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an adduces the evidenc os the country eople o the royaldemesnes Who have earne stom the ather lio much in thepound the are t pay the theriandri contains a passage Whicli ake two mi fleadin assertions a that blanch arm is notmentione in omesday, b that lanch arm a invente by Roger os Salisbu . his alter passage may e thin be aselyrejectedis a glos o literar ground alone. It contradictionis the res of the Dialogus may be helesto confirm that ieW. In another passage 2, while the assertio that money aid in by the heriis is lanched by assa remains, e find that the sarmos aiundus silanched by the profit os the hundred court This,lahe with the passage referre to bove, eem to impi that a)the tenant at an extra allowanc sor blanchin at a fixe scale,
Videtur autem . . . annotantur.'
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whicli subsequently accounted numero ere Cornwall, Cumberland , Lancaster the honour, no the countyὶ Northumberland Rutland, Shropshire, Susse may accordingi conclude that nocount accounted blanch unles it containe ancient demesne δ. No the form os money paymen recorde in omesda maybe divide into sive groups a sol lows I. aymen by tale numeratas, ad numerum ad
II. Paymenta tale os coin os standard eight- de viginti in ora, ad numerum de viginti in ora, and in a single inStance, ad pondus de viginti in ora si e twent to the ounce δ. III. y eight- pensatas, ad pensum,' ad pensam, ad
pondus, ad peis, 'de . . . oris,' cum pensione,' ad penSum regiS,'
Eustace ad pensum comitis.'IU B weight in silver os approved sinenesS- arsas et pensatas,' ad arsuram et pensum, ad pensum et arsuram,' ad pondus et arSuram,' ad pensam et arsuram,' cum pondere et arsione, ad ignem et ad pensum, together With a grouinos apparenti equivalent expressions albas, candidas,' de firma alba, de albo argento,' 'lancas, and blanS.'V. B tale in coin os standard weight andineness- blancas deviginti in ora, 'de viginti in ora et albas, alborum nummorum,' de albis nummis, ' candidorum nummorum,' de candidis denariis,' de albis denariis,' ad numerum de albis denariis 'There are also paymenis puri argenti in Derbystiire, an in various countie in gold. In ver man caSeS, O COUrSe the methodo paymen is no specified. In Mur counties, vi g. Middiesex, Shropshire, Chesllire, and Nottingliam sitire, o insormation a topaymen is Supplied, and the ni insormatio in Susse relatesto ostiam. O preparin a chari toralio the distribution os these methodsos payment, obtainextitile resti insormation. The mos strihingseatur is that the paymenis in Grou Ware confine to Mur counties, vig the Iste of ight Gloucestersitire, Heresordshire, and Cambridgesilire of these, ali except HeresordShire mahe payments
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3. There are traces of the commutationis paymenis in hind into
There are a se exceptions note above. Comparison os in Exeter Domesda wit the Excheque Domesda entilles us to assim stat theabSene or presence of an note a to the for of paymen is the resulto iis absence or presence in the origina inquisitions and that the lac ofinformation a to renis o private properi Suggest that o questions ereput o that Polat.
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mone paymenis. Some os the forme stili remain, speciallyhone paymenis; ut generali Speahing the rma unius noctis
had been commuted sor a money payment. The rent Were OnSequently certain, an payable at a fixe rate in money, or at allevent on a silver basis.
. Mr. Round has potnted ut that the 'firma comitatus Wasalaeady in existence in the time os Edward the Consessor . Thesar os amichshire, o instance, as 65 unde Edward Witha hone rent commute sor 24 s.; total, 89 s. Under William I it was I 5, and there ere ther paymentsy. Thelalter sum include pleas of the county, and thus is strictly parallel illi the arm o the Pipe Rolis.
5. The money used a coine at various provincia minis, mos of the counties coining their Wn mone at the county
Henr I contain Strihin evidence of the many changes that musthave ahen place belween the time os Domesda and the year II 3o. The system os lanch paymenis is in sui operatio in addition topament made numero an ad sensum . Comparison of this ron With Domesda suggests, in laci, that hat at therars dat was an exceptionat thing had thenaecome normal. There is more Ver Some reason sor supposing that in II 3o transition a takin placerat the Exciteque between the periodin hicli sarms ere aid ad sensum and the perio in hichaheyWere pald, at an rate largely, in blanchiones There are also traces os a reorganizationis the sam os counties, particulari in the case of the large groupis counties in the handsos Αubre de Vere and Richard Basset There had certainly been a change since omesday. Oxsordshire, the omesda sarm ofWhic Was 249 s. d. , it siet sextarii' os honey worthabout 4 , o pay more than 332 M. Od. The sarm of Vamichshire, o the ther hand appears o have salien to about Lia 6s. d.
Commu=ie of London, p. 72. omes in I. f. 238 a. There is no mention o pamenta ad scalam. ut the existence of this form of payment is prove by iis occurreno in arant to the church o Holy Trinity, London, frica ad scalam ut of the far o Exeter The ore sponding ent in the Pipe Rod shows that the allowance Was made at the rateo 6ii in the is, a state in the Dialo s. Se J. H. Round Commune of Lonaeon, P. 85.
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The evidende os the Pipe olis os Henry II does no bear
directi on the statement of the Dialogus. In them e sin two SyStem O paymen only, ad numerum and lanch. e find thesarm os the counties graduali reconstitutes'. and there is abundant evidence that many of the count minis continue Working ill
We have no to conside the evidence of the chronicier in iis bearing on the questionis the originis the system os lanch paymenis It will e Mund that two monetar resorm are recordedduring the eign os Henr I vig. A. D. IIo 8 and A. D. II 25M: thel alter of these is confirmed by the Pipe Rollis 3 Henr I .
We ma no return to the account give by the Dialogus. That account is obviouslymo complete, an our ther materials domo enabi us to fili up the gaps On the ne and is, re- member that the account deal not illi the genera question os the paymentis money, ut illi the more limite question of thepament of the sar of the coun , it is no necessarii incorrect . O the ther and it certaint suggest Severa incorrect State-menis, though it is no clea that the author could have realige allthe meaning his language ould have borne to modern earS. We have attempte to constructis theor of the histor of the subjeci, hicli, offer as o the whole no inconsistent illi theauthorities here summariete&; ut it musti remembered that our attempted reconstructio resis pon flender Mundations. At thebottomis the armis the count lies the armis the royal demesne manor ' and the money arm os the demesne mano reSt upona basis os origina renis in hind estimate in term os supplies sora day. In omesda we n these rent in Mod expresse interm os money and we a gues that the meaning of this asthat he herist was charged With the mone value of these ood renis, and credite With the mone value Dan par of them that was ai directi to the royal ousehold. Eari in the eign os
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mone paymenis. Some os the forme stili remain, speciallyhone pamenis; ut generali Speahing the rma unius noctas
had been commuted sor a money payment. The rent Nere OnSequently certain, an payable at a fixe rate in money, or at allevent on a Silver basis.
. r. Round has potnted ut that the 'firma comitatus Wasalready in existenc in the time os Edward the Consessor . Thesarmis WarwichShire, sor instance, as 65 unde Edward witha hone rent commute sor et 8s. total, 89 s. Under William I it was I 5, and there ere ther paymenis'. Thelalter sam include pleas of the county, and thus is strictly parallel illi the arm o the Pipe Rolis.
5. The money used a coine at various provincia minis, mos of the counties coining their Wn mone at the county
Henr I contain strihin evidence of the many changes that musthave ahen place belween the time os DomeSda and the year II 3 o. The system os lanch paymenis is in sui operatio in addition topament made numero an ad sensum . Comparison of this olluith Domesda suggests, in laci, that What at therars dat was an exceptionat thing had thenaecome normal. There is moreover, Some reason sor Supposing that in II 3o transition as ahin placerat the Exciteque between the periodin hicli arm mere aid ad pensum and the perio in hichaheyWere pald, at an rate largely, in blancti money M. There are also traces of a reorganigationis the sarm os counties,
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The evidence of the Pipe olis os Henry II does no bear
directi on the statement of the Dialogus. In the we n two System O paymen Only, ad numerum and lanch. erand thesarm os the counties graduallyaeconstituted , and there is abundant evidence that many of the count minis continue Working ill
We have now to conside the evidence of the chroni clers in iis bearing on the questionis the originis the system os lanchia' ments. It will e Mund that two monetar resorm are recordedduring the eign os Henr I vig. A. D. IIo8 and A. D. II 25M thelalter of these is confirmed by the Pipe Rollis 3 Henr Iq. We ma no return to the account give by the Dialogus. That account is obviouslymo complete, an our ther materials domo enablem to fissimili gaps On the ne hand is, re- member that the account deal not illi the genera question os the paymen os money, but illi the more limite question of thepamen os the sar of the county, it is no necessarii incorrect . O the ther and it certaint suggest Severa incorrect State-menis, though it is no clea that the author could have realiae allthe meaning his language ould have borneri modern earS. We have attempte to constructis theor of the histor of the Subjeci, hicli, osse a o the whole no inconsistent illi theauthorities here summari ged; ut it musti remembered that our attempte reconstructio resis pon flender Mundations. At thehottomis the armis the count lies the armis the royal demesne manor' and the mone sar of the demesne mano reSt upona basis os origina renis in hind estimated in term os supplies sora day. In omesda we sin these rent in Mod expresse interm os money and w may gues that the meaning of this asthat he heriis Was charged With the mone value of these ood renis, an credi ted with the mone value Dan par of them that was ai directi to the roya household. Eari in the reim os
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Henr Pthis system a replaced by a syStem os money paymenis to the heris , and by him to the Exchequer; and the change asaccompani ed by a revaluatio of the sarms. e ma perhaps suggest Io8, the date of the rs resor of the coinage, as a possibi date so the introductio os monetar paymenis at the Exchequer, illi the provisio that the Shouldae made ad scalam. The second resorm of the coinage, in II 25 ma in the Same Waybe the time at hich paymen ad sensum a ensorced and the
that time ecome more common than the were in omeSJay, whil paymen ad sensum stili subsisted. e re no compelledio assume that the introduction o any of these three method of paymen necessarii coincide With iis invention. Blanching, certainly Was a proces of great antiquity, and the devices of paymenta scalam or ad sensum arealiel enough to have been empi edat an date. So sarras the questionis the antiquit os the Exciteque is affected, it is preti clea that the main basis of the system o payment onaccount os sarm is traceable to Saxon times, and that it received considerable modificatio belween the date of Domesda and II 3o. In considering the arithmetic employe at the Exchequer, eare immediatet confronte by tW contrivances the tali and the
excitequer. e are also tol that theremas a time,lien onlrtallies Were sed, and when there a no excitequer. The natur of the talisis preti weli understood, but the word excitequer has gatheredround it o many connotations that it ma be sesul to considerwhat the arithmetica deviceanown a the eXcheque WaS. It was,
rul in Was in quare o columns, but the comparison to a CheSS- boardi draught-board mahes it clea that it was ule in quares. In an case the columns are the important facis, the transverse lines are ni sor convenience. In ali here ere even columns ;
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TK things strihe one tince in this system os arithmetic thereis no gero, anxiis place is supplied by a system os columns Nowthis is the system os the abacus' and to save trouble e hallii latur spea of the exciteque in iis arithmetica sense a theabacus This distinctio belween the arithmetic os the Arabians and the system os the abacus a pro und There is in the Dialogus ne allusion to Arabian arithmetic , contrastiniit illithe system os the abacus, but the contrast is obscured by the factthat the ni operations employed in the Exchequer ere hos os additio an subtraction L It is no needsul to discus here theorigi and histor of the arithmetic of the abacus M, speciali as insome particular the method of the Xcheque mere peculia toliseis. The earlier abacisis seem to have Sed pieces, ach bearinga mar signisying one of themine digiis, o place in the columns of thei abacus. At the Exciteque the calculator emptos a device known a Vacervi numerales' The natur os these e hal nowconsideri' The earlies description of the system illae Mund in The round of Artes, eachin the wor and practice sarithmetic, publislied in 15 3 by Rober Recorde. In his book three methodsi rechoning by counter are described. The sirst systemdeat with arithmetici numbers, and oes no concern S. Thesecon system is calle the hercliant' use, an may be brie stydescribe d. The counter are arrange in rows, the pencemeareStto the operator ab ove them the hillings, then the ounds, then Scores of pounds, then hundreos, an So n. O the ence, Lis indicate by a counter place above the line, and the rem aining unit by counter o the line. For the hillings, Ios is indicated by a Ounter bove the line 5s by a counter o the line, but to theles hand of the uniis, and the nil by counter groupe on theline. The ound an scores siound are realed in the Same
The ordinar columns of the abacus ere so the uniis, tens, hundredS, c., os common numberS. It was necessar to adapt it to the computation os money f. Litire, S. V. schiqueter. Dialo us I. . , secundum consuetum cursum caecari non legibus arithmeticis.
Division o the abacus as a formidabie process. Is the divisor ereabOVera, . g. 7, the quotient Was obtaine by continuali divid in the dividendb Io an multiplyiniit hy 3, and addinginti the subsidiar quotient obtained by the successive divisions by Io. See Chasles Hist. Geom. I 83 7 Pp. 46 Seqq. Those it patiencerior therias may consul Gerberii gera Mathemarica, edite by Dr. Nicolaus Bubnou, Berlin, I 899. Dialogus, 1. V. L. Cf. Pipe Rod Society vol. VII. p. viii, forir. Hubertiati s discussionos the question.
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The nextruseris the auditor' use, i. e. the use of the Exchequer. Here the counter are placed in columns, and Recorde potnis ut that the unit are spread ver a many lines a the operator ab find convenient. I may be added that the are placed in t o rowS, and no more than three in a row. O the pence, a Single Counter above the nil signifies d. in the hillings, a single ounter above the unit o the right signifies , an a single ounter onthe est Io and the fame system applies to the Ounds, score os Pound S, an So n. e ma no se down aster the auditor's use the sum os L I98 9s. I Id. as besore -
It illi seen, o comparison that this scheme almos exactly coincides illi the scheme arrive a by r. Huber Hal in the Paper reserrexto above. The evidence of actualis of this deviceis naturali dissiculto discover. It must e fough in the casualus oscit by accountanis, marhing the figures of the counter bydot o the margins os accounts. ne suci instanc is mentioned by r. Hall. nother os a much eariter date, illi Mund in the Cartular os Stante Abbey, printes in the mal hi re Magazine, XV. p. 249, hicli probabi dates sto the thirteenth century Without insistin that the calculator of the Dialogus employed the auditor' use exacti a described by Recorde, it ma reasonablybe assumed that hic acervi numerales Were os the Same nature. W may now return to the earlies arithmetica device employedat the Exchequer, the tally A the description in the Dialogus
This is the sum sed by Recorde himself. Bymr Walter de Gra Bireh. The dot are sed to indicate the place Where ac deed Will e ound in the muniment room. The device employed differs hom in us describe above.