight. Rather, indeed, they trie keeo dt traditionae pth l account thein i s r traditionakeeo t y bese p th wa ts lwa fort i m- track of all that was due, and there was anyway massive bureaucratic inertia. For centuries clerks had been sewing lengths of parchment together to create the exchequer rolls, and mere

civil war, revolutio militard nan y conquest wer t goineno stoo gt p them.contemporare Th y 4

treasury accounts of the 1640s used largely long 12 hundreds.125 But roman numerals were on the retreat, and many of these accounts used arabic numerals for the sub-totals and totals - mose th t prestigious positions crowe th d n landsAn . produce th , e income from which kepe th t long hundred going, were increasingly marginalize e fiscath n li d seriesystemw ne f o so N . accounts used roman numeral r lonso g hundreds royae th ; l househol r Charlefo dp boou st kse

II in 1650 used arabic numerals, and the only hundreds (for of ale) were short ones. 6

The trend seems to have continued under the English occupation, though this is an even mor12 e under-researched topic than Covenanting finance drafA . t exchequer roln boo(i l k form), compile Englisy db h clerks produco ,n existss ha e t i lono ;accounts n go s hundred d an , s would have f beecolumno e n us possible e s th full t ybu , exploite e potentiadth f arabio l c numerals.127 Wit e Restorationhth e transitioth , e shorth o tnt hundre s swiftlwa d y completede Th . accounts of the crown lands were reorganized to convert produce income to cash locally, thus keeping most figures below 100. The remaining long hundreds were recalculated as short ones or simply forgotten. Sir William Purves wrote a treatise in 1681 to identify how far the rents were 'altered diminishe r convertedo rentalld d ol fro e mth s preceeding e 1603'h d an , quoted all the totals - now in arabic numerals, of course. All but one of his 'hundreds' were GOODARE: THE LONG HUNDRED IN SCOTLAND | 411

short, and he did not realize that (for instance) the '390 pair Cunings att 13s 4d the pair' whic e calculateh s wortda h '£26 originalld 0 000 ha ' y been 'iii Ixxxx'pairs0 45 e ,i ,

worth £300. He mentioned one figure 'comptinc g 5 score to the 100', and must have known abou e lon t th cleat g no s full hundreds ri wa thayt i e awarh t t bu ; d beee thaha o s nt i t universally used in the period to which he looked back across the turbulent mid-century. It is surprisin e crown'th g r thafo s eagl t sspo hi e te fac rightno ey eth t d t thadi s t modern arithmeti d reducecha d some renta sixth t y thib s bu ,s does show forcefully thae lonth t g past. e thina th hundrew f 12go no 8 s dwa The same pattern is visible in private accounts. Lady Grisell Baillie and Sir John Foulis of Ravelston both kept their accounts (covering 1692-1733 and 1691-1707 respectively) entirel n arabli y e numerals, -using column d zerosan s . Hens, threave f strawo s , herring, pound f porko s , paving-stones bolld an f ,grai o s n wer l reckoneal e e shorth y t db hundred ; there were no long hundreds. Herring, it should be noted, seems still to have been normally 129 reckoned in long hundreds in 1673, with a 'maise' of herring containing five long hundreds.130 Herring could stil e reckoneb l e lonth gy db hundre Irelann i de 19t th hn di century.13' However, example lone th gf so hundre d afte e 1640 th rraree sar buildin A . g contracf o t 1677 shows that it was now becoming a 'stylised quantity', as in England, rather than an independent uni f reckoningo t : al and haill the number of ane thowsand peace of ruch stones for heweing, accompting fyvescore anpeacn dte f goo eo suficiend dan t singell eixylyrpeacn te f d laneo an sg stones, bein f fougo r foot fyvd an se foots stones hundreth.k il o t , 132 Here the contracting parties were adopting their own definition of a 'hundred': 5 score 10 of kine f on stondo ef anothe o plu 0 1 s r kind concepA . t that coul redefinee db includo dt e non- homogeneous units had clearly been marginalized for the ordinary purposes of computation. A reckoning system thasurvived ha t d almost unchanged from medieval time beed sha n swept away in a matter of decades in the mid-17th century.

APPENDIX

GOODS RECKONE LONE TH G Y HUNDREDB D This appendix provide overvien sa goode th f wso that were (and were not) reckonee th y db long hundred. References will be found in the text, except that I have not thought it necessary to provide references to every century for all the goods in the Exchequer Rolls that continued to be reckoned by the long hundred after their first appearance. Goods were reckoned individually (eg cattle) if units are not given. Some goods were reckoned in other ways which did not give rise to hundreds - for instance, pipes or tuns of wine, lasts of salmon or lasts of herring. Further research would no doubt fill in some of the blanks, but most blanks are for less important commodities, or for ones that did not exist in such quantitie periode th n si . The following symbols are used: ••• Found in long hundreds; *** Found in short hundreds. In cases where bot foune har d more than once predominane th , t balanc indicates ei y db **•r o . * •• 412 SOCIET ANTIQUARIEF YO SCOTLANDF SO , 1993

1200-99 1300-99 1400-99 1500-99 1600-49 (gallonse Al ) Books #** *** Bread (Ib) Bullion (stones) *** *** Cattle Cheese (casks) Cheese (Ib) Clay (loads) ••* Cloth (ells) Coal (chalders) Dates (Ib) Dried fish Eels Ginger (Ib) Grain (chalders) Herring Hides (lasts) Iron (stones) **# *#* Lead (stones) **• *** Marts Nails Peat (loads) 99* Perche f lengths(o ) Poultry & capons Rabbits (pairs) Rice (Ib) 999 Salmon 999 99* Salt (chalders) 999 999 Sand (loads) 99* Sheep 99* Sheep carcasses 999 999 999 Skins 999 999 999 999 Stones (building) 999 99* Wax (stones) White fish 999 Wine (gallons) Wool (lasts) #** Woolfells

ACKNOWLEDGEMENTS I am grateful to Dr Alien Simpson and Dr Walter Makey for their comments and suggestions on an earlier version of this article. My greatest debt is to Dr Athol Murray, who provided numerous reference saved an froe s dm m several errors remaininy An . g deficienciey m e ar s own responsibility. Finally I must thank the Royal Society of Edinburgh for their support in appointing me to a Research Fellowship. GOODARE: THE LONG HUNDRED IN SCOTLAND 413

NOTES 1 Calderwood 1842-9 , 655v , . 2 Gouldesbrough 1967, 79-82. 3 Exch Rolls, vols3 2 . Some figures only were converte volsdn i . iii-xvii (1379-1542 t almos)bu l al t of them were in vols. xviii-xxiii (1543-1600). Another much-used work making the same mistake Donaldsos i n 1949. 4 Scottish Record Office [SRO] comptroller'S M , s accounts, E24/22 . 15r.-16rff , . 5 SRO, E24/23, f. 13r. Privyg Re 6 Council, , 287-8x . 7 Stevenson 1890. For the Anglo-Saxon numerals see also Bosworth & Toller 1898, s.vv; I am grateful to Prof. G W S Barrow for drawing my attention to this source. 8 Domesday Book , 336ai , , quote Rouny db d 1964. 66 , 9 Round 1964 . Round'67 , s argumen five-hide th n o t e unibees ha t n challenged evidence th n o t e bu , t wouli debate r oth ffa d o es see m prematur e Leaverejeco et Se . it tr 1988 referenced ,an s there cited. The debate has not yet reached the 'Danish' districts, but further research may shed light on the Scottish long hundred. 10 Smyth 1984, 195-207. 11 Lynch 1991, 23; Smyth 1984, 28-32, 65-6. 12 Easson 1987, 153-4 gratefum r Eassoa I .D o permissior t l nfo quoto nt e fro r thesismhe . 13 Bannerma t qualifieno nm a commen 1974o dt I . mane th 42 , n yo t complexitie f thiso r sD textd an , David Brow s currentli n y undertakin greassessmena e nameth f whoo o t st m these groupingf o s houses should poine applyth t t whicbu ; hwisI establiso ht h abou statistice th t hopeI , sis , clear. 14 Poole 1912, 45-6 quits facabacue wa n .I e t th i tsimpl e counting-boarr so us o et duodecimaa n di l version e shalw s l a ,see t quitbu , e impossibl romae us o net numerals e onlth , y ones currenn i t medieval usage. 15 Modern British duodecimalists recommend Jan : Mood£ n 1969. 5 , 16 Gordo Dobson& n 1771, 121. 17 Leges Quatuor Burgorum . 112c , Actsn i , Parl Scot, , 355i ; Scott Burgh Recs Miscellany,c So p. Ixiv. 18 Burghs Convention Recs,. 3 , i Privyg Re 9 Council,1 , 727e entrix Th . y immediately followin s 'Ani g e hundreth pai f worseto r t hoise, comptin e hundreth'x scoith sa go t r . Other items reckone e 'hundrethth y db ' lack this qualification; most likely the clerk was inspired to add a note explaining the hundred because he had grosse jusfula th r lt r lis Fo don.f fo commoditie o t o es s reckone dozee th r grossy no db e se , the Boo f Rateo k f Customso s , 1612, appende Inneo t d s 1867. Mos f theso t e were imported commodities, thus showing that the dozen (unlike the long hundred) was not a peculiarly Scottish uni f reckoningo t . 20 In theory they could have been adapted for such a system, making 'v' 6, 'x' 12, '!' 72, 'c' 144 and so on, but this did not happen. 21 Works Accts, i, 17. It might be noted here that the strictures on the clerks' arithmetic in the introduction to this volume (p. xi) arise largely from a failure to recognize the long hundred. lippie4 pecka 2 2 o st peck4 , firlota o st firlot4 , bolla boll 6 o chaldert sa 1 , o st . 23 Murray 1930, 396-8. 24 Works Accts, i, 192. 25 SRO, E24/23 . 46rf , . 6 SRO2 , E49/1 . 32vf , . 27 Works Accts, i, 176; cf. ibid., 18. 28 Acts Parl Scot, iii, 216, c. 12. thoughty M 9 thin 2 o s s subject have been shape discussiony db s wit r AliehD n Simpsons i o wh , workin comprehensiva n go e e Scottisstudth f o y h weight measuresd an e tendencs th r Fo .o t y 'progressive enlargement' of the grain measures, see Simpson 1992. 414 SOCIET ANTIQUARIEF YO SCOTLANDF SO , 1993

30 Thomas 1987, 123. 31 Lawri e(1152x53)1 190525 . no , . 2 Regesta3 Regum Scottorum, (1209x11)2 49 . no , ii . 33 Regesta Regum Scottorum, i, no. 34 (1136x52); cf. no. 206. This is a grant of lands in England held by the Scottish crown, and whether it represents Scottish or English practice would be hard to say. 34 Regesta Regum Scottorum, v, no. 342. 35 Regesta Regum Scottorum, ii, nos. 365 (1193x95), 39 (1165x70). 36 Ibid., no. 184(1173x77). 37 Exch Rolls, , 147i . 38 Ibid.,1. 39 Ibid., 17. 40 Ibid.,2\. 41 Ibid., 50. 2 Ibid.,4 121, 129, 147, 194, 198, 225, 290, 342, 408. 3 Exch4 Rolls,, 45141 , ;, 271 ii iii chalder)r 58 ,, pe ; 107 v vii(custo d 3 ; 12 ,,21 41 .s mwa 44 Exch Rolls, i, 294. 45 Exch Rolls, , 181,466ii . 46 Hanham 1971, 116-18. 7 Inne4 s 1867, 151. e solTh e exceptio8 4 s somni e 'pillari f bras'o s , weighe poundn di s reckone e lonth gy db hundred : ibid., 160. 9 Exch4 Rolls, , 508ii 308-9, ;vi . 0 Exch5 Rolls,: 'oct80 , oi millium quingentarum quinquies vigint t nouemdecie i m pellium lanutarum (eight thousand five hundred five score nineteen woolfells)'. The mere mention of '5 score' does not necessarily indicate tha e hundreformule th score6 tth s t dbu wa ,a here, '5 hundre5 d dan score' sura s i ,e sign. 51 Hanham 1971, 116-18. 52 Innes 1867, 19. 53 Burghs Convention Recs, , 269i . 54 Exch Rolls, xi, 121; xv, 51. The rate of custom was £2 13s 4d per last of 20 dacres. There is an example of '140' hides in 1454, but the customs rate appears to be wrong, so we cannot work out what kind of hundred it was: Exch Rolls, v, 609. 55 Innes 1867, 275. 56 Millar 1898, 51. 7 Quote5 Murran di y 1961b, app. 17a originae ;th SROn i s i l , E75/10. 58 Murray 1965, 127-30. r Simpson'D 9 5 s Scottise studth f yo h weight measured san s wil immensele b l y valuabl thin ei s field. 0 Hanna6 y 1915,21. 61 Ibid., 29, 31. 62 Ibid., , 18611 . 3 Ibid.,6 217. 64 Ibid., 164. 65 Ibid., 211,231,236. 66 Ibid., 290, 295. 67 Ibid., 280, 297. 8 Hanna6 y 1913. ,11 69 Ibid., 28. 70 Innes 1855,307, 308, 315. 71 Exch Rolls, , 135-6i . 72 Cochran-Patrick 1873, 89. 73 Works Accts, ii, 65, 370. GOODARE: THE LONG HUNDRED IN SCOTLAND 415

74 Exch Rolls,Challi; 66 , \ s 1977, 176-7. 75 Cochran-Patrick 1873, 15. 76 SRO, MS mint accounts, E101/2, f. Ir. 77 'Collection of the wills of printers and booksellers in Edinburgh, 1577-1687', Bannatyne Miscellany, ii (1836). The sole exception is on p. 197: 'fyve hundreth and fyve David Lyndesayis, unbund ,, pecee summaprics. th i f ii ,eo ' , s. Ixxx v x . x1 78 SRO, MS protocol books of North Berwick, B56/1/1-3. 79 Exch Rolls, ii, 474; ibid., 89. In 1362, £1,930 4s 7d was collected as custom on 'centum octoginta tresdecim lastarum vnius sacce quinque petrarum et dimidie petre lane . . . custuma sacci stante ad viginti solidos (a hundred and eighty thirteen lasts, one sack, five and a half stones of wool, the custo r sacmpe k twenty shillings)'. Threre wer sack0 laste1 a n si . 80 Exch Rolls,i, 81, 319, 173. 81 Short hundreds after 1410: 1412, 1414, 1416, 1428, 1430, 1446, 1447, 1456, 1460, 1462, 1463, 1465, 1467, 1468, 1469, 1474, 1475, 1476, 1515 (Exch Rolls, , 141iv , 200, 251, 435, 506 , 216v ; , 271; vi, 113, 580; vii, 144, 211, 362, 500, 588, 663; viii, 252, 311-12, 390; xiv, 102). 5 score: 1410, 1431, 1434, 1435, 1445, 1452, 1480, 1500, 1503, 1511, 1522, 1535 (Exch Rolls, , 114iv , 540, 573, 619 , 273, 178v ;xi ; ;, xii49678 , , ix ;162 ; xiii, 390; xiv, 442; xvi, 374). Long hundreds: 1413, 1425, 1448, 1537 (Exch Rolls, iv, 175, 380; v, 343; xvii, 48); all thereafter are long hundreds t arithmeti.bu Ove0 10 r c wrong: 1426, 1429, 1464 (Exch Rolls, , 409iv , 471; vii, 283). The rate of custom was £1 6s 8d per sack. 82 The use of the short hundred for wool may have marginal implications for the export statistics compile Isabey db l Guy, sinc claime esh havo t s e take l hundrednal 1982y , Gu longs a se 18 , Se . 1986y Gu . . cf ; 24 83 No copy of the first edition is known to exist. For what follows, see Recorde 1648, second dialogue: 'The accountin y counters'gb . Some further e subjecworkth e discussen o sar t n i d Barnard 1916 t the,littld parbu y ad Record, o et purposes3 r t ou r efo . 84 Jenkinson 1926, 274. 85 Moon 1971,28-9. 86 Works Accts, i, 138, 136. The last example was thought of, though not reckoned on the counting- board, as 12'/2 hundreds. 87 Murray 1961a. 95 , 88 Richard son of Nigel 1950, 24-5. 89 Described in Hawkins e? al. 1885, i, 150. Many more are illustrated in Mitchiner 1988-91. I am grateful to Mr Nick Holmes of the Museum for showing me a number of jetons and providing helpful information on them. 90 Works Accts, \\, 111,336. 91 James Law, Bishop of Orkney, to Sir Gideon Murray of Elibank, treasurer depute, n.d. [June 1614], Laing 1851 , 457*-8*i , . 92 Thomas 1987, 126. 3 Scottish9 Antiquary, (1889)v i , 147-8 (1890)v ; , 21-2. Works94 Accts, 320i, . 95 Hill 1965, ch. 2. 96 For references to some 17th-century English literary evidence of the decline of the counting-board in prestige, see Yeldham 1926, 89; Smith 1923-5, ii, 187-8. 7 Thi9 s doe t see no shavm o t e changed much , s reportesincwa t ei d recently thagraduate on tx si n ei has problems with basic numeracy: Guardian, Jun8 e 1992. 98 Hunter 1624, 11-12. 99 Warner 1893, p. xlii; Ramus 1569. Ramus dealt with arithmetic briefly in pp. 115-45, prefixing this section with a long philosophical introduction and following it with an equally lengthy exposition of Euclidean geometry. 0 MacDonal10 d 1971,70. 101 'Collection of the wills of printers and booksellers in Edinburgh', 195, 196, 201. 416 SOCIETY OF ANTIQUARIES OF SCOTLAND, 1993

e booth t k10 backge 2 t Millano . Attituded di r e 1898H numeraco . t s ,87 y migh e illuminateb t y db considering the circulation in Scotland of almanacs and chapbooks, which often contained arithmetical information. See Capp 1979, 201. 103 These are incorporated in the mint accounts: SRO, E103/3, ff. 6r.-8r. 104 SRO, E101/3, f. 20r. 105 SRO, E42/1. 106 SRO, E83/1, MS mines accounts, 1608-9, ff. 244r, 24Ir. 107 Works Accts, ii, 5. 108 Ibid., 1, 19. 109 Ibid., 28. 110 Ibid., 49. 111 Ibid., 50. 112 Ibid., 52. 113 Ibid., 132. 114 Ibid., 232-3. 115 Stevenson 1973. ,55 116 Works Accts, ii, 238. 117 Ibid., 250. 8 Ibid.,11 278, 281, 283 r SimpsoD . thae quantificatioe m s pointeth t o nha t t e glase dou th th n f i s o n third entry here presents further difficulties; if the glass was English, the 'foot' would be 8 inches, if Scottish inches9 , . 119 Ibid., 329. 120 Ibid., 405, 410. 121 Ibid., 431. 122 SRO, E24/42. 123 SRO, E26/4. 124 SRO, E38 series. 125 SRO, E26/5-7 (1642-6), E26/10 (1648-9). An exception is the charge of marts in 1644, totalled using the short hundred: E26/6, f. 8r. 126 SRO householS ,M d book, 1650-1, E31/19 . 30rf , . 127 SRO exchequeS M , r roll, 1652-3, E38/646A. 128 Purves 1897, 33, 90, 103 and passim. The single long hundred ('188 Capones att 6s 8d the peice: e alsSe o . SRO79 treasurS . p ,M t 08'6 a 0 s yi )9 accounts£6 , 1671, E26/11/1 r shorfo d t an ; hundreds used for chalders of grain, SRO, MS accounts of the rents of Orkney and Shetland, 1669-70, E41/12/1. 129 Scott-Moncrieff 1911, 60, 79, 85, 115, 240; Hallen 1894, 454. This last item is only a partial payment s interpretatioit o s , t certain f previouno i s t ni bu , s instalments wer rounn ei d figures (a s was usually the case) then it must be the ordinary hundred: cf. ibid., 209, 391. 130 Reg Privy Council, 3rd ser., iv, 40. 1 Glasgow13 Herald, Sept3 1 . 1886, 4/2Irise Th .h herring fishery involved many Scottish boats. 2 Dunba13 Davie& r s 1990, 301. 'Eixylyrs ashlars= ' .

REFERENCES Acts Parl Scot Acts of the Parliaments of Scotland, Thomson, T & Innes. C (eds), Edinburgh, 1814-75. Bannerman, J 1974 Studies in the History of Dalriada. Edinburgh. Barnard, F P 1916 The Casting-Counter and the Counting-Board. Oxford. Bosworth Toller& J ,N 189 T , Anglo-Saxonn 8A Dictionary, ednd 2n . Oxford. Burghs Convention Recs Records of the Convention of the Royal Burghs of Scotland, Marwick, J D (ed), Edinburgh, 1866-90. Calderwood, David 1842-9 Historye Kirk th f Scotland, o f o Thomson Laing& T , (eds)D , . 8v , Wodrow Soc. GOODARE: THE LONG HUNDRED IN SCOTLAND 417

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MANUSCRIPT SOURCES (all in the Scottish Record Office, Edinburgh):

Accounts of rents of Orkney and Shetland, 1669-70, E41/12/1. Bullion accounts E103n i , . Comptroller's accounts, E24. Exchequer roll, 1652-3, E38/646A. Lordship of Dunfermline accounts, E42. Memorandu customsn mo , 1597, E75/10. Mint accounts, E101. New augmentations accounts, E49. North Berwick protocol books, B56/1/1-3. Royal household book, 1650-51, E31/19. Treasury accounts, E26.