99,transcrib]'s ,note3 ,! foll[+ errors f\nd 9 ! orig9al h be5 left z is4 ,*apt] ,i1 #ad? p>agraph3 drop d\ble quote be=e ',x is said'2 ,*apt] ,,iv1 #a/ p>agraph3 's simil> ?an' read 's simil> t'2 ,*apt] ,,iv1 table ( ,hebrew num]als 7ne> footnote #add73 ins]t comma aft] '%emoneh'2 ,*apt] ,v1 table ( ,tahuatan num]als 7ne> footnote #bja73 'tahi1' read 'tahi4'2 ,same table3 ' #bj1jjj4 tufa' read '#bjj1jjj4 tufa'2 ,*apt] ,,vi1 table ( ,bagrimma num]als 7ne> footnote #bei73 'm>ta #e #b' read 'm>ta #e #c'2 ,same table3 'd-s #e #c' read 'd-s #e #d'2 ,*apt] ,,vii1 table ( ,nahuatl num]als 7ne> footnote #cfe73 '#ij-aj' read '#hj-aj'2 ,9 p>agraph foll[+ t table3 ' 7#ae #d7 #djj #hjj' read '7#ae #d7 #bj #djj #hjjj 7#ae #d7 #djj #hjjj'2 ,9 text ( footnote #big3 ',,ii4 ,i4 p4 #agi' read ',,ii4 i4 p4 #agi'2 99 ,,! ,,macmillan ,,company ,,new ,,york ,,bo/on ,,*icago ,,dallas ,,atlanta ,,san ,,francisco ,,macmillan ,,co41 ,,limit$ ,,london ,,bombay ,,calcutta ,,melb\rne ,,! ,,macmillan ,,company ,,( ,,canada1 ,,limit$ ,,toronto ,,! ,,numb] ,,concept ,,its ,,orig9 ,,& ,,developm5t ,,by ,,levi ,,leon>d ,,conant1 ,,ph4,d4 ,,associate ,,pr(essor ,,( ,,ma!matics ,,9 ,,! ,,worce/] ,,polyte*nic ,,in/itute ,new ,york ,,macmillan ,,& ,,co4 ,,& ,,london #aica ,,copyright1 #ahif1 ,,by ,,! ,,macmillan ,,company4 ,,copyright1 #aibd1 ,,by ,,emma ,b4 ,,conant4 ,all rights res]v$--no "p ( ?is book may be reproduc$ 9 any =m )\t p]mission 9 writ+ f ! publi%]4 ,set up & electrotyp$4 ,publi%$ ,july1 #ahif4 ,norwood ,press ,j4,s4 ,cu%+ ,co4--,b]wick ,smi? ,co4 ,norwood1 ,mass41 ,u4,s4,a4 ,,preface4 ,9 ! selection ( au?orities :i* h be5 consult$ 9 ! prep>ation ( ?is "w1 & to :i* ref]5ce is made 9 ! foll[+ pages1 great c>e has be5 tak54 ,orig9al s\rces h be5 drawn ^u 9 ! majority ( cases1 & ne>ly all ( ^! are ! mo/ rec5t atta9able4 ,:5ev] x has n be5 possible to cite orig9al & rec5t works1 ! au?or has quot$ only su* z are mo/ /&>d & tru/wor?y4 ,9 ! *oice ( or?ography ( prop] names & num]al words1 ! =ms h1 9 almo/ all cases1 be5 writt5 z !y 7 f\nd1 ) no attempt to r$uce !m to a sy/ematic ,engli% basis4 ,9 _m in/ances ?is w\ld h be5 q impossible2 &1 ev5 if possible1 x w\ld h be5 altoge!r unimportant4 ,h5ce ! =ms1 :e!r ,g]man1 ,fr5*1 ,italian1 ,spani%1 or ,dani% 9 _! transcription1 are left un*ang$4 ,diacritical m>ks are omitt$1 h[ev]1 s9ce ! prop] key c\ld h>dly be furni%$ 9 a "w ( ?is k9d4 ,) ! above exceptions1 ?is /udy w1 x is hop$1 be f\nd to be q complete2 & z ! subject "h inve/igat$ has nev] be=e be5 treat$ 9 any ?or\gh & compreh5sive mann]1 x is hop$ t ?is book may be f\nd helpful4 ,! collections ( num]al sy/ems illu/rat+ ! use ( ! b9>y1 ! qu9>y1 & o!r numb] sy/ems1 are1 tak5 toge!r1 believ$ to be ! mo/ ext5sive n[ exi/+ 9 any language4 ,only ! c>d9al num]als h be5 consid]$4 ,! ord9als pres5t no m>k$ peculi>ities :i* w\ld1 9 a "w ( ?is k9d1 r5d] a sep>ate discussion necess>y4 ,accord+ly !y h1 ?\gh ) "s reluctance1 be5 omitt$ entirely4 ,s9c]e ?anks are due to ^? :o h assi/$ ! au?or 9 ! prep>ation ( 8 mat]ials4 ,especial ackn[l$gm5t %\ld be made to ,horatio ,hale1 ,dr4 ,d4,g4 ,br9ton1 ,frank ,hamilton ,cu%+1 & ,dr4 ,a4,f4 ,*amb]la94 ,,worce/]1 ,,mass41 ,nov4 #ab1 #ahie4 ,,cont5ts4 ,*apt] ,i4 ,c\nt+ #a ,*apt] ,,ii4 ,numb] ,sy/em ,limits #ba ,*apt] ,,iii4 ,orig9 ( ,numb] ,words #cg ,*apt] ,,iv4 ,orig9 ( ,numb] ,words 7cont9u$7 #gd ,*apt] ,v4 ,miscellane\s ,numb] ,bases #ajj ,*apt] ,,vi4 ,! ,qu9>y ,sy/em #acd ,*apt] ,,vii4 ,! ,vigesimal ,sy/em #agf 99 99 99 99 99 ,index #baa ,,! ,,numb] ,,concept3 ,,its ,,orig9 ,,& ,,developm5t4 ,,*apt] ,i4 ,,c\nt+4 ,among ! speculative que/ions :i* arise 9 connection ) ! /udy ( ari?metic f a hi/orical /&po9t1 ! orig9 ( numb] is "o t has provok$ mu* lively discussion1 & has l$ to a great am\nt ( le>n$ rese>* among ! primitive & savage languages ( ! human race4 ,a few simple consid]ations w1 h[ev]1 %[ t su* rese>* mu/ necess>ily leave ?is "q entirely unsettl$1 & w indicate cle>ly t x is1 f ! v nature ( ?+s1 a "q to :i* no def9ite & f9al answ] c be giv54 ,among ! b>b>\s tribes ^: languages h be5 /udi$1 ev5 9 a mo/ cursory mann]1 none h ev] be5 discov]$ :i* did n %[ "s famili>ity ) ! numb] concept4 ,! k ?us indicat$ has (t5 prov$ to be mo/ limit$2 n ext5d+ beyond ! numb]s #a & #b1 or #a1 #b1 & #c4 ,examples ( ?is pov]ty ( numb] k are f\nd among ! =e/ tribes ( ,brazil1 ! native races ( ,au/ralia & else:]e1 & !y are consid]$ 9 "s detail 9 ! next *apt]4 ,at fir/ ?\ght x seems q inconceivable t any human be+ %\ld be de/itute ( ! p[] ( c\nt+ beyond #b4 ,b su* is ! case2 & 9 a few in/ances languages h be5 f\nd to be absolutely de/itute ( pure num]al words4 ,! ,*iquitos ( ,bolivia _h no real num]als :atev]1#a b express$ _! idea = "o by ! ^w etama1 mean+ alone4 ,! ,tacanas ( ! same c\ntry h no num]als except ^? borr[$ f ,spani%1 or f ,aym>a or ,p5o1 languages ) :i* !y h long be5 9 contact4#b ,a few o!r ,s\? ,am]ican languages are almo/ equally de/itute ( num]al words4 ,b ev5 "h1 rudim5t>y z ! numb] s5se und\bt$ly is1 x is n :olly lack+2 & "s indirect expression1 or "s =m ( circumlocution1 %[s a conception ( ! diff]5ce betwe5 "o & two1 or at lea/1 betwe5 "o & _m4 ,^! facts mu/ ( necessity det] ! ma!matician f seek+ to pu% 8 inve/igation too f> back t[>d ! v orig9 ( numb]4 ,philosoph]s h endeav\r$ to e/abli% c]ta9 propositions conc]n+ ?is subject1 b1 z might h be5 expect$1 h fail$ to rea* any common gr\nd ( agreem5t4 ,:ewell has ma9ta9$ t su* propositions z t two & ?ree make five are necess>y tru?s1 conta9+ 9 !m an elem5t ( c]ta9ty beyond t :i* m]e exp]i5ce c give4 ,mill1 on ! o!r h&1 argues t any su* /atem5t m]ely expresses a tru? d]iv$ f e>ly & con/ant exp]i5ce2 & 9 ?is view he is he>tily support$ by ,tylor4#c ,b :y ?is "q %\ld provoke controv]sy1 x is difficult = ! ma!matician to und]/&4 ,ei!r view w\ld seem to be correct1 accord+ to ! /&po9t f :i* ! "q is approa*$4 ,we "k ( no language 9 :i* ! sugge/ion ( numb] does n appe>1 & we mu/ admit t ! words :i* give expression to ! numb] s5se w\ld be among ! e>ly words to be =m$ 9 any language4 ,!y express ideas :i* are1 at fir/1 :olly concrete1 :i* are ( ! greate/ possible simplicity1 & :i* seem 9 _m ways to be cle>ly und]/ood1 ev5 by ! high] ord]s ( ! brute creation4 ,! orig9 ( numb] w\ld 9 itself1 !n1 appe> to lie beyond ! prop] limits ( inquiry2 & ! primitive conception ( numb] to be fundam5tal ) human ?\ght4 ,9 connection ) ! ass]tion t ! idea ( numb] seems to be und]/ood by ! high] ord]s ( animals1 ! foll[+ brief quotation f a pap] by ,sir ,john ,lubbock may n be out ( place3 ,l]oy 444 m5tions a case 9 :i* a man 0 anxi\s to %oot a cr[4 ',to deceive ?is suspici\s bird1 ! plan 0 hit ^u ( s5d+ two m5 to ! wat* h\se1 "o ( :om pass$ on1 :ile ! o!r rema9$2 b ! cr[ c\nt$ & kept h] di/ance4 ,! next day ?ree w5t1 & aga9 %e p]ceiv$ t only two retir$4 ,9 f9e1 x 0 f\nd necess>y to s5d five or six m5 to ! wat* h\se to put h] out 9 h] calculation4 ,! cr[1 ?9k+ t ?is numb] ( m5 _h pass$ by1 lo/ no "t 9 return+4' ,f ?is he inf]r$ t cr[s c\ld c\nt up to f\r4 ,li*t5b]g m5tions a night+ale :i* 0 said to c\nt up to ?ree4 ,e day he gave x ?ree mealworms1 "o at a "t4 ,:5 x _h f9i%$ "o x return$ = ano!r1 b aft] ! ?ird x knew t ! fea/ 0 ov]4444 ,!re is an amus+ & sugge/ive rem>k 9 ,mr4 ,galton's int]e/+ ,n>rative ( an ,explor] 9 ,tropical ,s\? ,africa4 ,aft] describ+ ! ,dem>a's weakness 9 calculations1 he says3 ',once :ile ,i wat*$ a ,dem>a fl\nd]+ hopelessly 9 a calculation on "o side ( me1 ,i obs]v$1 ,d9ah1 my spaniel1 equally emb>rass$ on ! o!r2 %e 0 ov]look+ half a doz5 ( h] new-born puppies1 :i* _h be5 remov$ two or ?ree times f h]1 & h] anxiety 0 excessive1 z %e tri$ to f9d out if !y 7 all pres5t1 or if any 7 /ill miss+4 ,%e kept puzzl+ & runn+ h] eyes ov] !m backw>ds & =w>ds1 b c\ld n satisfy h]self4 ,%e evid5tly _h a vague notion ( c\nt+1 b ! figure 0 too l>ge = h] bra94 ,tak+ ! two z !y /ood1 dog & ,dem>a1 ! comp>ison reflect$ no great hon\r on ! man4444' ,accord+ to my bird-ne/+ recollections1 :i* ,i h refre%$ by m rec5t exp]i5ce1 if a ne/ conta9s f\r eggs1 "o may safely be tak52 b if two are remov$1 ! bird g5]ally des]ts4 ,"h1 !n1 x w\ld seem z if we _h "s reason = suppos+ t !re is suffici5t intellig5ce to di/+ui% ?ree f f\r4 ,an int]e/+ consid]ation arises ) ref]5ce to ! numb] ( ! victims allott$ to ea* cell by ! solit>y wasps4 ,"o species ( ,ammophila consid]s "o l>ge cat]pill> ( ,noctua segetum en\gh2 "o species ( ,eum5es supplies its "y ) five victims2 ano!r #aj1 #ae1 & ev5 up to #bd4 ,! numb] appe>s to be con/ant 9 ea* species4 ,h[ does ! insect "k :5 h] task is fulfill$8 ,n by ! cell be+ fill$1 = if "s be remov$1 %e does n replace !m4 ,:5 %e has br\ght h] complem5t %e consid]s h] task accompli%$1 :e!r ! victims are /ill !re or n4 ,h[1 !n1 does %e "k :5 %e has made up ! numb] #bd8 ,p]haps x w be said t ea* species feels "s my/]i\s & innate t5d5cy to provide a c]ta9 numb] ( victims4 ,?is w\ld1 "u no circum/ances1 be any explanation2 b x is n 9 accordance ) ! facts4 ,9 ! g5us ,eum5es ! males are mu* small] ?an ! females4444 ,if ! egg is male1 %e supplies five2 if female1 #aj victims4 ,does %e c\nt8 ,c]ta9ly ?is seems v l a comm5cem5t ( ari?metic4#d ,_m writ]s d n agree ) ! conclusions :i* ,lubbock rea*es2 ma9ta9+ t !re is1 9 all su* in/ances1 a p]ception ( great] or less quantity r ?an any idea ( numb]4 ,b a c>eful consid]ation ( ! objections (f]$ fails entirely to weak5 ! argum5t4 ,example aft] example ( a nature simil> to ^? j quot$ might be giv51 indicat+ on ! "p ( animals a p]ception ( ! diff]5ce betwe5 #a & #b1 or betwe5 #b & #c & #d2 & any reason+ :i* t5ds to %[ t x is quantity r ?an numb] :i* ! animal p]ceives1 w apply ) equal =ce to ! ,dem>a1 ! ,*iquito1 & ! ,au/ralian4 ,h5ce ! actual orig9 ( numb] may safely be exclud$ f ! limits ( inve/igation1 &1 = ! pres5t1 be left 9 ! field ( pure speculation4 ,a mo/ invit+ field = rese>* is1 h[ev]1 furni%$ by ! primitive me?ods ( c\nt+ & ( giv+ visible expression to ! idea ( numb]4 ,our />t+-po9t mu/1 ( c\rse1 be ! sign language1 :i* always prec$es intelligible spee*2 & :i* is s conv5i5t & s expressive a me?od ( communication t ! human family1 ev5 9 its mo/ highly develop$ bran*es1 nev] :olly lays x aside4 ,x may1 inde$1 be /at$ z a univ]sal law1 t "s practical me?od ( num]ation has1 9 ! *ildhood ( e nation or tribe1 prec$$ ! =mation ( num]al words4 ,practical me?ods ( num]ation are _m 9 numb] & div]se 9 k9d4 ,b ! "o primitive me?od ( c\nt+ :i* seems to h be5 almo/ univ]sal ?r\gh\t all "t is ! f+] me?od4 ,x is a matt] ( common exp]i5ce & obs]vation t e *ild1 :5 he beg9s to c\nt1 turns in/9ctively to 8 f+]s2 &1 ) ^! conv5i5t aids z c\nt]s1 tallies (f ! little numb] he has 9 m9d4 ,?is me?od is at once s natural & obvi\s t !re c be no d\bt t x has always be5 employ$ by savage tribes1 s9ce ! fir/ appe>ance ( ! human race 9 remote antiquity4 ,all rese>* among unciviliz$ peoples has t5d$ to confirm ?is view1 7 confirmation ne$$ ( any?+ s pat5t4 ,occasionally "s exception to ?is rule is f\nd2 or "s v>iation1 su* z is pres5t$ by ! =e/ tribes ( ,brazil1 :o1 in/ead ( c\nt+ on ! f+]s !mselves1 c\nt on ! jo9ts ( _! f+]s4#e ,z ! entire numb] sy/em ( ^! tribes appe>s to be limit$ to ?ree1 ?is v>iation is no cause = surprise4 ,! v>iety 9 practical me?ods ( num]ation obs]v$ among savage races1 & among civiliz$ peoples z well1 is s great t any detail$ acc\nt ( !m w\ld be almo/ impossible4 ,9 "o region we f9d /icks or spl9ts us$2 9 ano!r1 pebbles or %ells2 9 ano!r1 simple scrat*es1 or not*es cut 9 a /ick1 ,rob9son ,crusoe fa%ion2 9 ano!r1 k]nels or little heaps ( gra92 9 ano!r1 knots on a /r+2 & s on1 9 div]sity ( me?od almo/ endless4 ,su* are ! devices :i* h be51 & /ill are1 to be f\nd 9 ! daily habit ( great numb]s ( ,indian1 negro1 ,mongolian1 & ,malay tribes2 :ile1 to pass at a s+le /ep to ! o!r extremity ( intellectual developm5t1 ! ,g]man /ud5t keeps 8 be] score by *alk m>ks on ! table or on ! wall4 ,b back ( all ^! devices1 & =m+ a common orig9 to :i* all may be ref]r$1 is ! univ]sal f+] me?od2 ! me?od ) :i* all beg91 & :i* all f9d too conv5i5t ev] to rel9qui% entirely1 ev5 ?\gh _! civilization be ( ! highe/ type4 ,any su* mode ( c\nt+1 :e!r involv+ ! use ( ! f+]s or n1 is to be reg>d$ simply z an extrane\s aid 9 ! expression or compreh5sion ( an idea :i* ! m9d _c grasp1 or _c reta91 )\t assi/ance4 ,! ,g]man /ud5t scores 8 reckon+ ) *alk m>ks because he might o!rwise =get2 :ile ! ,&aman ,isl&] c\nts on 8 f+]s because he has no o!r me?od ( c\nt+1--or1 9 o!r words1 ( grasp+ ! idea ( numb]4 ,a s+le illu/ration may be giv5 :i* typifies all practical me?ods ( num]ation4 ,m ?an a c5tury ago travell]s 9 ,madagasc> obs]v$ a curi\s b simple mode ( asc]ta9+ ! numb] ( soldi]s 9 an army4#f ,ea* soldi] 0 made to g ?r\gh a passage 9 ! pres5ce ( ! pr9cipal *iefs2 & z he w5t ?r\gh1 a pebble 0 dropp$ on ! gr\nd4 ,?is cont9u$ until a heap ( #aj 0 obta9$1 :5 "o 0 set aside & a new heap begun4 ,^u ! completion ( #aj heaps1 a pebble 0 set aside to indicate #ajj2 & s on until ! entire army _h be5 numb]$4 ,ano!r illu/ration1 tak5 f ! v antipodes ( ,madagasc>1 rec5tly f\nd its way into pr9t 9 an incid5tal mann]1#g & is s good t x des]ves a place beside de ,flac\rt's "t-hon\r$ example4 ,mom ,cely1 a ,s\!rn negro ( unkn[n age1 f9ds h]self 9 debt to ! /orekeep]2 &1 unwill+ to believe t ! am\nt is z great z he repres5ts1 %e proce$s to inve/igate ! matt] 9 h] own peculi> way4 ,%e _h kept a tally ( ^! pur*ases by means ( a /r+1 9 :i* %e ti$ commemorative knots4 ,:5 h] cr$itor und]took to make ! matt] cle> to ,cely's compreh5sion1 he _h to proce$ ^u a sy/em ( h] own devis+4 ,a small not* 0 cut 9 a smoo? :ite /ick = e dime %e ow$1 & a l>ge not* :5 ! dimes am\nt$ to a doll>2 = e five doll>s a /r+ 0 ti$ 9 ! fif? big not*1 ,cely keep+ tally by ! knots 9 h] bit ( tw9e2 ?us1 :5 two /r+s 7 ti$ ab\t ! /ick1 ! t5 doll>s 7 se5 to be an indisputable fact4 ,?is int]e/+ me?od ( comput+ ! am\nt ( h] debt1 :e!r an inv5tion ( h] own or a survival ( ! ,african life ( h] p>5ts1 s]v$ ! old negro woman's purpose p]fectly2 & x illu/rates1 z well z a score ( examples c\ld1 ! me?ods ( num]ation to :i* ! *ildr5 ( b>b>ism resort :5 any numb] is to be express$ :i* exce$s ! numb] ( c\nt]s ) :i* nature has provid$ !m4 ,! f+]s are1 h[ev]1 (t5 employ$ 9 c\nt+ numb]s f> above ! fir/ decade4 ,aft] giv+ ! ,il-,oigob num]als up to #fj1 ,mll] adds3#h ,above #fj all numb]s1 indicat$ by ! prop] figure pantomime1 are express$ by means ( ! ^w ipi4 ,we "k1 moreov]1 t _m ( ! ,am]ican ,indian tribes c\nt "o t5 aft] ano!r on _! f+]s2 s t1 :atev] numb] !y are endeav\r+ to indicate1 we ne$ feel no surprise if ! savage cont9ues to use 8 f+]s ?r\gh\t ! entire ext5t ( 8 c\nts4 ,9 r>e in/ances we f9d tribes :i*1 l ! ,mairassis ( ! int]ior ( ,new ,gu9ea1 appe> to use no?+ b f+] pantomime4#i ,?is tribe1 ?\gh by no means de/itute ( ! numb] s5se1 is said to h no num]als :atev]1 b to use ! s+le ^w aw>i ) ea* %[ ( f+]s1 no matt] h[ few or h[ _m are display$4 ,9 ! me?ods ( f+] c\nt+ employ$ by savages a consid]able degree ( uni=mity has be5 obs]v$4 ,n only does he use 8 f+]s to assi/ him 9 8 tally1 b he almo/ always beg9s ) ! little f+] ( 8 left h&1 !nce proce$+ t[>ds ! ?umb1 :i* is #e4 ,f ?is po9t onw>d ! me?od v>ies4 ,sometimes ! second #e also is told (f on ! left h&1 ! same ord] be+ obs]v$ z 9 ! fir/ #e2 b (t5] ! f+]s ( ! "r h& are us$1 ) a rev]sal ( ! ord] previ\sly employ$2 i4e4 ! ?umb d5otes #f1 ! index f+] #g1 & s on to ! little f+]1 :i* completes ! c\nt to #aj4 ,at fir/ ?\ght !re w\ld seem to be no good reason = any m>k$ uni=mity ( me?od 9 f+] c\nt+4 ,obs]vation among *ildr5 fails to detect any su* ?+2 ! *ild beg9n+1 ) almo/ entire indiff]5ce1 on ! ?umb or on ! little f+] ( ! left h&4 ,my own obs]vation leads to ! conclusion t v "y *ildr5 h a slight1 ?\gh n decid$ pref]5ce = beg9n+ ) ! ?umb4 ,exp]im5ts 9 five diff]5t prim>y rooms 9 ! public s*ools ( ,worce/]1 ,mass41 %[$ t out ( a total ( #bjf *ildr51 #eg began ) ! little f+] & #adi ) ! ?umb4 ,b ! fact t ne>ly ?ree-f\r?s ( ! *ildr5 began ) ! ?umb1 & b "o-f\r? ) ! little f+]1 is really f> less significant ?an w\ld appe> at fir/ ?\ght4 ,*ildr5 ( ?is age1 f\r to eight ye>s1 w c\nt 9 ei!r way1 & sometimes seem at a loss !mselves to "k :]e to beg94 ,9 "o s*ool room :]e ?is exp]im5t 0 tri$ ! tea*] incauti\sly ask$ "o *ild to c\nt on 8 f+]s1 :ile all ! o!r *ildr5 9 ! room wat*$ eag]ly to see :at he w\ld d4 ,he began ) ! little f+]--& s did e *ild 9 ! room aft] him4 ,9 ano!r case ! same error 0 made by ! tea*]1 & ! *ild fir/ ask$ began ) ! ?umb4 ,e o!r *ild 9 ! room did ! same1 ea* foll[+1 consci\sly or unconsci\sly1 ! example ( ! lead]4 ,! results f ^! two s*ools 7 ( c\rse reject$ f ! totals :i* are giv5 above2 b !y s]ve an excell5t purpose 9 %[+ h[ slight is ! pref]5ce :i* v "y *ildr5 h 9 ?is p>ticul>4 ,s slight is x t no def9ite law c be po/ulat$ ( ?is age2 b ! t5d5cy seems to be to hold ! palm ( ! h& d[nw>d1 & !n beg9 ) ! ?umb4 ,! writ] once saw a boy ab\t sev5 ye>s old try+ to multiply #c by #f2 & 8 me?od ( proc$ure 0 z foll[s3 hold+ 8 left h& ) its palm d[n1 he t\*$ ) ! =ef+] ( 8 "r h& ! ?umb1 =ef+]1 & middle f+] successively ( 8 left h&4 ,!n return+ to 8 />t+-po9t1 he told (f a second ?ree 9 ! same mann]4 ,?is process he cont9u$ until he _h obta9$ #f ?rees1 & !n he ann\nc$ 8 result correctly4 ,if he _h be5 a few ye>s old]1 he might n h turn$ s readily to 8 ?umb z a />t+-po9t = any digital c\nt4 ,! indiff]5ce manife/$ by v "y *ildr5 gradually disappe>s1 & at ! age ( twelve or ?irte5 ! t5d5cy is decid$ly 9 ! direction ( beg9n+ ) ! little f+]4 ,fully ?ree-f\r?s ( all p]sons above t age w be f\nd to c\nt f ! little f+] t[>d ! ?umb1 ?us rev]s+ ! proportion t 0 f\nd to obta9 9 ! prim>y s*ool rooms exam9$4 ,) respect to f+] c\nt+ among civiliz$ peoples1 we fail1 !n1 to f9d any univ]sal law2 ! mo/ t c be said is t m beg9 ) ! little f+] ?an ) ! ?umb4 ,b :5 we proce$ to ! /udy ( ?is slight b important p>ticul> among savages1 we f9d !m employ+ a c]ta9 ord] ( succession ) su* sub/antial uni=mity t ! conclusion is inevitable t !re mu/ lie back ( ?is "s well-def9$ reason1 or p]haps in/9ct1 :i* guides !m 9 _! *oice4 ,?is in/9ct is und\bt$ly ! outgr[? ( ! almo/ univ]sal "r-h&$ness ( ! human race4 ,9 f+] c\nt+1 :e!r among *ildr5 or adults1 ! beg9n+ is made on ! left h&1 except 9 ! case ( left-h&$ individuals2 & ev5 !n ! />t is almo/ z likely to be on ! left h& z on ! "r4 ,savage tribes1 z might be expect$1 beg9 ) ! left h&4 ,n only is ?is cu/om almo/ inv>iable1 :5 tribes z a :ole are consid]$1 b ! little f+] is ne>ly always call$ into requisition fir/4 ,to acc\nt = ?is uni=mity1 ,lieut5ant ,gu%+ gives ! foll[+ !ory1#aj :i* is well consid]$1 & is bas$ on ! results ( c>eful /udy & obs]vation among ! ,zui ,indians ( ! ,s\?we/3 ,primitive man :5 abroad nev] lightly quit hold ( 8 weapons4 ,if he want$ to c\nt1 he did z ! ,zui afield does to-day2 he tuck$ 8 in/rum5t "u 8 left arm1 ?us con/ra9+ ! latt]1 b leav+ ! "r h& free1 t he might *eck (f ) x ! f+]s ( ! rigidly elevat$ left h&4 ,f ! nature ( ?is position1 h[ev]1 ! palm ( ! left h& 0 pres5t$ to ! face ( ! c\nt]1 s t he _h to beg9 8 score on ! little f+] ( x1 & cont9ue 8 c\nt+ f ! "r leftw>d4 ,an inh]itance ( ?is may be detect$ to-day 9 ! confirm$ habit ! ,zui has ( ge/iculat+ f ! "r leftw>d1 ) ! f+]s ( ! "r h& ov] ^? ( ! left1 :e!r he be c\nt+ & summ+ up1 or relat+ 9 any ord]ly mann]4 ,"h1 !n1 is ! reason = ?is o!rwise unacc\ntable ph5om5on4 ,if savage man is univ]sally "r-h&$1 he w almo/ inevitably use ! index f+] ( 8 "r h& to m>k ! f+]s c\nt$1 & he w beg9 8 c\nt j :]e x is mo/ conv5i5t4 ,9 8 case x is ) ! little f+] ( ! left h&4 ,9 ! case ( ! *ild try+ to multiply #c by #f1 x 0 ) ! ?umb ( ! same h&4 ,he _h no?+ to tuck "u 8 arm2 s1 9 rais+ 8 left h& to a position :]e bo? eye & c\nt+ f+] c\ld readily run ov] its f+]s1 he held ! palm turn$ away f 8 face4 ,! same *oice ( />t+-po9t !n foll[$ z ) ! savage--! f+] ne>e/ 8 "r h&2 only 9 ?is case ! f+] 0 a ?umb4 ,! deaf mute is sometimes taught 9 ?is mann]1 :i* is = him an entirely natural mann]4 ,a left-h&$ *ild might be expect$ to c\nt 9 a left-to-"r mann]1 beg9n+1 probably1 ) ! ?umb ( 8 "r h&4 ,to ! law j giv51 t savages beg9 to c\nt on ! little f+] ( ! left h&1 !re h be5 a few exceptions not$2 & x has be5 obs]v$ t ! me?od ( progression on ! second h& is by no means z inv>iable z on ! fir/4 ,! ,otomacs#aa ( ,s\? ,am]ica began _! c\nt ) ! ?umb1 & to express ! numb] #c w\ld use ! ?umb1 =ef+]1 & middle f+]4 ,! ,maipures1#ab oddly en\gh1 seem to h begun1 9 "s cases at lea/1 ) ! =ef+]2 = !y are report$ z express+ #c by means ( ! =e1 middle1 & r+ f+]s4 ,! ,&amans#ac beg9 ) ! little f+] ( ei!r h&1 tapp+ ! nose ) ea* f+] 9 succession4 ,if !y h b "o to express1 !y use ! =ef+] ( ei!r h&1 pron\nc+ at ! same "t ! prop] ^w4 ,! ,bahn>s1#ad "o ( ! native tribes ( ! int]ior ( ,co*9 ,*9a1 exhibit no p>ticul> ord] 9 ! sequ5ce ( f+]s us$1 ?\gh !y employ _! digits freely to assi/ !m 9 c\nt+4 ,among c]ta9 ( ! negro tribes ( ,s\? ,africa#ae ! little f+] ( ! "r h& is us$ = #a1 & _! c\nt proce$s f "r to left4 ,) !m1 #f is ! ?umb ( ! left h&1 #g ! =ef+]1 & s on4 ,!y hold ! palm d[nw>d in/ead ( upw>d1 & ?us =m a complete & /rik+ exception to ! law :i* has be5 f\nd to obta9 ) su* sub/antial uni=mity 9 o!r p>ts ( ! unciviliz$ _w4 ,9 ,melanesia a few examples ( pref]5ce = beg9n+ ) ! ?umb may also be notic$4 ,9 ! ,banks ,isl&s ! natives beg9 by turn+ d[n ! ?umb ( ! "r h&1 & !n ! f+]s 9 succession to ! little f+]1 :i* is #e4 ,?is is foll[$ by ! f+]s ( ! left h&1 bo? h&s ) clos$ fi/s be+ held up to %[ ! complet$ #aj4 ,9 ,lep]s' ,isl&1 !y beg9 ) ! ?umb1 b1 hav+ rea*$ #e ) ! little f+]1 !y d n pass to ! o!r h&1 b ?r[ up ! f+]s !y h turn$ d[n1 beg9n+ ) ! =ef+] & keep+ ! ?umb = #aj4af ,9 ! use ( ! s+le h& ?is p is q peculi>4 ,! second #e is almo/ inv>iably told (f by savage tribes on ! second h&1 ?\gh 9 pass+ f ! "o to ! o!r primitive man does n foll[ any inv>iable law4 ,he m>ks #f ) ei!r ! ?umb or ! little f+]4 ,probably ! =m] is ! m common practice1 b ! /atem5t _c be made ) any degree ( c]ta9ty4 ,among ! ,zulus ! sequ5ce is f ?umb to ?umb1 z is ! case among ! o!r ,s\? ,african tribes j m5tion$2 :ile ! ,veis & num]\s o!r ,african tribes pass f ?umb to little f+]4 ,! ,eskimo1 & ne>ly all ! ,am]ican ,indian tribes1 use ! correspond5ce betwe5 #f & ! ?umb2 b ?is habit is by no means univ]sal4 ,respect+ progression f "r to left or left to "r on ! toes1 !re is no g5]al law ) :i* ! au?or is famili>4 ,_m tribes nev] use ! toes 9 c\nt+1 b signify ! close ( ! fir/ #aj by clapp+ ! h&s toge!r1 by a wave ( ! "r h&1 or by designat+ "s object2 aft] :i* ! f+]s are aga9 us$ z be=e4 ,"o o!r detail 9 f+] c\nt+ is wor?y ( a mom5t's notice4 ,x seems to h be5 ! op9ion ( e>li] inve/igators t 9 8 passage f "o f+] to ! next1 ! savage w\ld inv>iably b5d d[n1 or close1 ! la/ f+] us$2 t is1 t ! c\nt began ) ! f+]s op5 & outspread4 ,?is op9ion is1 h[ev]1 errone\s4 ,sev]al ( ! ,indian tribes ( ! ,we/#ag beg9 ) ! h& cl5*$1 & op5 ! f+]s "o by "o z !y proce$4 ,?is me?od is mu* less common ?an ! o!r1 b t x exi/s is beyond "q4 ,9 ! ,muralug ,isl&1 9 ! we/]n "p ( ,torres ,/rait1 a some:at rem>kable me?od ( c\nt+ =m]ly exi/$1 :i* grew out (1 & is to be reg>d$ z an ext5sion (1 ! digital me?od4 ,beg9n+ ) ! little f+] ( ! left h&1 ! natives c\nt$ up to #e 9 ! usual mann]1 & !n1 in/ead ( pass+ to ! o!r h&1 or repeat+ ! c\nt on ! same f+]s1 !y express$ ! numb]s f #f to #aj by t\*+ & nam+ successively ! left wri/1 left elb[1 left %\ld]1 left brea/1 & /]num4 ,!n ! numb]s f #aa to #ai 7 indicat$ by ! use1 9 inv]se ord]1 ( ! correspond+ portions ( ! "r side1 arm1 & h&1 ! little f+] ( ! "r h& signify+ #ai4 ,! words us$ 7 9 ea* case ! actual names ( ! p>ts t\*$2 ! same ^w1 = example1 /&+ = #f & #ad2 b !y 7 nev] us$ 9 ! num]ical s5se unless accompani$ by ! prop] ge/ure1 & be> no resemblance to ! common num]als1 :i* are b few 9 numb]4 ,?is me?od ( c\nt+ is rapidly dy+ out among ! natives ( ! isl&1 & is at ! pres5t "t us$ only by old p4#ah ,v>iations on ?is mo/ unusual cu/om h be5 f\nd to exi/ 9 o!rs ( ! neighb\r+ isl&s1 b none 7 exactly simil> to x4 ,"o is also rem9d$ by x ( a cu/om#ai :i* has = c5turies prevail$ among b>ga9]s 9 ! ,ea/1 ( signify+ numb]s by t\*+ ! jo9ts ( ea* o!r's f+]s "u a clo?4 ,e jo9t has a special signification2 & ! entire sy/em is und\bt$ly a developm5t f f+] c\nt+4 ,! buy] or sell] w by ?is me?od express #f or #fj by /ret*+ out ! ?umb & little f+] & clos+ ! re/ ( ! f+]s4 ,! addition ( ! f\r? f+] to ! two ?us us$ signifies #g or #gj2 & s on4 ,x is said t betwe5 two brok]s settl+ a price by ?us snipp+ ) ! f+]s1 clev]ness 9 b>ga9+1 (f]+ a little m1 hesitat+1 express+ an ob/9ate refusal to g fur!r1 etc41 are z cle>ly indicat$ z ?\gh ! b>ga9+ 7 be+ c>ri$ on 9 words4 ,! place occupi$1 9 ! intellectual developm5t ( man1 by f+] c\nt+ & by ! _m o!r artificial me?ods ( reckon+1--pebbles1 %ells1 knots1 ! abacus1 etc41--seems to be ?is3 ,! ab/ract processes ( addition1 subtraction1 multiplication1 division1 & ev5 c\nt+ itself1 pres5t to ! m9d a c]ta9 degree ( difficulty4 ,to assi/ 9 ov]com+ t difficulty1 ^! artificial aids are call$ 92 &1 among savages ( a l[ degree ( developm5t1 l ! ,au/ralians1 !y make c\nt+ possible4 ,a little high] 9 ! intellectual scale1 among ! ,am]ican ,indians1 = example1 !y are employ$ m]ely z an artificial aid to :at c\ld be done by m5tal ef=t alone4 ,f9ally1 among semi-civiliz$ & civiliz$ peoples1 ! same processes are reta9$1 & =m a "p ( ! daily life ( almo/ e p]son :o has to d ) c\nt+1 reckon+1 or keep+ tally 9 any mann] :atev]4 ,!y are no long] necess>y1 b !y are s conv5i5t & s useful t civilization c nev] disp5se ) !m4 ,! use ( ! abacus1 9 ! =m ( ! ord9>y num]al frame1 has increas$ greatly )9 ! pa/ few ye>s2 & ! "t may come :5 ! abacus 9 its prop] =m w aga9 f9d 9 civiliz$ c\ntries a use z common z t ( five c5turies ago4 ,9 ! elaborate calculat+ ma*9es ( ! pres5t1 su* z are us$ by life insurance actu>ies & o!rs hav+ difficult computations to make1 we h ! extreme ( developm5t 9 ! direction ( artificial aid to reckon+4 ,b in/ead ( appe>+ m]ely z an extrane\s aid to a defective intellig5ce1 x n[ pres5ts itself z a ma*9e s complex t a high degree ( intellectual p[] is requir$ = ! m]e grasp ( its con/ruction & me?od ( work+4 ,,*apt] ,,ii4 ,,numb] ,,sy/em ,,limits4 ,) respect to ! limits to :i* ! numb] sy/ems ( ! v>i\s unciviliz$ races ( ! e>? ext5d1 rec5t an?ropological rese>* has develop$ _m int]e/+ facts4 ,9 ! case ( ! ,*iquitos & a few o!r native races ( ,bolivia we f\nd no di/9ct numb] s5se at all1 z f> z c\ld be judg$ f ! abs5ce1 9 _! language1 ( num]als 9 ! prop] s5se ( ! ^w4 ,h[ !y indicat$ any numb] great] ?an "o is a po9t /ill requir+ inve/igation4 ,9 all o!r kn[n in/ances we f9d actual numb] sy/ems1 or :at may = ! sake ( uni=mity be dignifi$ by t "n4 ,9 _m cases1 h[ev]1 ! num]als exi/+ are s few1 & ! ability to c\nt is s limit$1 t ! t]m numb] sy/em is really an entire misnom]4 ,among ! rude/ tribes1 ^? ^: mode ( liv+ approa*es mo/ ne>ly to utt] savag]y1 we f9d a c]ta9 uni=mity ( me?od4 ,! entire numb] sy/em may consi/ ( b two words1 "o & _m2 or ( ?ree words1 "o1 two1 _m4 ,or1 ! c\nt may proce$ to #c1 #d1 #e1 #aj1 #bj1 or #ajj2 pass+ always1 or almo/ always1 f ! di/9ct num]al limit to ! indef9ite _m or sev]al1 :i* s]ves = ! expression ( any numb] n readily grasp$ by ! m9d4 ,z a matt] ( fact1 mo/ races c\nt z high z #aj2 b to ?is /atem5t ! exceptions are s num]\s t !y des]ve exam9ation 9 "s detail4 ,9 c]ta9 p>ts ( ! _w1 notably among ! native races ( ,s\? ,am]ica1 ,au/ralia1 & _m ( ! isl&s ( ,polynesia & ,melanesia1 a surpris+ paucity ( num]al words has be5 obs]v$4 ,! ,encabellada ( ! ,rio ,napo h b two di/9ct num]als2 tey1 #a1 & cayapa1 #b4bj ,! ,*aco languages#ba ( ! ,guaycuru /ock are also notably poor 9 ?is respect4 ,9 ! ,mbocobi dialect ( ?is language ! only native num]als are ya tvak1 #a1 & yfioaca1 #b4 ,! ,puris#bb c\nt omi1 #a1 curiri1 #b1 prica1 _m2 & ! ,botocudos#bc mok5am1 #a1 uruhu1 _m4 ,! ,fuegans1#bd suppos$ to h be5 able at "o "t to c\nt to #aj1 h b ?ree num]als1--ka\eli1 #a1 compaipi1 #b1 mat51 #c4 ,! ,campas ( ,p]u#be possess only ?ree sep>ate words = ! expression ( numb]1--patrio1 #a1 pitt5i1 #b1 mahuani1 #c4 ,above #c !y proce$ by comb9ations1 z #a & #c = #d1 #a & #a & #c = #e4 ,c\nt+ above #aj is1 h[ev]1 entirely inconceivable to !m1 & any numb] beyond t limit !y indicate by toha9e1 _m4 ,! ,conibos1#bf ( ! same region1 _h1 be=e _! contact ) ! ,spani%1 only at*\pre1 #a1 & rrabui1 #b2 ?\gh !y made "s slight progress above #b by means ( r$uplication4 ,! ,orejones1 "o ( ! l[1 degrad$ tribes ( ! ,upp] ,amazon1#bg h no names = numb] except nayhay1 #a1 n5acome1 #b1 f59i*acome1 #c1 ononoeom]e1 #d4 ,9 ! ext5sive vocabul>ies giv5 by ,von ,m>t9s1#bh _m simil> examples are f\nd4 ,= ! ,bororos he gives only c\ai1 #a1 mae\ai1 #b1 ouai1 #c4 ,! la/ ^w1 ) ! prop] f+] pantomime1 s]ves also = any high] numb] :i* falls )9 ! grasp ( _! compreh5sion4 ,! ,gua*i manage to rea* #e1 b _! num]ation is ( ! rude/ k9d1 z ! foll[+ scale %[s3 tamak1 #a1 eu-e*o1 #b1 eu-e*o-kailau1 #c1 eu-e*o-way1 #d1 localau1 #e4 ,! ,c>ajas c\nt$ by a scale equally rude1 & _! conception ( numb] seem$ equally vague1 until contact ) ! neighb\r+ tribes furni%$ !m ) ! means ( go+ beyond _! orig9al limit4 ,_! scale %[s cle>ly ! unc]ta91 feeble numb] s5se :i* is s m>k$ 9 ! int]ior ( ,s\? ,am]ica4 ,x conta9s wadewo1 #a1 wadebo?oa1 #b1 wadeboaheodo1 #c1 wadebojeodo1 #d1 wadewaj\clay1 #e1 wadewasori1 #f1 or _m4 ,turn+ to ! languages ( ! ext9ct1 or fa/ vani%+1 tribes ( ,au/ralia1 we f9d a /ill m notewor?y abs5ce ( num]al expressions4 ,9 ! ,gudang dialect#bi b two num]als are f\nd--pirman1 #a1 & ilabiu1 #b2 9 ! ,we$ook>ry1 ekkamurda1 #a1 & koot]a1 #b2 & 9 ! ,queanbeyan1 midjemban1 #a1 & bollan1 #b4 ,9 a score or m ( in/ances ! num]als /op at #c4 ,! natives ( ,keppel ,bay c\nt webb51 #a1 booli1 #b1 koorel1 #c2 ( ! ,boyne ,riv]1 k>roon1 #a1 boodla1 #b1 numma1 #c2 ( ! ,fl9d]s ,riv]1 kooro91 #a1 kurto1 #b1 kurto kooro91 #c2 at ! m\? ( ! ,norman ,riv]1 lum1 #a1 bugg>1 #b1 or9*1 #c2 ! ,eaw tribe1 koo!a1 #a1 woo!r1 #b1 m>ronoo1 #c2 ! ,moree1 mal1 #a1 bool>1 #b1 kooliba1 #c2 ! ,port ,ess+ton1#cj erad1 #a1 n>g>ick1 #b1 n>g>ickel]ad1 #c2 ! ,d>nly ,isl&]s1#ca netat1 #a1 naes1 #b1 naesa netat1 #c2 & s on ?r\gh a long li/ ( tribes ^: num]al scales are equally scanty4 ,a /ill l>g] numb] ( tribes %[ an ability to c\nt "o /ep fur!r1 to #d2 b beyond ?is limit ! majority ( ,au/ralian & ,tasmanian tribes d n g4 ,x seems mo/ rem>kable t any human be+ %\ld possess ! ability to c\nt to #d1 & n to #e4 ,! numb] ( f+]s on "o h& furni%es s obvi\s a limit to any ( ^! rudim5t>y sy/ems1 t positive evid5ce is ne$$ be=e "o c accept ! /atem5t4 ,a c>eful exam9ation ( ! num]als 9 upw>ds ( a hundr$ ,au/ralian dialects leaves no d\bt1 h[ev]1 t su* is ! fact4 ,! ,au/ralians 9 almo/ all cases c\nt by pairs2 & s pron\nc$ is ?is t5d5cy t !y pay b little att5tion to ! f+]s4 ,"s tribes d n appe> ev] to c\nt beyond #b--;a s+le pair4 ,_m m g "o /ep fur!r2 b if !y d1 !y are z likely z n to designate _! next num]al z two-"o1 or possibly1 "o-two4 ,if ?is /ep is tak51 we may or may n f9d "o m add$ to x1 ?us complet+ ! second pair4 ,/ill1 ! ,au/ralian's capacity = und]/&+ any?+ :i* p]ta9s to numb] is s pa9fully limit$ t ev5 "h !re is sometimes an indef9ite expression =m$1 z _m1 heap1 or pl5ty1 in/ead ( any di/9ct num]al2 & x is probably true t no ,au/ralian language conta9s a pure1 simple num]al = #d4 ,curr1 ! be/ au?ority on ?is subject1 believes t1 :]e a di/9ct ^w = #d is giv51 inve/igators h be5 deceiv$ 9 e case4#cb ,if c\nt+ is c>ri$ beyond #d1 x is always by means ( r$uplication4 ,a few tribes gave expressions = #e1 few] /ill = #f1 & a v small numb] appe>$ able to rea* #g4 ,possibly ! ability to c\nt ext5d$ /ill fur!r2 b if s1 x consi/$ und\bt$ly 9 reckon+ "o pair aft] ano!r1 )\t any consci\sness :atev] ( ! sum total save z a l>g] numb]4 ,! num]als ( a few additional tribes w %[ cle>ly t all di/9ct p]ception ( numb] is lo/ z soon z ^! races attempt to c\nt above #c1 or at mo/1 #d4 ,! ,yuckaburra#cc natives c g no fur!r ?an wigs91 #a1 bull>oo1 #b1 goolbora1 #c4 ,above "h all is ref]r$ to z moorgha1 _m4 ,! ,m>a*[ies#cd h b ?ree di/9ct num]als1--cooma1 #a1 coot]a1 #b1 murra1 #c4 ,= #d !y say m9na1 _m4 ,at ,/reaky ,bay we f9d a simil> li/1 ) ! same words1 kooma & koot]a1 = #a & #b1 b entirely diff]5t t]ms1 k>boo & yalkata = #c & _m4 ,! same me?od obta9s 9 ! ,m9nal ,yung> tribe1 :]e ! only num]als are ka91 #a1 kujal1 #b1 moa1 #c1 & bulla1 pl5ty4 ,9 ! ,p9j>ra dialect we f9d doomb>t1 #a1 gugal1 #b1 murd9e1 #c1 boola1 pl5ty2 & 9 ! dialect describ$ z belong+ to ,eyre's ,s& ,pat*1 ?ree def9ite t]ms are giv5--kean1 #a1 koojal1 #b1 yalgatta1 #c1 :ile a f\r?1 murna1 s]v$ to describe any?+ great]4 ,9 all ^! examples ! f\r? num]al is indef9ite2 & ! same /atem5t is true ( _m o!r ,au/ralian languages4 ,b m commonly /ill we f9d #d1 & p]haps #c also1 express$ by r$uplication4 ,9 ! ,port ,mackay dialect#ce ! latt] num]al is comp\nd1 ! c\nt be+ w>pur1 #a1 bool]a1 #b1 bool]a w>pur1 #c4 ,= #d ! t]m is n giv54 ,9 ! dialect :i* prevail$ betwe5 ! ,alb]t & ,twe$ riv]s#cf ! scale appe>s z yaburu1 #a1 bool>oo1 #b1 bool>oo yaburu1 #c1 & gurul = #d or any?+ beyond4 ,! ,wiraduroi#cg h numbai1 #a1 bula1 #b1 bula numbai1 #c1 bungu1 #d1 or _m1 & bungu galan or bian galan1 #e1 or v _m4 ,! ,kamil>oi#ch scale is /ill m irregul>1 comp\nd+ above #d ) little app>5t me?od4 ,! num]als are mal1 #a1 bul>1 #b1 guliba1 #c1 bul> bul>1 #d1 bul> guliba1 #e1 guliba guliba1 #f4 ,! la/ two num]als %[ t #e is to ^! natives simply #b-c1 & #f is #c-c4 ,= additional examples ( a simil> nature ! ext5d$ li/ ( ,au/ralian scales giv5 9 ,*apt] ,v4 may be consult$4 ,tak5 z a :ole1 ! ,au/ralian & ,tasmanian tribes seem to h be5 di/9ctly inf]ior to ^? ( ,s\? ,am]ica 9 _! ability to use & to compreh5d num]als4 ,9 all b two or ?ree cases ! ,tasmanians#ci 7 f\nd to be unable to proce$ beyond #b2 & z ! =ego+ examples h indicat$1 _! ,au/ralian neighb\rs 7 b little bett] (f4 ,9 "o or two in/ances we d f9d ,au/ralian num]al scales :i* rea* #aj1 & p]haps we may safely say #bj4 ,"o ( ^! is giv5 9 full 9 a subsequ5t *apt]1 & its /ructure gives rise to ! suspicion t x 0 orig9ally z limit$ z ^? ( k9dr$ tribes1 & t x und]w5t a consid]able developm5t aft] ! natives _h come 9 contact ) ! ,europeans4 ,!re is good reason to believe t no ,au/ralian 9 8 wild /ate c\ld ev] c\nt intellig5tly to #g4dj ,9 c]ta9 portions ( ,asia1 ,africa1 ,melanesia1 ,polynesia1 & ,nor? ,am]ica1 are to be f\nd races ^: numb] sy/ems are almo/ & sometimes q z limit$ z are ^? ( ! ,s\?4 ,am]ican & ,au/ralian tribes already cit$1 b n[h]e else d we f9d ^! s abundant z 9 ! two cont95ts j m5tion$1 :]e example aft] example might be cit$ ( tribes ^: ability to c\nt is circumscrib$ )9 ! n>r[e/ limits4 ,! ,v$das#da ( ,ceylon h b two num]als1 ekkamei1 #a1 dekkame1 #b4 ,beyond ?is !y c\nt otameeka1 otameeka1 otameeka1 etc42 i4e4 & "o m1 & "o m1 & "o m1 & s on indef9itely4 ,! ,&amans1#db inhabitants ( a gr\p ( isl&s 9 ! ,bay ( ,b5gal1 are equally limit$ 9 _! p[] ( c\nt+4 ,!y h ubatulda1 #a1 & ikporda1 #b2 b !y c g no fur!r1 except 9 a mann] simil> to t ( ! ,v$das4 ,above two !y proce$ :olly by means ( ! f+]s1 say+ z !y tap ! nose ) ea* successive f+]1 anka1 & ?is4 ,only ! m intellig5t ( ! ,&amans c c\nt at all1 _m ( !m seem+ to be z ne>ly de/itute ( ! numb] s5se z x is possible = a human be+ to be4 ,! ,bu%m5#dc ( ,s\? ,africa h b two num]als1 ! pronunciation ( :i* c h>dly be indicat$ )\t o!r res\rces ?an ^? ( ! ,engli% alphabet4 ,_! ^w = #c means1 simply1 _m1 z 9 ! case ( "s ( ! ,au/ralian tribes4 ,! ,wat*&ies#dd h b two simple num]als1 & _! entire numb] sy/em is cooteon1 #a1 utaura1 #b1 ut>ra cooteoo1 #c1 at>ra ut>ra1 #d4 ,beyond ?is !y c only say1 bool?a1 _m1 & bool?a bat1 v _m4 ,al?\gh !y h ! expressions "h giv5 = #c & #d1 !y are reluctant to use !m1 & only d s :5 absolutely requir$4 ,! natives ( ,l[] ,cali=nia#de _c c\nt above #e4 ,a few ( ! m intellig5t among !m und]/& ! mean+ ( #b fives1 b ?is numb] seems entirely beyond ! compreh5sion ( ! ord9>y native4 ,! ,coman*es1 curi\sly en\gh1 are s reluctant to employ _! numb] words t !y appe> to pref] f+] pantomime in/ead1 ?us giv+ rise to ! impression :i* at "o "t became curr5t1 t !y _h no num]als at all = ord9>y c\nt+4 ,aside f ! specific examples already giv51 a consid]able numb] ( sweep+ g5]alizations may be made1 t5d+ to %[ h[ rudim5t>y ! numb] s5se may be 9 aborig9al life4 ,scores ( ! native dialects ( ,au/ralia & ,s\? ,am]ica h be5 f\nd conta9+ numb] sy/ems b little m ext5sive ?an ^? allud$ to above4 ,! negro tribes ( ,africa give ! same te/imony1 z d _m ( ! native races ( ,c5tral ,am]ica1 ,mexico1 & ! ,pacific coa/ ( ! ,unit$ ,/ates & ,canada1 ! nor!rn "p ( ,sib]ia1 ,gre5l&1 ,labrador1 & ! arctic ar*ipelago4 ,9 speak+ ( ! ,eskimos ( ,po9t ,b>r[1 ,murdo*#df says3 ,x 0 n easy to obta9 any accurate in=mation ab\t ! num]al sy/em ( ^! p1 s9ce 9 ord9>y conv]sation !y are n 9 ! habit ( specify+ any numb]s above five4 ,c\nt+ is (t5 c>ri$ high] ?an ?is among c]ta9 ( ^! nor!rn tribes1 b1 save = occasional examples1 x is limit$ at be/4 ,dr4 ,franz ,boas1 :o has travell$ ext5sively among ! ,eskimos1 & ^: obs]vations are always ( ! mo/ accurate nature1 once told ! au?or t he nev] met an ,eskimo :o c\ld c\nt above #ae4 ,_! num]als actually d ext5d mu* high]2 & a /ray num]al ( ,dani% orig9 is n[ & !n met )1 %[+ t ! m intellig5t among !m are able to compreh5d numb]s ( mu* great] magnitude ?an ?is4 ,b z ,dr4 ,boas 0 engag$ 9 active "w among !m = ?ree ye>s1 we may conclude t ! ,eskimo has an ari?metic b little m ext5d$ ?an t :i* suffic$ = ! ,au/ralians & ! =e/ tribes ( ,brazil4 ,e>ly ,russian explor]s among ! nor!rn tribes ( ,sib]ia notic$ ! same difficulty 9 ord9>y1 e-day reckon+ among ! natives4 ,at fir/ ?\ght we might1 !n1 /ate x z a g5]al law t ^? races :i* are l[e/ 9 ! scale ( civilization1 h ! feeble/ numb] s5se also2 or 9 o!r words1 ! lea/ possible p[] ( grasp+ ! ab/ract idea ( numb]4 ,b to ?is law !re are _m & important exceptions4 ,! concurr5t te/imony ( explor]s seems to be t savage races possess1 9 ! great majority ( cases1 ! ability to c\nt at lea/ z high z #aj4 ,?is limit is (t5 ext5d$ to #bj1 & n infrequ5tly to #ajj4 ,aga91 we f9d #ajjj z ! limit2 or p]haps #aj1jjj2 & sometimes ! savage c>ries 8 numb] sy/em on into ! hundr$s ( ?\s&s or millions4 ,inde$1 ! high limit to :i* "s savage races c>ry _! num]ation is f> m wor?y ( rem>k ?an ! entire abs5ce ( ! numb] s5se exhibit$ by o!rs ( app>5tly equal intellig5ce4 ,if ! life ( any tribe is su* z to induce trade & b>t] ) _! neighb\rs1 a consid]able quickness 9 reckon+ w be develop$ among !m4 ,o!rwise ?is p[] w rema9 dormant because !re is b little 9 ! ord9>y life ( primitive man to call = its ex]cise4 ,9 giv+ #a1 #b1 #c1 #e1 #aj1 or any o!r small numb] z a sy/em limit1 x mu/ n be ov]look$ t ?is limit m5tion$ is 9 all cases ! limit ( ! spok5 num]als at ! savage's comm&4 ,! actual ability to c\nt is almo/ always1 & "o is tempt$ to say always1 some:at great] ?an _! vocabul>ies w\ld indicate4 ,! ,bu%man has no numb] ^w t w express = him any?+ high] ?an #b2 b ) ! assi/ance ( 8 f+]s he gropes 8 way on z f> z #aj4 ,! ,v$das1 ! ,&amans1 ! ,gua*i1 ! ,botocudos1 ! ,eskimos1 & ! ?\s& & "o o!r tribes :i* furni% su* scanty num]al sy/ems1 almo/ all proce$ ) m or less read9ess z f> z _! f+]s w c>ry !m4 ,z a matt] ( fact1 ?is limit is frequ5tly ext5d$ to #bj2 ! toes1 ! f+]s ( a second man1 or a rec\nt ( ! savage's own f+]s1 s]v+ z a tale = ! second #aj4 ,allusion is aga9 made to ?is 9 a lat] *apt]1 :]e ! subject ( c\nt+ on ! f+]s & toes is exam9$ m 9 detail4 ,9 say+ t a savage c c\nt to #aj1 to #bj1 or to #ajj1 b little idea is giv5 ( 8 real m5tal conception ( any except ! smalle/ numb]s4 ,want ( famili>ity ) ! use ( numb]s1 & lack ( conv5i5t means ( comp>ison1 mu/ result 9 extreme indef9it5ess ( m5tal conception & almo/ entire abs5ce ( exactness4 ,! exp]i5ce ( ,capta9 ,p>ry1#dg :o f\nd t ! ,eskimos made mi/akes be=e !y rea*$ #g1 & ( ,humboldt1#dh :o says t a ,*ayma might be made to say t 8 age 0 ei!r #ah or #fj1 has be5 duplicat$ by all inve/igators :o h _h actual exp]i5ce among savage races4 ,nor1 on ! o!r h&1 is ! developm5t ( a num]al sy/em an infallible index ( m5tal p[]1 or ( any real approa* t[>d civilization4 ,a cont9u$ use ( ! trad+ & b>ga9+ faculties mu/ & does result 9 a famili>ity ) numb]s suffici5t to enable savages to p]=m unexpect$ feats 9 reckon+4 ,among "s ( ! ,we/ ,african tribes ?is has actually be5 f\nd to be ! case2 & among ! ,yorubas ( ,abeokuta#di ! extraord9>y say+1 ,y may seem v clev]1 b y c't tell n9e times n9e1 %[s h[ surpris+ly ?is faculty has be5 develop$1 consid]+ ! g5]al condition ( savag]y 9 :i* ! tribe liv$4 ,!re c be no d\bt t1 9 g5]al1 ! gr[? ( ! numb] s5se keeps pace ) ! gr[? ( ! intellig5ce 9 o!r respects4 ,b :5 x is rememb]$ t ! ,tonga ,isl&]s h num]als up to #ajj1jjj1 & ! ,tembus1 ! ,f+oes1 ! ,pondos1 & a doz5 o!r ,s\? ,african tribes g z high z #a1jjj1jjj2 & t ,leigh ,hunt nev] c\ld le>n ! multiplication table1 "o mu/ confess t ?is law occasionally pres5ts to our consid]ation rem>kable exceptions4 ,:ile consid]+ ! ext5t ( ! savage's ari?metical k1 ( 8 ability to c\nt & to grasp ! mean+ ( numb]1 x may n be amiss to ask ourselves ! "q1 :at is ! ext5t ( ! developm5t ( our own numb] s5se8 ,to :at limit c we absorb ! idea ( numb]1 ) a complete appreciation ( ! idea ( ! numb] ( units involv$ 9 any writt5 or spok5 quantity8 ,our p]fect sy/em ( num]ation enables u to express )\t difficulty any desir$ numb]1 no matt] h[ great or h[ small x be4 ,b h[ mu* ( actually cle> compreh5sion does ! numb] ?us express$ convey to ! m9d8 ,we say t "o place is #ajj miles f ano!r2 t ,a paid ,b #ajjj doll>s = a c]ta9 piece ( prop]ty2 t a giv5 city conta9s #aj1jjj inhabitants2 t #ajj1jjj bu%els ( :eat 7 %ipp$ f ,dulu? or ,odessa on su* a day2 t #a1jjj1jjj feet ( lumb] 7 de/roy$ by ! fire ( ye/]day1--& z we pass f ! smalle/ to ! l>ge/ ( ! numb]s ?us in/anc$1 & f ! l>ge/ on to ^? /ill l>g]1 we repeat ! "q j ask$2 & we repeat x ) a new s5se ( our own m5tal limitation4 ,! numb] #ajj unque/ionably /&s = a di/9ct conception4 ,p]haps ! same may be said = #ajjj1 ?\gh ?is c\ld n be po/ulat$ ) equal c]ta9ty4 ,b :at ( #aj1jjj8 ,if t numb] ( p]sons 7 ga!r$ toge!r into a s+le hall or amphi!atre1 c\ld an e/imate be made by ! av]age onlook] :i* w\ld approximate ) any degree ( accuracy ! size ( ! assembly8 ,or if an obs]v] 7 /ation$ at a c]ta9 po9t1 & #aj1jjj p]sons 7 to pass him 9 s+le file )\t 8 c\nt+ !m z !y pass$1 :at sort ( an e/imate w\ld he make ( _! numb]8 ,! tru? seems to be t our m5tal conception ( numb] is mu* m limit$ ?an is commonly ?\ght1 & t we unconsci\sly adopt "s new unit z a /&>d ( comp>ison :5 we wi% to r5d] intelligible to our m9ds any numb] ( consid]able magnitude4 ,= example1 we say t ,a has a =tune ( #a1jjj1jjj4 ,! impression is at once convey$ ( a consid]able degree ( weal?1 b x is r f ! fact t t =tune repres5ts an annual income ( #dj1jjj ?an1 f ! actual magnitude ( ! =tune itself4 ,! numb] #a1jjj1jjj is1 9 itself1 s greatly 9 excess ( any?+ t ent]s into our daily exp]i5ce t we h b a vague conception ( x1 except z some?+ v great4 ,we are n1 aft] all1 s v mu* bett] (f ?an ! *ild :o1 ) 8 arms ab\t 8 "m's neck1 in=ms h] ) p]fect gravity & s9c]ity t he loves h] a million bu%els4 ,8 idea is m]ely ( "s v great am\nt1 & our own is (t5 b little cle>] :5 we use ! expressions :i* are s easily repres5t$ by a few digits4 ,among ! un$ucat$ portions ( civiliz$ communities ! limit ( cle> compreh5sion ( numb] is n only relatively1 b absolutely1 v l[4 ,travell]s 9 ,russia h in=m$ ! writ] t ! peasants ( t c\ntry h no di/9ct idea ( a numb] consi/+ ( b a few hundr$ ev54 ,!re is no reason to d\bt ?is te/imony4 ,! entire life ( a peasant might be pass$ )\t 8 ev] hav+ occasion to use a numb] z great z #ejj1 & z a result he might h respect+ t numb] an idea less di/9ct ?an a tra9$ ma!matician w\ld h ( ! di/ance f ! e>? to ! sun4 ,de ,qu9cey#ej incid5tally m5tions ?is *>act]i/ic 9 n>rat+ a conv]sation :i* occurr$ :ile he 0 at ,c>n>von1 a little t[n 9 ,wales4 ,x 0 on ?is occasion1 he says1 t ,i le>n$ h[ vague are ! ideas ( numb] 9 unpractis$ m9ds4 ',:at numb] ( p d y ?9k1' ,i said to an eld]ly p]son1 'w be assembl$ ?is day at ,c>n>von8' ',:at numb]8' rejo9$ ! p]son address$2 ':at numb]8 ,well1 really1 n[1 ,i %\ld reckon--p]haps a matt] ( f\r million4' ,f\r millions ( extra p 9 little ,c>n>von1 t c\ld b>ely f9d accommodation 7,i %\ld calculate7 = an extra f\r hundr$6 ,s ! ,eskimo & ! ,s\? ,am]ican ,indian are1 aft] all1 n s v f> beh9d ! eld]ly p]son ( ,c>n>von1 9 ! di/9ct p]ception ( a numb] :i* famili>ity r5d]s to u absurdly small4 ,,*apt] ,,iii4 ,,! ,,orig9 ,,( ,,numb] ,,words4 ,9 ! comp>ison ( languages & ! se>* = primitive root =ms1 no class ( expressions has be5 subject$ to clos] scrut9y ?an ! little clu/] ( words1 f\nd 9 ea* language1 :i* con/itutes a "p ( ! daily vocabul>y ( almo/ e human be+--! words ) :i* we beg9 our c\nt+4 ,x is assum$1 & ) good reason1 t ^! are among ! e>li] words to appe> 9 any language2 & 9 ! mutations ( human spee*1 !y are f\nd to suff] less ?an almo/ any o!r portion ( a language4 ,k9%ip betwe5 tongues remote f ea* o!r has 9 _m in/ances be5 detect$ by ! simil>ity f\nd to exi/ among ! e-day words ( ea*2 & among ^! words "o may look ) a good degree ( c]ta9ty = ! #a1 #b1 #c1 etc41 ( ! numb] scale4 ,s fruitful has be5 ?is l9e ( rese>*1 t ! attempt has be5 made1 ev51 to e/abli% a common orig9 = all ! races ( mank9d by means ( a comp>ison ( num]al words4#ea ,b 9 ?is in/ance1 z 9 s _m o!rs t w readily occur to ! m9d1 ! result has be5 t ! !ory has f9ally tak5 possession ( ! au?or & r$uc$ him to complete subjugation1 in/ead ( rema9+ 8 s]vant & submitt+ to ! legitimate results ( pati5t & c>eful inve/igation4 ,l+ui/ic rese>* is s full ( sn>es & pitfalls t ! /ud5t mu/ ne$s employ ! greate/ degree ( discrim9ation be=e ass]t+ k9%ip ( race because ( resemblances 9 vocabul>y2 or ev5 relation%ip betwe5 words 9 ! same language because ( "s *ance lik5ess ( =m t may exi/ betwe5 !m4 ,probably no "o w\ld argue t ! ,engli% & ! ,babusess ( ,c5tral ,africa 7 ( ! same primitive /ock simply because 9 ! language ( ! latt] five atano means #e1 & t5 kumi means #aj4eb ,b1 on ! o!r h&1 _m w argue t1 because ! ,g]man zehn means #aj1 & zeh5 means toes1 ! ance/ors ( ! ,g]mans c\nt$ on _! toes2 & t ) !m1 #aj 0 ! complete c\nt ( ! toes4 ,x may be s4 ,we c]ta9ly h no evid5ce ) :i* to disprove ?is2 b1 be=e accept+ x z a fact1 or ev5 z a reasonable hypo!sis1 we may be p>don$ = dem&+ "s evid5ce aside f ! m]e resemblance 9 ! =m ( ! words4 ,if1 9 ! /udy ( num]al words1 =m is to con/itute our *ief guide1 we mu/ expect n[ & !n to be confront$ ) facts :i* are n easily reconcil$ ) any pet !ory4 ,! scope ( ! pres5t "w w admit ( no m ?an a ha/y exam9ation ( num]al =ms1 9 :i* only actual & well asc]ta9$ mean+s w be consid]$4 ,b "h we are at ! outset confront$ ) a class ( words ^: orig9al mean+s appe> to be entirely lo/4 ,!y are :at may be t]m$ ! num]als prop]--! native1 uncomp\nd$ words us$ to signify numb]4 ,su* words are ! "o1 two1 ?ree1 etc41 ( ,engli%2 ! e9s1 zwei1 drei1 etc41 ( ,g]man2 words :i* mu/ at "s "t1 9 "s prehi/oric language1 h _h def9ite mean+s entirely ap>t f ^? :i* !y n[ convey to our m9ds4 ,9 savage languages x is sometimes possible to detect ^! mean+s1 & ?us to obta9 possession ( ! clue t leads to ! developm5t1 9 ! b>b>ian's rude m9d1 ( a c\nt scale--a numb] sy/em4 ,b 9 languages l ^? ( mod]n ,europe1 ! p$igree claim$ by num]als is s long t1 9 ! successive *anges ?r\gh :i* !y h pass$1 all trace ( _! orig9 seems to h be5 lo/4 ,! actual numb] ( su* words is1 h[ev]1 surpris+ly small 9 any language4 ,9 ,engli% we c\nt by simple words only to #aj4 ,f ?is po9t onw>d all our num]als except hundr$ & ?\s& are comp\nds & comb9ations ( ! names ( small] numb]s4 ,! words we employ to designate ! high] ord]s ( units1 z million1 billion1 trillion1 etc41 are appropriat$ bodily f ! ,italian2 & ! native words pair1 tale1 brace1 doz51 gross1 & score1 c h>dly be class$ z num]als 9 ! /rict s5se ( ! ^w4 ,g]man possesses exactly ! same numb] ( native words 9 its num]al scale z ,engli%2 & ! same may be said ( ! ,teutonic languages g5]ally1 z well z ( ! ,celtic1 ! ,lat91 ! ,slavonic1 & ! ,basque4 ,?is is1 9 fact1 ! univ]sal me?od obs]v$ 9 ! =mation ( any num]al scale1 ?\gh ! actual numb] ( simple words may v>y4 ,! ,*iquito language has b "o num]al ( any k9d :atev]2 ,engli% conta9s twelve simple t]ms2 ,sanskrit has tw5ty-sev51 :ile ,japanese possesses tw5ty-f\r1 & ! ,*9ese a numb] almo/ equally great4 ,v _m languages1 z might be expect$1 conta9 special num]al expressions1 su* z ! ,g]man dutz5d & ! ,fr5* diza9e2 b ^!1 l ! ,engli% doz5 & score1 are n to be reg>d$ z num]als prop]4 ,! =mation ( num]al words %[s at a glance ! g5]al me?od 9 :i* any numb] scale has be5 built up4 ,! primitive savage c\nts on 8 f+]s until he has rea*$ ! end ( "o1 or m probably ( bo?1 h&s4 ,!n1 if he wi%es to proce$ f>!r1 "s m>k is made1 a pebble is laid aside1 a knot ti$1 or "s simil> device employ$ to signify t all ! c\nt]s at 8 disposal h be5 us$4 ,!n ! c\nt beg9s anew1 & to avoid multiplication ( words1 z well z to assi/ ! memory1 ! t]ms already us$ are aga9 resort$ to2 & ! "n by :i* ! fir/ halt+-place 0 designat$ is repeat$ ) ea* new num]al4 ,h5ce ! ?irte51 f\rte51 fifte51 etc41 :i* are contractions ( ! full] expressions ?ree-&-t51 f\r-&-t51 five-&-t51 etc4 ,! specific me?od ( comb9ation may n always be ! same1 z witness ! eighte51 or eight-t51 9 ,engli%1 & dix-huit1 or t5-eight1 9 ,fr5*2 =ty-five1 or f\r-t5s-five1 9 ,engli%1 & fnf und vi]zig1 or five & f\r t5s 9 ,g]man4 ,b ! g5]al me?od is ! same ! _w ov]1 pres5t+ u ) no?+ b local v>iations1 :i* are1 relatively speak+1 entirely unimportant4 ,) ?is fact 9 m9d1 we c cease to wond] at ! small numb] ( simple num]als 9 any language4 ,x might1 inde$1 be qu]i$1 :y d any languages1 ,engli% & ,g]man1 = example1 h unusual comp\nds = #aa & #ab8 ,x w\ld seem z ?\gh ! regul> me?od ( comp\nd+ %\ld beg9 ) #aj & #a1 in/ead ( #aj & #c1 9 any language us+ a sy/em ) #aj z a base4 ,an exam9ation ( sev]al hundr$ num]al scales %[s t ! ,teutonic languages are some:at exceptional 9 ?is respect4 ,! words elev5 & twelve are und\bt$ly comb9ations1 b n 9 ! same direct s5se z ?irte51 tw5ty-five1 etc4 ,! same may be said ( ! ,fr5* onze1 d\ze1 treize1 quatorze1 qu9ze1 & seize1 :i* are obvi\s comp\nds1 b n =m$ 9 ! same mann] z ! num]als above t po9t4 ,almo/ all civiliz$ languages1 h[ev]1 except ! ,teutonic1 & practically all unciviliz$ languages1 beg9 _! direct num]al comb9ations z soon z !y h pass$ _! numb] base1 :atev] t may be4 ,to give an illu/ration1 select$ q at r&om f among ! b>b>\s tribes ( ,africa1 ! ,ki-,swahili num]al scale runs z foll[s3#ec #a4 moyyi1 #b4 mbiri1 #c4 tato1 #d4 ena1 #e4 tano1 #f4 seta1 #g4 saba1 #h4 nani1 #i4 k5da1 #aj4 kumi1 #aa4 kumi na moyyi1 #ab4 kumi na mbiri1 #ac4 kumi na tato1 etc4 ,! words = #aa1 #ab1 & #ac1 are se5 at a glance to signify t5-&-"o1 t5-&-two1 t5-&-?ree1 & ! c\nt proce$s1 z might be inf]r$1 9 a simil> mann] z f> z ! numb] sy/em ext5ds4 ,our ,engli% comb9ations are a little clos] ?an ^!1 & ! comb9ations f\nd 9 c]ta9 o!r languages are1 9 turn1 clos] ?an ^? ( ! ,engli%2 z witness ! once1 #aa1 doce1 #ab1 trece1 #ac1 etc41 ( ,spani%4 ,b ! process is ess5tially ! same1 & ! law may be accept$ z practically inv>iable1 t all num]als great] ?an ! base ( a sy/em are express$ by comp\nd words1 except su* z are necess>y to e/abli% "s new ord] ( unit1 z hundr$ or ?\s&4 ,9 ! scale j giv51 x w be notic$ t ! l>g] numb] prec$es ! small]1 giv+ #aj #a1 #aj #b1 etc41 in/ead ( #a #aj1 #b #aj1 etc4 ,?is seems entirely natural1 & h>dly calls = any comm5t :atev]4 ,b we h only to consid] ! =mation ( our ,engli% te5s to see t our own me?od is1 at its inception1 j ! rev]se ( ?is4 ,?irte51 #ad1 & ! rema9+ num]als up to #ai are =m$ by prefix+ ! small] numb] to ! base2 & x is only :5 we pass #bj t we return to ! m direct & obvi\s me?od ( giv+ prec$5ce to ! l>g]4 ,9 ,g]man & o!r ,teutonic languages ! inv]se me?od is cont9u$ /ill fur!r4 ,"h #be is fnf und zwanzig1 #e & #bj2 #ib is zwei und neunzig1 #b & #ij1 & s on to #ii4 ,above #ajj ! ord] is made direct1 z 9 ,engli%4 ,( c\rse1 ?is mode ( =mation betwe5 #bj & #ajj is p]missible 9 ,engli%1 :]e five & tw5ty is j z correct a =m z tw5ty-five4 ,b x is ar*aic1 & w\ld soon pass out ( ! language altoge!r1 7 x n = ! influ5ce ( "s ( ! old] writ+s :i* h _h a /rong influ5ce 9 pres]v+ = u _m ( old] & m ess5tially ,saxon =ms ( expression4 ,bo? ! me?ods describ$ above are f\nd 9 all p>ts ( ! _w1 b :at ,i h call$ ! direct is f> m common ?an ! o!r4 ,9 g5]al1 :]e ! small] numb] prec$es ! l>g] x signifies multiplication in/ead ( addition4 ,?us1 :5 we say ?irty1 i4e4 ?ree-t51 we mean #c #aj2 j z ?ree hundr$ means #c #ajj4 ,:5 ! l>g] prec$es ! small]1 we mu/ usually und]/& addition4 ,b to bo? ^! rules !re are v _m exceptions4 ,among high] numb]s ! inv]se ord] is v r>ely us$2 ?\gh ev5 "h an occasional exception is f\nd4 ,! ,ta5sa ,indians1 = example1 place ! small] numb]s be=e ! l>g]1 no matt] h[ f> _! scale may ext5d4 ,to say #ahha !y make a complete inv]sion ( our own ord]1 beg9n+ ) #a & end+ ) #ajjj4 ,_! full num]al = ?is is yeha av wabki m>-u-wab m>-u-haki1 :i* means1 lit]ally1 #a #hj #ajj #h #ajj #aj4ed ,su* exceptions are1 h[ev]1 q r>e4 ,"o o!r me?od ( comb9ation1 t ( subtraction1 rema9s to be consid]$4 ,e /ud5t ( ,lat9 w recall at once ! duodevig9ti1 #b f #bj1 & undevig9ti1 #a f #bj1 :i* 9 t language are ! regul> =ms ( expression = #ah & #ai4 ,at fir/ !y seem decid$ly odd2 b famili>ity soon accu/oms "o to !m1 & !y cease entirely to attract any special att5tion4 ,?is pr9ciple ( subtraction1 :i*1 9 ! =mation ( num]al words1 is q =eign to ! g5ius ( ,engli%1 is /ill ( su* common occurr5ce 9 o!r languages t ! ,lat9 examples j giv5 cease to be solit>y in/ances4 ,! orig9 ( num]als ( ?is class is to be f\nd 9 ! idea ( ref]5ce1 n necess>ily to ! la/1 b to ! ne>e/1 halt+-po9t 9 ! scale4 ,_m tribes seem to reg>d #i z almo/ #aj1 & to give x a "n :i* conveys ?is ?\ght4 ,9 ! ,mississaga1 "o ( ! num]\s ,algonqu9 languages1 we h1 = example1 ! ^w cangaswi1 incomplete #aj1 = #i4ee ,9 ! ,kwakiutl ( ,briti% ,columbia1 #h z well z #i is =m$ 9 ?is way2 ^! two numb]s be+ matlguanatl1 #aj - #b1 & nanema1 #aj - #a1 respectively4#ef ,9 _m ( ! languages ( ,briti% ,columbia we f9d a simil> =mation = #h & #i1 or = #i alone4 ,! same =mation occurs 9 ,malay1 result+ 9 ! num]als delapan1 #aj - #b1 & sambilan #aj - #a4eg ,9 ,gre5 ,isl&1 "o ( ! ,new ,irel& gr\p1 ^! become simply &ra-lua1 less #b1 & &ra-si1 less #a4eh ,9 ! ,admiralty ,isl&s ?is =mation is c>ri$ back "o /ep fur!r1 & n only gives u %ua-luea1 less #b1 & %u-ri1 less #a1 b also makes #g appe> z sua-tolu1 less #c4ei ,surpris+ z ?is num]al is1 x is m ?an mat*$ by ! ,a9u scale1 :i* c>ries subtraction back /ill ano!r /ep1 & calls #f1 #aj - #d4 ,! f\r num]als f #f to #i 9 ?is scale are respectively1 iwa1 #aj - #d1 arawa1 #aj - #c1 tupe-san1 #aj - #b1 & s9epe-san1 #aj - #a4fj ,num]\s examples ( ?is k9d ( =mation w be f\nd 9 lat] *apt]s ( ?is "w2 b !y w usually be f\nd to occur 9 "o or bo? ( ! num]als1 #h & #i4 ,occasionally !y appe> among ! high] numb]s2 z 9 ! ,maya languages1 :]e1 = example1 #ii ye>s is "o s+le ye> lack+ f five score ye>s1#fa & 9 ! ,arik>a dialects1 :]e #ih & #ii are #e m5 m9us & #e m5 #a n4#fb ,! ,wel%1 ,dani%1 & o!r languages less easily accessible ?an ^! to ! g5]al /ud5t1 also furni% int]e/+ examples ( a simil> "*4 ,m r>ely yet are in/ances met ) ( languages :i* make use ( subtraction almo/ z freely z addition1 9 ! composition ( num]als4 ,)9 ! pa/ few ye>s su* an in/ance has be5 notic$ 9 ! case ( ! ,bellacoola language ( ,briti% ,columbia4 ,9 _! num]al scale #ae1 "o foot1 is foll[$ by #af1 "o man less #d2 #ag1 "o man less #c2 #ah1 "o man less #b2 #ai1 "o man less #a2 & #bj1 "o man4 ,tw5ty-five is "o man & "o h&2 #bf1 "o man & two h&s less #d2 #cf1 two m5 less #d2 & s on4 ,?is me?od ( =mation prevails ?r\gh\t ! entire num]al scale4#fc ,"o ( ! be/ kn[n & mo/ int]e/+ examples ( subtraction z a well-def9$ pr9ciple ( =mation is f\nd 9 ! ,maya scale4 ,up to #dj no special peculi>ity appe>s2 b z ! c\nt progresses beyond t po9t we f9d a succession ( num]als :i* "o is almo/ tempt$ to call #fj - #ai1 #fj - #ah1 #fj - #ag1 etc4 ,lit]ally translat$ ! mean+s seem to be #a to #fj1 #b to #fj1 #c to #fj1 etc4 ,! po9t ( ref]5ce is #fj1 & ! ?\ght und]ly+ ! words may probably be express$ by ! p>aphrases1 #a on ! ?ird score1 #b on ! ?ird score1 #c on ! ?ird score1 etc4 ,simil>ly1 #fa is #a on ! f\r? score1 #ha is "o on ! fif? score1 #cha is #a on ! n9ete5? score1 & s on to #djj4 ,at #dda ! same =mation reappe>s2 & x cont9ues to *>act]ize ! sy/em 9 a regul> & consi/5t mann]1 no matt] h[ f> x is ext5d$4#fd ,! ,yoruba language ( ,africa is ano!r example ( mo/ lavi% use ( subtraction2 b x "h results 9 a sy/em mu* less consi/5t & natural ?an t j consid]$4 ,"h we f9d n only #e1 #aj1 & #bj subtract$ f ! next high] unit1 b also #dj1 & ev5 #ajj4 ,= example1 #cfj is #djj - #dj2 #dfj is #ejj - #dj2 #ejj is #fjj - #ajj2 #acjj is #adjj - #ajj1 etc4 ,"o ( ! ,yoruba units is #bjj2 & all ! odd hundr$s up to #bjjj1 ! next high] unit1 are =m$ by subtract+ #ajj f ! next high] multiple ( #bjj4 ,! sy/em is q complex1 & v artificial2 & seems to h be5 develop$ by int]c\rse ) trad]s4#fe ,x has already be5 /at$ t ! primitive mean+s ( our own simple num]als h be5 lo/4 ,?is is also true ( ! languages ( ne>ly all o!r civiliz$ peoples1 & ( num]\s savage races z well4 ,we are at lib]ty to suppose1 & we d suppose1 t 9 v _m cases ^! words once express$ mean+s closely connect$ ) ! names ( ! f+]s1 or ) ! f+]s !mselves1 or bo?4 ,n[ & !n a case is met ) 9 :i* ! num]al ^w frankly av[s its mean+--z 9 ! ,botocudo language1 :]e #a is express$ by podzik1 f+]1 & #b by kripo1 d\ble f+]2#ff & 9 ! ,eskimo dialect ( ,hudson's ,bay1 :]e e]kitkoka means bo? #aj & little f+]4#fg ,su* cases are1 h[ev]1 some:at exceptional4 ,9 a few notewor?y in/ances1 ! words compos+ ! num]al scale ( a language h be5 c>efully inve/igat$ & _! orig9al mean+s accurately det]m9$4 ,! simple /ructure ( _m ( ! rude languages ( ! _w %\ld r5d] ?is possible 9 a multitude ( cases2 b inve/igators are too (t5 cont5t ) ! m]e num]als !mselves1 & make no inquiry respect+ _! mean+s4 ,b ! foll[+ exposition ( ! ,zui scale1 giv5 by ,lieut5ant ,gu%+#fh leaves no?+ to be desir$3 #a4 tp9te tak5 to />t )4 #b4 kwilli put d[n toge!r )4 #c4 ha'i ! equally divid+ f+]4 #d4 awite all ! f+]s all b done )4 #e4 pte ! not*$ (f4 ,?is f9i%es ! li/ ( orig9al simple num]als1 ! ,zui /opp+1 or not*+ (f1 :5 he f9i%es ! f+]s ( "o h&4 ,comp\nd+ n[ beg9s4 #f4 topalk'ya ano!r br\ght to add to ! done )4 #g4 kwillilk'ya two br\ght to & held up ) ! re/4 #h4 hailk'ye ?ree br\ght to & held up ) ! re/4 #i4 t5alk'ya all b all are held up ) ! re/4 #aj4 /em'?ila all ! f+]s4 #aa4 /em'?la topay'?l'tona all ! f+]s & ano!r ov] above held4 ,! process ( =mation indicat$ 9 #aa is us$ 9 ! succe$+ num]als up to #ai4 #bj4 kwillik'yn/em'?lan two times all ! f+]s4 #ajj4 ssi/em'?lak'ya ! f+]s all ! f+]s4 #ajjj4 ssi/em'?lanak'yn/em'?la ! f+]s all ! f+]s times all ! f+]s4 ,! only num]als call+ = any special note are ^? = #aa & #i4 ,= #i we %\ld naturally expect a ^w correspond+ 9 /ructure & mean+ to ! words = #g & #h4 ,b in/ead ( ! f\r br\ght to & held up ) ! re/1 = :i* we naturally look1 ! ,zui1 to %[ t he has us$ all ( 8 f+]s b "o1 says all b all are held up ) ! re/4 ,to express #aa he _c use a simil> =m ( composition1 s9ce he has already us$ x 9 con/ruct+ 8 ^w = #f1 s he says all ! f+]s & ano!r ov] above held4 ,! "o rem>kable po9t to be not$ ab\t ! ,zui scale is1 aft] all1 ! =mation ( ! words = #a & #b4 ,:ile ! savage almo/ always c\nts on 8 f+]s1 x does n seem at all c]ta9 t ^! words w\ld necess>ily be ( f+] =mation4 ,! savage c always di/+ui% betwe5 "o object & two objects1 & x is h>dly reasonable to believe t any ext]nal aid is ne$$ to arrive at a di/9ct p]ception ( ?is diff]5ce4 ,! num]als = #a & #b w\ld be ! e>lie/ to be =m$ 9 any language1 & 9 mo/1 if n all1 cases !y w\ld be =m$ long be=e ! ne$ w\ld be felt = t]ms to describe any high] numb]4 ,if ?is !ory be correct1 we %\ld expect to f9d f+] names = num]als beg9n+ n l[] ?an #c1 & (t5] ) #e ?an ) any o!r numb]4 ,! highe/ au?ority has v5tur$ ! ass]tion t all num]al words h _! orig9 9 ! names ( ! f+]s2#fi sub/antially ! same conclusion 0 rea*$ by ,pr(essor ,pott1 ( ,halle1 ^: "w on num]al nom5clature l$ him deeply into ! /udy ( ! orig9 ( ^! words4 ,b we h abundant evid5ce at h& to %[ t1 univ]sal z f+] c\nt+ has be51 f+] orig9 = num]al words has by no means be5 univ]sal4 ,t x is m frequ5tly met ) ?an any o!r orig9 is unque/ionably true2 b 9 _m in/ances1 :i* w be m fully consid]$ 9 ! foll[+ *apt]1 we f9d /rictly non-digital d]ivations1 especially 9 ! case ( ! l[e/ memb]s ( ! scale4 ,b 9 ne>ly all languages ! orig9 ( ! words = #a1 #b1 #c1 & #d are s entirely unkn[n t speculation respect+ !m is almo/ useless4 ,an excell5t illu/ration ( ! ord9>y me?od ( =mation :i* obta9s among numb] scales is furni%$ by ! ,eskimos ( ,po9t ,b>r[1#gj :o h pure num]al words up to #e1 & !n beg9 a sy/ematic c\rse ( ^w =mation f ! names ( _! f+]s4 ,if ! names ( ! fir/ five num]als are ( f+] orig91 !y h s completely lo/ _! orig9al =m1 or else ! names ( ! f+]s !mselves h s *ang$1 t no resemblance is n[ to be detect$ betwe5 !m4 ,?is scale is s int]e/+ t x is giv5 ) consid]able fulness1 z foll[s3 #a4 atauzik4 #b4 madro4 #c4 p9asun4 #d4 sisaman4 #e4 tudlemut4 #f4 atautyim9 akb9ig9 tudlimu7t7 #e & #a on ! next4 #g4 madron9 akb9ig9 twice on ! next4 #h4 p9asun9 akb9ig9 ?ree times on ! next4 #i4 kodl9otaila t :i* has n its #aj4 #aj4 kodl9 ! upp] "p--i4e4 ! f+]s4 #ad4 akimiaxotaityuna ,i h n #ae4 #ae4 akimia4 ,?is seems to be a real num]al ^w4 #bj4 inyu9a a man come to an end4 #be4 inyu9a tudlimun9 akb9idig9 a man come to an end & #e on ! next4 #cj4 inyu9a kodl99 akb9idig9 a man come to an end & #aj on ! next4 #ce4 inyu9a akimiam9 aipal9 a man come to an end accompani$ by #a fifte5 times4 #dj4 madro inyu9a #b m5 come to an end4 ,9 ?is scale we f9d ! f+] orig9 appe>+ s cle>ly & s repeat$ly t "o feels "s degree ( surprise at f9d+ #e express$ by a pure num]al in/ead ( by "s ^w mean+ h& or f+]s ( "o h&4 ,9 ?is respect ! ,eskimo dialects are some:at exceptional among scales built up ( digital words4 ,! sy/em ( ! ,gre5l& ,eskimos1 ?\gh diff]+ slightly f t ( _! ,po9t ,b>r[ c\s9s1 %[s ! same peculi>ity4 ,! fir/ t5 num]als ( ?is scale are3#ga #a4 atausek4 #b4 m>dluk4 #c4 p+asut4 #d4 sisamat4 #e4 tatdlimat4 #f4 arf9ek-atausek to ! o!r h& #a4 #g4 arf9ek-m>dluk to ! o!r h& #b4 #h4 arf9ek-p+asut to ! o!r h& #c4 #i4 arf9ek-sisamat to ! o!r h& #d4 #aj4 kulit4 ,! same process is n[ repeat$1 only ! feet in/ead ( ! h&s are us$2 & ! completion ( ! second #aj is m>k$ by ! ^w innuk1 man4 ,x may be t ! ,eskimo ^w = #e is1 orig9ally1 a digital ^w1 b if s1 ! fact has n yet be5 detect$4 ,f ! analogy furni%$ by o!r languages we are ju/ifi$ 9 suspect+ t ?is may be ! case2 = :5ev] a numb] sy/em conta9s digital words1 we expect !m to beg9 ) five1 z1 = example1 9 ! ,arawak scale1#gb :i* runs3 #a4 abba4 #b4 biama4 #c4 kabbuh94 #d4 bibiti4 #e4 abbatekkbe #a h&4 #f4 abbatiman #a ( ! o!r4 #g4 biamattiman #b ( ! o!r4 #h4 kabbuh9timan #c ( ! o!r4 #i4 bibitiman #d ( ! o!r4 #aj4 biamantekbbe #b h&s4 #aa4 abba kutihib5a #a f ! feet4 #bj4 abba lukku h&s feet4 ,! f\r sets ( num]als j giv5 may be reg>d$ z typify+ "o ( ! mo/ common =ms ( primitive c\nt+2 & ! words !y conta9 s]ve z illu/rations ( ! means :i* g to make up ! numb] scales ( savage races4 ,frequ5tly ! f+] & toe orig9 ( num]als is p]fectly app>5t1 z 9 ! ,arawak sy/em j giv51 :i* exhibits ! simple/ & cle>e/ possible me?od ( =mation4 ,ano!r ev5 m int]e/+ sy/em is t ( ! ,montagnais ( nor!rn ,canada4#gc ,"h1 z 9 ! ,zui scale1 ! words are digital f ! outset4 #a4 inl'are ! end is b5t4 #b4 nak'e ano!r is b5t4 #c4 t'are ! middle is b5t4 #d4 d9ri !re are no m except ?is4 #e4 se-sunla-re ! r[ on ! h&4 #f4 elkke-t'are #c f ea* side4 #g4 t'a-ye-oy]tan !re are /ill #c ( !m4 inl'z d9ri on "o side !re are #d ( !m4 #h4 elkke-d9ri #d on ea* side4 #i4 inl'a-ye-oy]t'an !re is /ill #a m4 #aj4 on]nan f9i%$ on ea* side4 #aa4 on]nan inl'are tt*>idhel #a complete & #a4 #ab4 on]nan nak'e tt*>idhel #a complete & #b1 etc4 ,! =mation ( #f1 #g1 & #h ( ?is scale is some:at diff]5t f t ord9>ily f\nd4 ,to express #f1 ! ,montagnais sep>ates ! ?umb & =ef+] f ! ?ree rema9+ f+]s ( ! left h&1 & br++ ! ?umb ( ! "r h& close to !m1 says3 #c f ea* side4 ,= #g he ei!r subtracts f #aj1 say+3 !re are /ill #c ( !m1 or he br+s ! ?umb & =ef+] ( ! "r h& up to ! ?umb ( ! left1 & says3 on "o side !re are #d ( !m4 ,he calls #h by ! same "n z _m ( ! o!r ,canadian tribes1 t is1 two #d's2 & to %[ ! prop] numb] ( f+]s1 he closes ! ?umb & little f+] ( ! "r h&1 & !n puts ! ?ree rema9+ f+]s beside ! ?umb ( ! left h&4 ,?is me?od is1 9 "s ( ^! p>ticul>s1 diff]5t f any o!r ,i h ev] exam9$4 ,x (t5 happ5s t ! composition ( num]al words is less easily und]/ood1 & ! orig9al mean+s m difficult to recov]1 ?an 9 ! examples already giv54 ,b 9 se>*+ = numb] sy/ems :i* %[ 9 ! =mation ( _! words ! influ5ce ( f+] c\nt+1 x is n unusual to f9d ^? 9 :i* ! d]ivation f native words signify+ f+]1 h&1 toe1 foot1 & man1 is j z frankly obvi\s z 9 ! case ( ! ,zui1 ! ,arawak1 ! ,eskimo1 or ! ,montagnais scale4 ,among ! ,tamanacs1#gd "o ( ! num]\s ,indian tribes ( ! ,or9oco1 ! num]als are z /rictly digital z 9 any ( ! sy/ems already exam9$4 ,! g5]al /ructure ( ! ,tamanac scale is %[n by ! foll[+ num]als3 #e4 amgnaitone #a h& complete4 #f4 itacono amgna pona tev9itpe #a on ! o!r h&4 #aj4 amgna acepon>e all ( ! #b h&s4 #aa4 puitta pona tev9itpe #a on ! foot4 #af4 itacono puitta pona tev9itpe #a on ! o!r foot4 #bj4 tev9 itoto #a man4 #ba4 itacono itoto jamgn> bona tev9itpe #a on ! h&s ( ano!r man4 ,9 ! ,gu>ani#ge language ( ,p>aguay ! same me?od is f\nd1 ) a diff]5t =m ( expression = #bj4 ,"h ! num]als 9 "q are #e4 asepopetei "o h&4 #aj4 asepomokoi two h&s4 #bj4 asepo asepi abe h&s & feet4 ,ano!r slight v>iation is furni%$ by ! ,kiriri language1#gf :i* is also "o ( ! num]\s ,s\? ,am]ican ,indian =ms ( spee*1 :]e we f9d ! words to be #e4 mi bi*e misa "o h&4 #aj4 mikriba misa sai bo? h&s4 #bj4 mikriba misa ide*o ibi sai bo? h&s toge!r ) ! feet4 ,illu/rations ( ?is k9d might be multipli$ almo/ indef9itely2 & x is well to note t !y may be drawn f all p>ts ( ! _w4 ,s\? ,am]ica is peculi>ly ri* 9 native num]al words ( ?is k9d2 &1 z ! examples above cit$ %[1 x is ! field to :i* "o in/9ctively turns :5 ?is subject is "u discussion4 ,! ,zamuco num]als are1 among o!rs1 exce$+ly int]e/+1 giv+ u /ill a new v>iation 9 me?od4 ,!y are#gg #a4 tsom>a4 #b4 g>4 #c4 gadiok4 #d4 gahagani4 #e4 tsu5a yimana-ite end$ #a h&4 #f4 tsom>a-hi #a on ! o!r4 #g4 g>i-hi #b on ! o!r4 #h4 gadiog-ihi #c on ! o!r4 #i4 gahagani-hi #d on ! o!r4 #aj4 tsu5a yimana-die end$ bo? h&s4 #aa4 tsom>a yiri-tie #a on ! foot4 #ab4 g> yiritie #b on ! foot4 #bj4 tsu5a yiri-die end$ bo? feet4 ,z is "h indicat$1 ! =m ( progression f #e to #aj1 :i* we %\ld expect to be h&-#a1 or h&-&-#a1 or "s k9dr$ expression1 signify+ t "o h& _h be5 complet$1 is simply #a on ! o!r4 ,aga91 ! expressions = #aa1 #ab1 etc41 are m]ely #a on ! foot1 #b on ! foot1 etc41 :ile #bj is bo? feet end$4 ,an equally int]e/+ scale is furni%$ by ! language ( ! ,maipures#gh ( ! ,or9oco1 :o c\nt #a4 papita4 #b4 avanume4 #c4 apekiva4 #d4 apekipaki4 #e4 papita]ri capiti #a only h&4 #f4 papita yana pauria capiti pur5a #a ( ! o!r h& we take4 #aj4 apanum]ri capiti #b h&s4 #aa4 papita yana kiti pur5a #a ( ! toes we take4 #bj4 papita camonee #a man4 #dj4 avanume camonee #b m54 #fj4 apekiva camonee #c m51 etc4 ,9 all ! examples ?us f> giv51 #bj is express$ ei!r by ! equival5t ( man or by "s =mula introduc+ ! ^w feet4 ,bo? ^! modes ( express+ :at our own ance/ors t]m$ a score1 are s common t "o hesitates to say :i* is ( ! m frequ5t use4 ,! foll[+ scale1 f "o ( ! ,betoya dialects#gi ( ,s\? ,am]ica1 is q rem>kable among digital scales1 mak+ no use ( ei!r man or foot1 b reckon+ solely by fives1 or h&s1 z ! num]als indicate4 #a4 tey4 #b4 cayapa4 #c4 toazumba4 #d4 cajezea #b ) plural t]m9ation4 #e4 te5te h&4 #f4 tey5tetey h& #a4 #g4 tey5te cayapa h& #b4 #h4 tey5te toazumba h& #c4 #i4 tey5te caesea h& #d4 #aj4 caya ente1 or caya hu5a #b h&s4 #aa4 caya ente-tey #b h&s #a4 #ae4 toazumba-ente #c h&s4 #af4 toazumba-ente-tey #c h&s #a4 #bj4 caesea ente #d h&s4 ,9 ! la/ *apt] m5tion 0 made ( ! scanty num]al sy/ems ( ! ,au/ralian tribes1 b a s+le scale 0 allud$ to z rea*+ ! comp>atively high limit ( #bj4 ,?is sy/em is t belong+ to ! ,pikumbuls1#hj & ! c\nt runs ?us3 #a4 mal4 #b4 bul>4 #c4 guliba4 #d4 bul>bul> #b-b4 #e4 mulanbu4 #f4 malmulanbu mummi #a & #e add$ on4 #g4 bul>mulanbu mummi #b & #e add$ on4 #h4 gulibamulanbu mummi #c & #e add$ on4 #i4 bul>bul>mulanbu mummi #d & #e add$ on4 #aj4 bul>9 murra belong+ to ! #b h&s4 #aa4 mald9na mummi #a ( ! toes add$ on 7to ! #aj f+]s74 #ab4 bul> d9na mummi #b ( ! toes add$ on4 #ac4 guliba d9na mummi #c ( ! toes add$ on4 #ad4 bul> bul> d9na mummi #d ( ! toes add$ on4 #ae4 mulanba d9na #e ( ! toes add$ on4 #af4 mal d9na mulanbu #a & #e toes4 #ag4 bul> d9na mulanbu #b & #e toes4 #ah4 guliba d9na mulanbu #c & #e toes4 #ai4 bul> bul> d9na mulanbu #d & #e toes4 #bj4 bul>9 d9na belong+ to ! #b feet4 ,z has already be5 /at$1 !re is good gr\nd = believ+ t ?is sy/em 0 orig9ally z limit$ z ^? obta9$ f o!r ,au/ralian tribes1 & t its ext5sion f #d1 or p]haps f #e onw>d1 is ( comp>atively rec5t date4 ,a some:at peculi> num]al nom5clature is f\nd 9 ! language ( ! ,klama? ,indians ( ,oregon4 ,! fir/ t5 words 9 ! ,klama? scale are3#ha #a4 na%1 or nas4 #b4 lap h&4 #c4 ndan4 #d4 vunep h& up4 #e4 tunep h& away4 #f4 nad%k%apta #a ,i h b5t ov]4 #g4 lapk%apta #b ,i h b5t ov]4 #h4 ndank%apta #c ,i h b5t ov]4 #i4 nad%skek% #a left ov]4 #aj4 taunep h& h&8 ,9 describ+ ?is sy/em ,mr4 ,gats*et says3 ,if ! orig9 ( ! ,klama? num]als is ?us correctly trac$1 _! inv5tors mu/ h c\nt$ only ! f\r long f+]s )\t ! ?umb1 & #e 0 c\nt$ :ile say+ h& away6 h& (f6 ,! 'f\r1' or h& high6 h& up6 intimates t ! h& 0 held up high aft] c\nt+ its f\r digits2 & "s t]m express+ ?is ge/ure 01 9 ! case ( n9e1 sub/itut$ by '"o left ov]' 444 :i* means to say1 'only "o is left until all ! f+]s are c\nt$4' ,x w be obs]v$ t ! ,klama? introduces n only ! ord9>y f+] manipulation1 b a ge/ure ( ! entire h& z well4 ,x is a common ?+ to f9d some?+ ( ! k9d to indicate ! completion ( #e or #aj1 & 9 "o or two in/ances x has already be5 allud$ to4 ,sometimes "o or bo? ( ! clos$ fi/s are held up2 sometimes ! op5 h&1 ) all ! f+]s ext5d$1 is us$2 & sometimes an entirely indep5d5t ge/ure is introduc$4 ,^! are1 9 g5]al1 ( no special importance2 b "o cu/om 9 vogue among "s ( ! prairie tribes ( ,indians1 to :i* my att5tion 0 call$ by ,dr4 ,j4 ,ow5 ,dorsey1#hb %\ld be m5tion$4 ,x is a ge/ure :i* signifies multiplication1 & is p]=m$ by ?r[+ ! h& to ! left4 ,?us1 aft] c\nt+ #e1 a wave ( ! h& to ! left means #ej4 ,z multiplication is r unusual among savage tribes1 ?is is notewor?y1 & w\ld seem to indicate on ! "p ( ! ,indian a high] degree ( intellig5ce ?an is ord9>ily possess$ by unciviliz$ races4 ,9 ! num]al scale z we possess x 9 ,engli%1 we f9d x necess>y to reta9 ! "n ( ! la/ unit ( ea* k9d us$1 9 ord] to describe def9itely any num]al employ$4 ,?us1 fifte51 "o hundr$ =ty-two1 six ?\s& sev5 hundr$ tw5ty-sev51 give 9 full detail ! numb]s !y are int5d$ to describe4 ,9 primitive scales ?is is n always consid]$ necess>y2 ?us1 ! ,zamucos express _! te5s )\t us+ _! ^w = #aj at all4 ,!y say simply1 #a on ! foot1 #b on ! foot1 etc4 ,correspond+ abbreviations are (t5 met2 s (t51 inde$1 t no fur!r m5tion ( !m is ne$$4 ,!y m>k "o extreme1 ! extreme ( brevity1 f\nd 9 ! savage me?od ( build+ up h&1 foot1 & f+] names = num]als2 :ile ! ,zui scale m>ks ! extreme ( prolixity 9 ! =mation ( su* words4 ,a some:at rud] composition ?an any yet notic$ is %[n 9 ! num]als ( ! ,vilelo scale1#hc :i* are3 #a4 agit1 or yaagit4 #b4 uke4 #c4 nipetuei4 #d4 yepkatalet4 #e4 isig-nisle-yaagit h& f+]s #a4 #f4 isig-teet-yaagit h& ) #a4 #g4 isig-teet-uke h& ) #b4 #h4 isig-teet-nipetuei h& ) #c4 #i4 isig-teet-yepkatalet h& ) #d4 #aj4 isig-uke-nisle second h& f+]s 7lit4 h&-two-f+]s74 #aa4 isig-uke-nisle-teet-yaagit second h& f+]s ) #a4 #bj4 isig-ape-nisle-lauel h& foot f+]s all4 ,9 ! examples ?us f> giv51 x w be notic$ t ! actual names ( individual f+]s d n appe>4 ,9 g5]al1 su* words z ?umb1 =ef+]1 little f+]1 are n f\nd1 b r ! h&-#a1 #a on ! next1 or #a ov] & above1 :i* we h already se51 are ! type =ms = :i* we are to look4 ,individual f+] names d occur1 h[ev]1 z 9 ! scale ( ! ,hudson's ,bay ,eskimos1#hd :]e ! ?ree foll[+ words are us$ bo? z num]als & z f+] names3 #h4 kittukleemoot middle f+]4 #i4 mikkeelukkamoot f\r? f+]4 #aj4 e]kitkoka little f+]4 ,words ( simil> orig9 are f\nd 9 ! orig9al ,jiviro scale1#he :]e ! native num]als are3 #a4 ala4 #b4 catu4 #c4 cala4 #d4 encatu4 #e4 alactegladu #a h&4 #f4 intimutu ?umb 7( second h&74 #g4 tannituna index f+]4 #h4 tannituna cabiasu ! f+] next ! index f+]4 #i4 bit9 tegla cabiasu h& next to complete4 #aj4 catgladu #b h&s4 ,z if to emphasize ! r>ity ( ?is me?od ( =m+ num]als1 ! ,jiviros aft]w>d disc>d$ ! la/ five ( ! above scale1 replac+ !m by words borr[$ f ! ,qui*uas1 or anci5t ,p]uvians4 ,! same process may h be5 foll[$ by o!r tribes1 & 9 ?is way num]als :i* 7 orig9ally digital may h disappe>$4 ,b we h no evid5ce t ?is has ev] happ5$ 9 any ext5sive mann]4 ,we are1 r1 impell$ to accept ! occasional num]als ( ?is class z exceptions to ! g5]al rule1 until we h at our disposal fur!r evid5ce ( an exact & critical nature1 :i* w\ld cause u to modify ?is op9ion4 ,an elaborate philological /udy by ,dr4 ,j4,h4 ,trumbull#hf ( ! num]als us$ by _m ( ! ,nor? ,am]ican ,indian tribes reveals ! pres5ce 9 ! languages ( ^! tribes ( a few1 b only a few1 f+] names :i* are us$ )\t *ange z num]al expressions also4 ,sometimes ! f+] gives a "n n its own to ! num]al ) :i* x is associat$ 9 c\nt+--z 9 ! ,*ippeway dialect1 :i* has nawi-n9dj1 middle ( ! h&1 & nisswi1 #c2 & ! ,*ey5ne1 :]e notoyos1 middle f+]1 & na-nohhtu1 #h1 are closely relat$4 ,9 o!r p>ts ( ! _w isolat$ examples ( ! transf]5ce ( f+] names to num]als are also f\nd4 ,( ^! a well-kn[n example is furni%$ by ! ,zulu num]als1 :]e tatisitupa1 tak+ ! ?umb1 becomes a num]al = six4 ,!n ! v]b komba1 to po9t1 indicat+ ! =ef+]1 or 'po9t]1' makes ! next num]al1 sev54 ,?us1 answ]+ ! "q1 ',h[ mu* did y\r ma/] give y8' a ,zulu w\ld say1 ',u kombile1' ',he po9t$ ) 8 =ef+]1' i4e4 ',he gave me sev5'2 & ?is curi\s way ( us+ ! num]al v]b is also %[n 9 su* an example z 'amahasi akombile1' '! horses h po9t$1' i4e4 '!re 7 sev5 ( !m4' ,9 l mann]1 ,kijangalobili1 'keep back two f+]s1' i4e4 eight1 & ,kijangalolunje1 'keep back "o f+]1' i4e4 n9e1 lead on to kumi1 t54#hg ,return+ = a mom5t to ! consid]ation ( numb] sy/ems 9 ! =mation ( :i* ! influ5ce ( ! h& has be5 p>am\nt1 we f9d /ill fur!r v>iations ( ! me?od already notic$ ( con/ruct+ names = ! fives1 t5s1 & tw5ties1 z well z = ! int]m$iate numb]s4 ,in/ead ( ! simple words h&1 foot1 etc41 we n infrequ5tly meet ) "s p>aphrase = "o or = all ^! t]ms1 ! d]ivation ( :i* is unmi/akable4 ,! ,n5gones1#hh an isl& tribe ( ! ,indian ,ocean1 ?\gh us+ ! ^w man = #bj1 d n employ explicit h& or foot words1 b c\nt #a4 sa4 #b4 rewe4 #c4 t9i4 #d4 etse4 #e4 se dono ! end 7( ! fir/ h&74 #f4 dono ne sa end & #a4 #g4 dono ne rewe end & #b4 #h4 dono ne t9i end & #c4 #i4 dono ne etse end & #d4 #aj4 rewe tub59e #b s]ies 7( f+]s74 #aa4 rewe tub59e ne sa re tsem5e #b s]ies & #a on ! next8 #bj4 sa re nome #a man4 #cj4 sa re nome ne rewe tub59e #a man & #b s]ies4 #dj4 rewe ne nome #b m54 ,examples l ! above are n infrequ5t4 ,! ,aztecs us$ = #aj ! ^w matlactli1 h&-half1 i4e4 ! h& half ( a man1 & = #bj cempoalli1 "o c\nt+4#hi ,! ,po9t ,b>r[ ,eskimos call #aj kodl91 ! upp] "p1 i4e4 ( a man4 ,"o ( ! ,ewe dialects ( ,we/]n ,africa#ij has ewo1 done1 = #aj2 :ile1 curi\sly en\gh1 #i1 asieke1 is a digital ^w1 mean+ to "p 7f7 ! h&4 ,9 num]\s in/ances also "s *>act]i/ic ^w n ( h& d]ivation is f\nd1 l ! ,yoruba ogodzi1 /r+1 :i* becomes a num]al = #dj1 because #dj c[ries made a /r+2 & ! ,maori tekau1 bun*1 :i* signifies #aj4 ,! orig9 ( ?is seems to h be5 ! cu/om ( c\nt+ yams & fi% by bun*es ( t5 ea*4#ia ,ano!r me?od ( =m+ num]al words above #e or #aj is f\nd 9 ! pres5ce ( su* expressions z second #a1 second #b1 etc4 ,9 languages ( rude con/ruction & incomplete developm5t ! simple num]al scale is (t5 f\nd to end ) #e1 & all succe$+ num]als to be =m$ f ! fir/ #e4 ,! progression f t po9t may be #e-a1 #e-b1 etc41 z 9 ! num]\s qu9>y scales to be notic$ lat]1 or x may be second #a1 second #b1 etc41 z 9 ! ,niam ,niam dialect ( ,c5tral ,africa1 :]e ! scale is#ib #a4 sa4 #b4 uwi4 #c4 biata4 #d4 biama4 #e4 biswi4 #f4 batissa #b;d #a4 #g4 batiwwi #b;d #b4 #h4 batti-biata #b;d #c4 #i4 batti-biama #b;d #d4 #aj4 bauw #b;d #e4 ,t ?is me?od ( progression is n conf9$ to ! lea/ develop$ languages1 h[ev]1 is %[n by a mo/ cursory exam9ation ( ! num]als ( our ,am]ican ,indian tribes1 :]e num]al =mation l t exhibit$ above is exce$+ly common4 ,9 ! ,koot5ay dialect1#ic ( ,briti% ,columbia1 qaetsa1 #d1 & wo-qaetsa1 #h1 are obvi\sly relat$1 ! latt] ^w probably mean+ a second #d4 ,mo/ ( ! native languages ( ,briti% ,columbia =m _! words = #g & #h f ^? :i* signify #b & #c2 z1 = example1 ! ,heiltsuk1#id :i* %[s 9 ! foll[+ words a mo/ obvi\s correspond5ce3 #b4 matl4 #g4 matlaaus4 #c4 yutq4 #h4 yutquaus4 ,9 ! ,*octaw language#ie ! relation betwe5 #b & #g1 & #c & #h1 is no less cle>4 ,"h ! words are3 #b4 tuklo4 #g4 untuklo4 #c4 tu*9a4 #h4 untu*9a4 ,! ,nez ,p]cs#if repeat ! fir/ ?ree words ( _! scale 9 _! #f1 #g1 & #h respectively1 z a comp>ison ( ^! num]als w %[4 #a4 naks4 #f4 oilaks4 #b4 lapit4 #g4 o9apt4 #c4 mitat4 #h4 oimatat4 ,9 all ^! cases ! ess5tial po9t ( ! me?od is conta9$ 9 ! repetition1 9 "o way or ano!r1 ( ! num]als ( ! second qu9ate1 )\t ! use ) ea* "o ( ! ^w = #e4 ,?is may make #f1 #g1 #h1 & #i appe> z second #a1 second #b1 etc41 or ano!r #a1 ano!r #b1 etc42 or1 m simply /ill1 z #a m1 #b m1 etc4 ,x is ! me?od :i* 0 briefly discuss$ 9 ! e>ly "p ( ! pres5t *apt]1 & is by no means uncommon4 ,9 a decimal scale ?is repetition w\ld beg9 ) #aa in/ead ( #f2 z 9 ! sy/em f\nd 9 use 9 ,tagala & ,pampanaga1 two ( ! ,philipp9e ,isl&s1 :]e1 = example1 #aa1 #ab1 & #ac are3#ig #aa4 labi-n-isa ov] #a4 #ab4 labi-n-dalaua ov] #b4 #ac4 labi-n-tatlo ov] #c4 ,a precisely simil> me?od ( num]al build+ is us$ by "s ( our ,we/]n ,indian tribes4 ,select+ a few ( ! ,ass9ibo9e num]als#ih z an illu/ration1 we h #aa4 ak kai wa%e m #a4 #ab4 ak kai noom pah m #b4 #ac4 ak kai yam me nee m #c4 #ad4 ak kai to pah m #d4 #ae4 ak kai zap tah m #e4 #af4 ak kai %ak pah m #f1 etc4 ,a /ill m primitive /ructure is %[n 9 ! num]als ( ! ,mb\%as#ii ( ,equatorial ,africa4 ,in/ead ( us+ #e-a1 #e-b1 #e-c1 #e-d1 or #b;d #a1 #b;d #b1 #b;d #c1 #b;d #d1 9 =m+ _! num]als f #f to #i1 !y proce$ 9 ! foll[+ rem>kable &1 at fir/ ?\ght1 inexplicable mann] to =m _! comp\nd num]als3 #a4 ivoco4 #b4 beba4 #c4 belalo4 #d4 b5ai4 #e4 betano4 #f4 ivoco beba #a-b4 #g4 ivoco belalo #a-c4 #h4 ivoco b5ai #a-d4 #i4 ivoco betano #a-e4 #aj4 di\m4 ,no explanation is giv5 by ,mr4 du ,*aillu = su* an app>5tly incompreh5sible =m ( expression z1 = example1 #a-c1 = #g4 ,"s peculi> f+] pantomime may accompany ! c\nt+1 :i*1 7 x kn[n1 w\ld enlight5 u on ! ,mb\%a's me?od ( arriv+ at s anomal\s a scale4 ,m]e repetition 9 ! second qu9ate ( ! words us$ 9 ! fir/ might readily be expla9$ by suppos+ ! use ( f+]s absolutely indisp5sable z an aid to c\nt+1 & t a c]ta9 ^w w\ld h "o mean+ :5 associat$ ) a c]ta9 f+] ( ! left h&1 & ano!r mean+ :5 associat$ ) "o ( ! f+]s ( ! "r4 ,su* scales are1 if ! foll[+ are correct1 actually 9 exi/5ce among ! isl&s ( ! ,pacific4 ,,balad4#ajj ,,uea4#ajj #a4 p>ai4 #a4 tahi4 #b4 p>oo4 #b4 lua4 #c4 p>g54 #c4 tolu4 #d4 p>bai4 #d4 fa4 #e4 panim4 #e4 lima4 #f4 p>ai4 #f4 tahi4 #g4 p>oo4 #g4 lua4 #h4 p>g54 #h4 tolu4 #i4 p>bai4 #i4 fa4 #aj4 panim4 #aj4 lima4 ,su* examples are1 ,i believe1 entirely unique among primitive numb] sy/ems4 ,9 num]al scales :]e ! =mative process has be5 ( ! g5]al nature j exhibit$1 irregul>ities ( v>i\s k9ds are ( frequ5t occurr5ce4 ,h& num]als may appe>1 & !n sudd5ly disappe>1 j :]e we %\ld look = !m ) ! greate/ degree ( c]ta9ty4 ,9 ! ,ende1#aja a dialect ( ! ,flores ,isl&s1 #e1 #f1 & #g are ( h& =mation1 :ile #h & #i are ( entirely diff]5t orig91 z ! scale %[s4 #a4 sa4 #b4 zua4 #c4 telu4 #d4 wutu4 #e4 lima #f4 lima sa h& #a4 #g4 lima zua h& #b4 #h4 rua butu #b #d4 #i4 trasa #aj - #a8 #aj4 sabulu4 ,"o special po9t to be notic$ 9 ?is scale is ! irregul>ity t prevails betwe5 #g1 #h1 #i4 ,! =mation ( #g is ( ! mo/ ord9>y k9d2 #h is #b f\rs--common en\gh duplication2 :ile #i appe>s to be #aj - #a4 ,all ( ^! modes ( comp\nd+ are1 9 _! own way1 regul>2 b ! irregul>ity consi/s 9 us+ all ?ree ( !m 9 connective num]als 9 ! same sy/em4 ,b1 odd z ?is jumble seems1 x is m ?an mat*$ by t f\nd 9 ! scale ( ! ,k>ankawa ,indians1#ajb an ext9ct tribe =m]ly inhabit+ ! coa/ region ( ,texas4 ,! fir/ t5 num]als ( ?is s+ul> array are3 #a4 natsa4 #b4 haikia4 #c4 ka*ayi4 #d4 hayo hakn #b #b4 #e4 natsa behema #a fa!r1 i4e4 ( ! f+]s4 #f4 hayo haikia #c #b8 #g4 haikia natsa #b #e8 #h4 haikia behema #b fa!rs8 #i4 haikia doatn #b;d f #aj8 #aj4 doatn habe4 ,sy/ems l ! above1 :]e *aos in/ead ( ord] seems to be ! rul+ pr9ciple1 are ( occasional occurr5ce1 b !y are decid$ly ! exception4 ,9 "s ( ! cases t h be5 adduc$ = illu/ration x is to be notic$ t ! process ( comb9ation beg9s ) #g in/ead ( ) #f4 ,among o!rs1 ! scale ( ! ,pigmies ( ,c5tral ,africa#ajc & t ( ! ,mosquitos#ajd ( ,c5tral ,am]ica %[ ?is t5d5cy4 ,9 ! ,pigmy scale ! words = #a & #f are s closely ak9 t "o _c resi/ ! impression t #f 0 to !m a new #a1 & 0 ?us nam$4 ,,mosquito4 ,,pigmy4 #a4 kumi4 ujju4 #b4 wal4 ib>i4 #c4 niupa4 ik>o4 #d4 wal-wal #b-b4 ikwanganya4 #e4 mata-sip f+]s ( #a h&4 bumuti4 #f4 matlalkabe4 ijju4 #g4 matlalkabe pura kumi #f & #a4 bumutti-na-ibali #e & #b4 #h4 matlalkabe pura wal #f & #b4 bumutti-na-ik>o #e & #c4 #i4 matlalkabe pura niupa #f & #c4 bumutti-na-ikwanganya #e & #d4 #aj4 mata wal sip f+]s ( #b h&s4 mabo half man4 ,! ,mosquito scale is q exceptional 9 =m+ #g1 #h1 & #i f #f1 in/ead ( f #e4 ,! usual me?od1 :]e comb9ations appe> betwe5 #f & #aj1 is exhibit$ by ! ,pigmy scale4 ,/ill ano!r species ( num]al =m1 q diff]5t f any t h already be5 notic$1 is f\nd 9 ! ,yoruba#aje scale1 :i* is 9 _m respects "o ( ! mo/ peculi> 9 exi/5ce4 ,"h ! words = #aa1 #ab1 etc41 are =m$ by add+ ! suffix -la1 great1 to ! words = #a1 #b1 etc41 ?us3 #a4 eni1 or okan4 #b4 edzi4 #c4 eta4 #d4 er94 #e4 arun4 #f4 efa4 #g4 edze4 #h4 edzo4 #i4 esan4 #aj4 ewa4 #aa4 okanla great #a4 #ab4 edzila great #b4 #ac4 etala great #c4 #ad4 er9la great #d1 etc4 #dj4 ogodzi /r+4 #bjj4 igba heap4 ,! ^w = #dj 0 adopt$ because c[rie %ells1 :i* are us$ = c\nt+1 7 /rung by =ties2 & igba1 #bjj1 because a heap ( #bjj %ells 0 five /r+s1 & ?us =m$ a conv5i5t high] unit = reckon+4 ,proce$+ 9 ?is curi\s mann]1#ajf !y call$ #ej /r+s #a afo or head2 & to illu/rate _! s+ul> mode ( reckon+--! k+ ( ! ,dahomans1 hav+ made w> on ! ,yorubans1 & attack$ _! army1 0 repuls$ & defeat$ ) a loss ( two heads1 tw5ty /r+s1 & tw5ty c[ries ( m51 or #dhbj4 ,! numb] scale ( ! ,abipones1#ajg "o ( ! l[ tribes ( ! ,p>aguay region1 conta9s two g5u9e curiosities1 & by reason ( ^? x des]ves a place among any collection ( num]al scales design$ to exhibit ! =mation ( ?is class ( words4 ,x is3 #a4 init>a #a alone4 #b4 inoaka4 #c4 inoaka yeka9i #b & #a4 #d4 gey5knate toes ( an o/ri*4 #e4 ne5halek a five col\r$1 spott$ hide1 or hanambeg5 f+]s ( #a h&4 #aj4 lanamrihegem f+]s ( bo? h&s4 #bj4 lanamrihegem cat gra*]haka anami*irihegem f+]s ( bo? h&s toge!r ) toes ( bo? feet4 ,t ! numb] s5se ( ! ,abipones is b little1 if at all1 above t ( ! native ,au/ralian tribes1 is %[n by _! express+ #c by ! comb9ation #b & #a4 ,?is limitation1 z we h already se51 is %>$ by ! ,botocudos1 ! ,*iquitos1 & _m ( ! o!r native races ( ,s\? ,am]ica4 ,b ! ,abipones1 9 seek+ = words ) :i* to enable !mselves to pass beyond ! limit #c1 inv5t$ ! s+ul> t]ms j giv5 = #d & #e4 ,! o/ri*1 hav+ ?ree toes 9 front & "o beh9d on ea* foot pres5t$ !m ) a liv+ example ( #c #a2 h5ce toes ( an o/ri* became _! num]al = #d4 ,simil>ly1 ! numb] ( col\rs 9 a c]ta9 hide be+ five1 ! "n = t hide 0 adopt$ z _! next num]al4 ,at ?is po9t !y began to resort to digital num]ation also2 & any high] numb] is express$ by t me?od4 ,9 ! s5se 9 :i* ! ^w is def9$ by ma!maticians1 numb] is a pure1 ab/ract concept4 ,b a mom5t's reflection w %[ t1 z x orig9ates among savage races1 numb] is1 & f ! limitations ( _! intellect mu/ be1 entirely concrete4 ,an ab/ract conception is some?+ q =eign to ! ess5tially primitive m9d1 z mission>ies & explor]s h f\nd to _! *agr94 ,! savage c =m no m5tal concept ( :at civiliz$ man means by su* a ^w z s\l2 nor w\ld 8 idea ( ! ab/ract numb] #e be mu* cle>]4 ,:5 he says five1 he uses1 9 _m cases at lea/1 ! same ^w t s]ves him :5 he wi%es to say h&2 & 8 m5tal concept :5 he says five is ( a h&4 ,! concrete idea ( a clos$ fi/ or an op5 h& ) out/ret*$ f+]s1 is :at is upp]-mo/ 9 8 m9d4 ,he kn[s no m & c>es no m ab\t ! pure numb] #e ?an he does ab\t ! law ( ! cons]vation ( en]gy4 ,he sees 9 8 m5tal picture only ! real1 mat]ial image1 & 8 only compreh5sion ( ! numb] is1 ^! objects are z _m z ! f+]s on my h&4 ,!n1 9 ! lapse ( ! long int]val ( c5turies :i* int]v5e betwe5 l[e/ b>b>ism & highe/ civilization1 ! ab/ract & ! concrete become sl[ly dissociat$1 ! "o f ! o!r4 ,fir/ ! actual h& picture fades away1 & ! numb] is recogniz$ )\t ! orig9al assi/ance furni%$ by ! d]ivation ( ! ^w4 ,b ! numb] is /ill = a long "t a c]ta9 numb] ( objects1 & n an indep5d5t concept4 ,x is only :5 ! savage ceases to be :olly an animal1 & becomes a ?9k+ human be+1 t numb] 9 ! ab/ract c come )9 ! grasp ( 8 m9d4 ,x is at ?is po9t t m]e reckon+ ceases1 & ari?metic beg9s4 ,,*apt] ,,iv4 ,,! ,,orig9 ,,( ,,numb] ,,words4 7,,cont9u$47 ,by ! sl[1 & (t5 pa9ful1 process incid5t to ! ext5sion & developm5t ( any m5tal conception 9 a m9d :olly unus$ to ab/ractions1 ! savage gropes 8 way onw>d 9 8 c\nt+ f #a1 or m probably f #b1 to ! v>i\s high] numb]s requir$ to =m 8 scale4 ,! p]ception ( unity (f]s no difficulty to 8 m9d1 ?\gh he is consci\s at fir/ ( ! object itself r ?an ( any idea ( numb] associat$ ) x4 ,! concept ( duality1 also1 is grasp$ ) p]fect read9ess4 ,?is concept is1 9 its simple/ =m1 pres5t$ to ! m9d z soon z ! individual di/+ui%es himself f ano!r p]son1 ?\gh ! idea is /ill ess5tially concrete4 ,p]haps ! fir/ glimm]+ ( any real numb] ?\ght 9 connection ) #b comes :5 ! savage contra/s "o s+le object ) ano!r--or1 9 o!r words1 :5 he fir/ recognizes ! pair4 ,at fir/ ! individuals compos+ ! pair are simply ?is "o1 & t "o1 or ?is & t2 & 8 numb] sy/em n[ halts = a "t at ! /age :5 he c1 rudely en\gh x may be1 c\nt #a1 #b1 _m4 ,!re are c]ta9 cases :]e ! =ms ( #a & #b are s simil> ?an "o may readily imag9e t ^! numb]s really 7 ?is & t 9 ! savage's orig9al conception ( !m2 & ! same lik5ess also occurs 9 ! words = #c & #d1 :i* may readily en\gh h be5 a second ?is & a second t4 ,9 ! ,lu%u tongue ! words = #a & #b are tizi & tazi respectively4 ,9 ,koriak we f9d ngroka1 #c1 & ngraka1 #d2 9 ,kolyma1 niyokh1 #c1 & niyakh1 #d2 & 9 ,kamts*atkan1 tsuk1 #c1 & tsaak1 #d4ajh ,sometimes1 z 9 ! case ( ! ,au/ralian races1 ! entire ext5t ( ! c\nt is c>ri$ ?r\gh by means ( pairs4 ,b ! natural !ory "o w\ld =m is1 t #b is ! halt+ place = a v long "t2 t up to ?is po9t ! f+]s may or may n h be5 us$--probably n2 & t :5 ! next />t is made1 & #c1 #d1 #e1 & s on are c\nt$1 ! f+]s fir/ come into requisition4 ,if ! grammatical /ructure ( ! e>li] languages ( ! _w's hi/ory is exam9$1 ! /ud5t is /ruck ) ! preval5ce ( ! dual numb] 9 !m--some?+ :i* t5ds to disappe> z language und]goes ext5d$ developm5t4 ,! dual numb] po9ts unequivocally to ! "t :5 #a & #b 7 ! numb]s at mank9d's disposal2 to ! "t :5 8 ?ree num]al concepts1 #a1 #b1 _m1 ea* dem&$ di/9ct expression4 ,) increas+ k ! necessity = ?is diff]5tiatu9 w\ld pass away1 & b two numb]s1 s+ul> & plural1 w\ld rema94 ,incid5tally x is to be notic$ t ! ,indo-,european words = #c--?ree1 trois1 drei1 tres1 tri1 etc41 h ! same root z ! ,lat9 trans1 beyond1 & give u a h9t ( ! "t :5 our ,aryan ance/ors c\nt$ 9 ! mann] ,i h j describ$4 ,! fir/ real difficulty :i* ! savage exp]i5ces 9 c\nt+1 ! difficulty :i* comes :5 he attempts to pass beyond #b1 & to c\nt #c1 #d1 & #e1 is ( c\rse b slight2 & ^! numb]s are commonly us$ & readily und]/ood by almo/ all tribes1 no matt] h[ deeply sunk 9 b>b>ism we f9d !m4 ,b ! in/ances t h already be5 cit$ mu/ n be =gott54 ,! ,*iquitos d n1 9 _! primitive /ate1 prop]ly c\nt at all2 ! ,&amans1 ! ,v$das1 & _m ( ! ,au/ralian tribes h no num]als high] ?an #b2 o!rs ( ! ,au/ralians & _m ( ! ,s\? ,am]icans /op ) #c or #d2 & tribes :i* make #e _! limit are /ill m num]\s4 ,h5ce x is safe to ass]t t ev5 ?is insignificant numb] is n always rea*$ ) p]fect ease4 ,beyond #e primitive man (t5 proce$s ) ! greate/ difficulty4 ,mo/ savages1 ev5 ^? ( ! tribes j m5tion$1 c really c\nt above "h1 ev5 ?\gh !y h no words ) :i* to express _! ?\ght4 ,b !y d x ) reluctance1 & z !y g on !y quickly lose all s5se ( accuracy4 ,?is has already be5 comm5t$ on1 b to emphasize x afre% ! well-kn[n example giv5 by ,mr4 ,oldfield f 8 own exp]i5ce among ! ,wat*&ies may be quot$4#aji ,i once wi%$ to asc]ta9 ! exact numb] ( natives :o _h be5 sla9 on a c]ta9 occasion4 ,! individual ( :om ,i made ! inquiry began to ?9k ov] ! names 444 assign+ "o ( 8 f+]s to ea*1 & x 0 n until aft] _m failures1 & consequ5t fre% />ts1 t he 0 able to express s high a numb]1 :i* he at l5g? did by hold+ up 8 h& ?ree times1 ?us giv+ me to und]/& t fifte5 0 ! answ] to ?is mo/ difficult ari?metical "q4 ,?is meagr5ess ( k 9 all ?+s p]ta9+ to numb]s is (t5 f\nd to be %>ply emphasiz$ 9 ! names adopt$ by savages = _! num]al words4 ,:ile discuss+ 9 a previ\s *apt] ! limits ( numb] sy/ems1 we f\nd _m in/ances :]e any?+ above #b or #c 0 designat$ by "s "o ( ! compreh5sive t]ms mu*1 _m1 v _m2 ^! words1 or su* equival5ts z lot1 heap1 or pl5ty1 s]v+ z an aid to ! f+] pantomime necess>y to indicate numb]s = :i* !y h no real names4 ,! l[ degree ( intellig5ce & civilization reveal$ by su* words is br\ght q z %>ply into prom95ce by ! ^w occasionally f\nd = #e4 ,:5ev] ! f+]s & h&s are us$ at all1 x w\ld seem natural to expect = #e "s g5]al expression signify+ h&1 = #aj bo? h&s1 & = #bj man4 ,su* is1 z we h already se51 ! ord9>y me?od ( progression1 b x is n univ]sal4 ,a drop 9 ! scale ( civilization takes u to a po9t :]e #aj1 in/ead ( #bj1 becomes ! :ole man4 ,! ,kusaies1#aaj ( ,/rong's ,isl&1 call #aj sie-nul1 #a man1 #cj tol-nul1 #c m51 #dj a naul1 #d m51 etc42 & ! ,ku-,mbutti#aaa ( c5tral ,africa h mukko1 #aj1 & moku1 man4 ,if #aj is to be express$ by ref]5ce to ! man1 in/ead ( 8 h&s1 x might appe> m natural to employ "s su* expression z t adopt$ by ! ,african ,pigmies1#aab :o call #aj mabo1 & man mabo-mabo4 ,) !m1 !n1 #aj is p]haps half a man1 z x actually is among ! ,t[kas ( ,s\? ,am]ica2 & we h already se5 t ) ! ,aztecs x 0 matlactli1 ! h& half ( a man4#aac ,! same idea crops out 9 ! expression us$ by ! ,nicob> ,isl&]s = #cj--;heam-umdjome ruktei1 #a man 7& a7 half4#aad ,su* nom5clature is entirely natural1 & x accords ) ! analogy (f]$ by o!r words ( frequ5t occurr5ce 9 ! num]al scales ( savage races4 ,/ill1 to f9d #aj express$ by ! t]m man always conveys an impression ( m5tal pov]ty2 ?\gh x may1 ( c\rse1 be urg$ t ?is might arise f ! fact t "s races nev] use ! toes 9 c\nt+1 b g ov] ! f+]s aga91 or p]haps br+ into requisition ! f+]s ( a second man to express ! second #aj4 ,x is n safe to po/ulate an extremely l[ degree ( civilization f ! pres5ce ( c]ta9 peculi>ities ( num]al =mation4 ,only ! mo/ g5]al /atem5ts c be v5tur$ on1 & ^! are always subject to modification ?r\gh "s circum/ance connect$ ) environm5t1 mode ( liv+1 or int]c\rse ) o!r tribes4 ,two ,s\? ,am]ican races may be cit$1 :i* seem 9 ?is respect to give unmi/akable evid5ce ( be+ sunk 9 deepe/ b>b>ism4 ,^! are ! ,juri & ! ,cayriri1 :o use ! same ^w = man & = #e4 ,! =m] express #e by ghom5 apa1 #a man1#aae & ! latt] by ibi*o1 p]son4#aaf ,! ,tasmanians ( ,oy/] ,bay use ! native ^w ( simil> mean+1 puggana1 man1#aag = #e4 ,:]ev] ! num]al #bj is express$ by ! t]m man1 x may be expect$ t #dj w be #b m51 #fj1 #c m51 etc4 ,?is =m ( num]ation is usually1 ?\gh n always1 c>ri$ z f> z ! sy/em ext5ds2 & x sometimes leads to curi\s t]ms1 ( :i* a s+le illu/ration w suffice4 ,! ,san ,blas ,indians1 l almo/ all ! o!r ,c5tral & ,s\? ,am]ican tribes1 c\nt by digit num]als1 & =m _! tw5ties z foll[s3#aah #bj4 tula gu5a man #a4 #dj4 tula pogua man #b4 #ajj4 tula atala man #e4 #abj4 tula n]gua man #f4 #ajjj4 tula wala gu5a great #a man4 ,! la/ expression may1 p]haps1 be translat$ great hundr$1 ?\gh ! lit]al mean+ is ! "o giv54 ,if #aj1 in/ead ( #bj1 is express$ by ! ^w man1 ! multiples ( #aj foll[ ! law j giv5 = multiples ( #bj4 ,?is is suffici5tly indicat$ by ! ,kusaie scale2 or equally well by ! ,api words = #ajj & #bjj1 :i* are#aai duulimo toromomo #aj times ! :ole man4 duulimo toromomo va juo #aj times ! :ole man tak5 #b times4 ,z an illu/ration ( ! legitimate result :i* is produc$ by ! attempt to express high numb]s 9 ?is mann] ! t]m appli$ by educat$ native ,gre5l&]s#abj = a ?\s& may be cit$4 ,?is num]al1 :i* is1 ( c\rse1 n 9 common use1 is inuit kulit tatdlima nik kul]i>tut navdlugit #aj m5 #e times #aj times come to an end4 ,x is wor? not+ t ! ^w great1 :i* appe>s 9 ! scale ( ! ,san ,blas ,indians1 is n infrequ5tly made use ( 9 ! =mation ( high] num]al words4 ,! ,african ,mabas#aba call #aj atuk1 great #a2 ! ,hott5tots#abb & ! ,hidatsa ,indians call #ajj great #aj1 _! words be+ gei disi & pitikit/ia respectively4 ,! ,nic>aguans#abc express #ajj by guhamba1 great #aj1 & #djj by d9oamba1 great #bj2 & our own famili> ^w million1 :i* s _m mod]n languages h borr[$ f ! ,italian1 is no?+ m nor less ?an a d]ivative ( ! ,lat9 mille1 & really means great ?\s&4 ,! ,dakota#abd language %[s ! same orig9 = its expression ( #a1jjj1jjj1 :i* is kick ta opong wa tunkah1 great #ajjj4 ,! orig9 ( su* t]ms c h>dly be ascrib$ to pov]ty ( language4 ,x is f\nd1 r1 9 ! m5tal association ( ! l>g] ) ! small] unit1 & ! consequ5t repetition ( ! "n ( ! small]4 ,any unit1 :e!r x be a s+le ?+1 a doz51 a score1 a hundr$1 a ?\s&1 or any o!r unit1 is1 :5ev] us$1 a s+le & complete gr\p2 & :]e ! relation betwe5 !m is suffici5tly close1 z 9 our gross & great gross1 ?is =m ( nom5clature is natural en\gh to r5d] x a matt] ( "s surprise t x has n be5 employ$ m frequ5tly4 ,an old ,engli% nurs]y rhyme makes use ( ?is association1 only 9 a mann] precisely ! rev]se ( t :i* appe>s n[ & !n 9 num]al t]ms4 ,9 ! latt] case ! process is always "o ( enl>gem5t1 & ! associative ^w is great4 ,9 ! foll[+ rhyme1 con/ruct$ by ! mature = ! amusem5t ( ! *ildi% m9d1 ! process is "o ( dim9ution1 & ! associative ^w is little3 ,"o's none1 ,two's "s1 ,?ree's a _m1 ,f\r's a p5ny1 ,five's a little hundr$4#abe ,any real num]al =mation by ! use ( little1 ) ! "n ( "s high] unit1 w\ld1 ( c\rse1 be impossible4 ,! num]al scale mu/ be complete be=e ! nurs]y rhyme c be manufactur$4 ,x is n to be suppos$ f ! obs]vations t h be5 made on ! =mation ( savage num]al scales t all1 or ev5 ! majority ( tribes1 proce$ 9 ! awkw>d & falt]+ mann] indicat$ by _m ( ! examples quot$4 ,"s ( ! ,nor? ,am]ican ,indian tribes h num]al scales :i* are1 z f> z !y g1 z regul> & almo/ z simple z our own4 ,b :]e digital num]ation is ext5sively resort$ to1 ! expressions = high] numb]s are likely to become complex1 & to act z a real b> to ! ext5sion ( ! sy/em4 ,! same ?+ is true1 to an ev5 great] degree1 ( tribes ^: numb] s5se is s defective t !y beg9 almo/ f ! outset to use comb9ations4 ,if a savage expresses ! numb] #c by ! comb9ation #b-a1 x w at once be suspect$ t 8 num]als w1 by ! "t he rea*es #aj or #bj1 become s complex & confus$ t numb]s z high z ^! w be express$ by f+] pantomime r ?an by words4 ,su* is (t5 ! case2 & ! comm5t is frequ5tly made by explor]s t ! tribes !y h visit$ h no words = numb]s high] ?an #c1 #d1 #e1 #aj1 or #bj1 b t c\nt+ is c>ri$ beyond t po9t by ! aid ( f+]s or o!r objects4 ,s reluctant1 9 _m cases1 are savages to c\nt by words1 t limits h be5 assign$ = spok5 num]als1 :i* subsequ5t inve/igation prov$ to fall f> %ort ( ! real ext5t ( ! numb] sy/ems to :i* !y belong$4 ,"o ( ! s\?-we/]n ,indian tribes ( ! ,unit$ ,/ates1 ! ,coman*es1 0 = a "t suppos$ to h no num]al words bel[ #aj1 b to c\nt solely by ! use ( f+]s4 ,b ! entire scale ( ?is taciturn tribe 0 aft]w>d discov]$ & publi%$4 ,to illu/rate ! awkw>d & inconv5i5t =ms ( expression :i* ab\nd 9 primitive num]al nom5clature1 "o has only to draw f su* scales z ^? ( ! ,zui1 or ! ,po9t ,b>r[ ,eskimos1 giv5 9 ! la/ *apt]4 ,t]ms su* z are f\nd !re may readily be duplicat$ f almo/ any qu>t] ( ! globe4 ,! ,s\ss\s ( ,si]ra ,leone#abf call #ii tongo solo manani nun solo manani1 i4e4 to take 7#aj und]/ood7 #e #d times & #e #d4 ,! ,malagasy expression = #ahcb is#abg roambi/elo polo amby valonjato amby arivo1 #b #cj #hjj #ajjj4 ,! ,aztec equival5t = #cii is#abh caxtolli onnauh poalli ipan caxtolli onnaui1 7#ae #d7 #bj #ae #d2 & ! ,si\x require = #bi ! pond]\s comb9ation#abi wick a *im5 ne nompah sam pah nep e *u w9k a4 ,^! t]ms1 long & awkw>d z !y seem1 are only ! legitimate results :i* arise f comb9+ ! names ( ! high] & l[] numb]s1 accord+ to ! peculi> g5ius ( ea* language4 ,f "s ( ! ,au/ralian tribes are d]iv$ expressions /ill m complex1 z = #f1 m>h-j9-bang-ga-gudjir-gyn1 half ! h&s & #a2 & = #ae1 m>h-j9-belli-belli-gudjir-j9a-bang-ga1 ! h& on ei!r side & half ! feet4#acj ,! ,m> tribe1 "o ( ! num]\s isl& tribes ( ,melanesia1#aca requir$ = a translation ( ! num]al #ch1 :i* occurs 9 ,john v4 #e1 _h an infirmity ?irty & eight ye>s1 ! circumlocution1 "o man & bo? sides five & ?ree4 ,su* expressions1 curi\s z !y seem at fir/ ?\ght1 are no m ?an ! natural outgr[? ( sy/ems built up by ! sl[ & t$i\s process :i* s (t5 obta9s among primitive races1 :]e digit num]als are comb9$ 9 an almo/ endless v>iety ( ways1 & :]e m]e r$uplication (t5 s]ves 9 place ( any indep5d5t names = high] units4 ,to :at ext5t ?is may be c>ri$ is %[n by ! language ( ! ,cayubabi1#acb :o h = #aj ! ^w tunca1 & = #ajj & #ajjj ! comp\nds tunca tunca1 & tunca tunca tunca respectively2 or ( ! ,sapibocones1 :o call #aj bururu*e1 h& h&1 & #ajj buru*e buru*e1 h& h& h& h&4#acc ,m rem>kable /ill is ! ,ojibwa language1 :i* cont9ues its num]al scale )\t limit1 furni%+ comb9ations :i* are really rem>kable2 z1 e4g41 t = #a1jjj1jjj1jjj1 :i* is me das wac me das wac z he me das wac1#acd #ajjj #ajjj #ajjj4 ,! ,w9nebago expression = ! same numb]1#ace ho ke he hhuta hhu *5 a ho ke he ka ra pa ne za is no less =midable1 b x has e appe>ance ( be+ an hone/1 native comb9ation4 ,all su* primitive t]ms = l>g] numb]s mu/1 h[ev]1 be receiv$ ) caution4 ,savages are sometimes eag] to display a k !y d n possess1 & h be5 kn[n to inv5t num]al words on ! spot = ! sake ( c>ry+ _! scales to z high a limit z possible4 ,! ,*octaw words = million & billion are obvi\s attempts to incorporate ! correspond+ ,engli% t]ms into _! own language4#acf ,= million !y gave ! vocabul>y-hunt] ! phrase mil yan *uffa1 & = billion1 bil yan *uffa4 ,! ^w *uffa signifies #a1 h5ce ^! expressions are se5 at a glance to be co9$ solely = ! purpose ( gratify+ a little h>mless ,*octaw vanity4 ,b ?is is innoc5ce itself comp>$ ) ! fraud p]petrat$ on ,labill>dire by ! ,tonga ,isl&]s1 :o suppli$ ! a/oni%$ & delight$ inve/igator ) a num]al vocabul>y up to quadrillions4 ,_! real limit 0 aft]w>d f\nd to be #ajj1jjj1 & above t po9t !y _h palm$ (f z num]als a tol]ably complete li/ ( ! obsc5e words ( _! language1 toge!r ) a few nons5se t]ms4 ,^! 7 all accept$ & pr9t$ 9 good fai?1 & ! humiliat+ tru? 0 n discov]$ until ye>s aft]w>d4#acg ,"o notewor?y & int]e/+ fact relat+ to num]al nom5clature is ! v>iation 9 =m :i* words ( ?is class und]go :5 appli$ to diff]5t classes ( objects4 ,to "o accu/om$ z we are to absolute & unv>y+ =ms = num]als1 ?is seems at fir/ a novel & almo/ unacc\ntable l+ui/ic freak4 ,b x is n uncommon among unciviliz$ races1 & is ext5sively employ$ by s highly enlight5$ a p1 ev51 z ! ,japanese4 ,?is v>iation 9 =m is 9 no way analog\s to t produc$ by inflectional *anges1 su* z occur 9 ,hebrew1 ,greek1 ,lat91 etc4 ,x is suffici5t 9 _m cases to produce almo/ an entire *ange 9 ! =m ( ! ^w2 or to result 9 comp\nds :i* require close scrut9y = ! detection ( ! orig9al root4 ,= example1 9 ! ,c>ri]1 "o ( ! ,dn dialects ( we/]n ,canada1 ! ^w ?a means #c ?+s2 ?ane1 #c p]sons2 t1 #c times2 ?ato51 9 #c places2 ?auh1 9 #c ways2 ?ailtoh1 all ( ! #c ?+s2 ?ahoeltoh1 all ( ! #c p]sons2 & ?ahultoh1 all ( ! #c times4#ach ,9 ! ,tsim%ian language ( ,briti% ,columbia we f9d sev5 di/9ct sets ( num]als :i* are us$ = v>i\s classes ( objects t are c\nt$4 ,! fir/ set is us$ 9 c\nt+ :]e !re is no def9ite object ref]r$ to2 ! second class is us$ = c\nt+ flat objects & animals2 ! ?ird = c\nt+ r\nd objects & divisions ( "t2 ! f\r? = c\nt+ m52 ! fif? = c\nt+ long objects1 ! num]als be+ compos$ ) kan1 tree2 ! six? = c\nt+ canoes2 & ! sev5? = measures4 ,! la/ seem to be compos$ ) anon1 h&4#aci ,! fir/ t5 num]als ( ea* ( ^! classes is giv5 9 ! foll[+ table3 ---------------------------------------- --------------------------------------- ,no4 ,c\nt+ ,flat ,r\nd ,m5 ,long ,canoes ,measures ,objects ,objects ,objects ---------------------------------------- --------------------------------------- #a gyak gak g'erel k'al k'awutskank'amaet k'al #b t'epqat t'epqat g\pel t'epqadal gaopskan g'alpeeltkgulbel #c guant guant gutle gulal galtskan galtskantk guleont #d tqalpq tqalpq tqalpq tqalpqdal tqaapskan tqalpqsk tqalpqalont #e kctonckctonckctonckc5ecal k'eto5tskankctoonsk kctonsilont #f k'alt k'alt k'alt k'aldal k'aoltskan k'altk k'aldelont #g t'epqalt t'epqalt t'epqalt t'epqaldalt'epqaltskant'epqaltk t'epqaldelont #h gu&alt yuktalt yuktalt yuktleadalek'tla$skanyuktaltk yuktaldelont #i kctemac kctemac kctemac kctemacal kctemae/kankctemack kctemasilont #aj gy'ap gy'ap kpeel kpal kpeetskangy'apsk kpeont ---------------------------------------- --------------------------------------- ,rem>kable z ?is li/ may appe>1 x is by no means z ext5sive z t d]iv$ f _m ( ! o!r ,briti% ,columbian tribes4 ,! num]als ( ! ,%u%wap1 ,/latlumh1 ,okanak51 & o!r languages ( ?is region exi/ 9 sev]al diff]5t =ms1 & c also be modifi$ by any ( ! innum]able suffixes ( ^! tongues4#adj ,to illu/rate ! almo/ illimitable numb] ( sets t may be =m$1 a table is giv5 ( a few classes1 tak5 f ! ,heiltsuk dialect4#ada ,x appe>s f ^! examples t ! numb] ( classes is unlimit$4 ---------------------------------------- ------------------------ ,"o4 ,two4 ,?ree4 ---------------------------------------- ------------------------ ,animate4 m5ok maalok yutuk ,r\nd4 m5skam masem yutqsem ,long4 m5ts'ak mats'ak yututs'ak ,flat4 m5aqsa matlqsa yutqsa ,day4 op'enequls matlp'enequls yutqp'enequls ,fa?om4 op'enkh matlp'enkh yutqp'enkh ,gr\p$ toge!r4 ---- matl\tl yut\tl ,gr\ps ( objects4 nemtsmots'utlmatltsmots'utlyutqtsmots'ut l ,fill$ cup4 m5qtlala matl'aqtlala yutqtlala ,empty cup4 m5qtla matl'aqtla yutqtla ,full box4 m5skamala masemala yutqsemala ,empty box4 m5skam masem yutqsem ,load$ canoe4 m5tsake mats'ake yututs'ake ,canoe ) crew4 m5ts'akis mats'akla yututs'akla ,toge!r on bea*4 ---- maalis ---- ,toge!r 9 h\se1 etc4---- maalitl ---- ---------------------------------------- ------------------------ ,v>iation 9 num]al =ms su* z is exhibit$ 9 ! above tables is n conf9$ to any "o qu>t] ( ! globe2 b x is m univ]sal among ! ,briti% ,columbian ,indians ?an among any o!r race1 & x is a m *>act]i/ic l+ui/ic peculi>ity ( ?is ?an ( any o!r region1 ei!r 9 ! ,old ,_w or 9 ! ,new4 ,x 0 to "s ext5t employ$ by ! ,aztecs1#adb & its use is curr5t among ! ,japanese2 9 ^: language ,crawfurd f9ds f\rte5 diff]5t classes ( num]als )\t exhau/+ ! li/4#adc ,9 exam9+ ! num]als ( diff]5t languages x w be f\nd t ! t5s ( any ord9>y decimal scale are =m$ 9 ! same mann] z 9 ,engli%4 ,tw5ty is simply #b times #aj2 #cj is #c times #aj1 & s on4 ,! ^w times is1 ( c\rse1 n express$1 any m ?an 9 ,engli%2 b ! expressions briefly are1 #b t5s1 #c t5s1 etc4 ,b a s+ul> exception to ?is me?od is pres5t$ by ! ,hebrew1 & o!r ( ! ,semitic languages4 ,9 ,hebrew ! ^w = #bj is ! plural ( ! ^w = #aj2 & #cj1 #dj1 #ej1 etc4 to #ij are plurals ( #c1 #d1 #e1 #f1 #g1 #h1 #i4 ,^! num]als are z foll[s3#add #aj1 es]1 #bj1 es]im1 #c1 %alo%1 #cj1 %alo%im1 #d1 arba1 #dj1 arbaim1 #e1 *ame%1 #ej1 *ami%%im1 #f1 %e%1 #fj1 %e%%im1 #g1 %eba1 #gj1 %ibim1 #h1 %emoneh #hj1 %emonim1 #i1 te%a1 #ij1 ti%im4 ,! same =mation appe>s 9 ! num]als ( ! anci5t ,pho5icians1#ade & seems1 inde$1 to be a well-m>k$ *>act]i/ic ( ! v>i\s bran*es ( ?is division ( ! ,caucasian race4 ,an analog\s me?od appe>s 9 ! =mation ( ! t5s 9 ! ,bisayan1#adf "o ( ! ,malay num]al scales1 :]e #cj1 #dj1 444 #ij1 are con/ruct$ f #c1 #d1 444 #i1 by add+ ! t]m9ation -an4 ,no m int]e/+ contribution has ev] be5 made to ! lit]ature ( num]al nom5clature ?an t 9 :i* ,dr4 ,trumbull embodies ! results ( 8 s*ol>ly rese>* among ! languages ( ! native ,indian tribes ( ?is c\ntry4#adg ,z might be expect$1 we are ev]y:]e confront$ ) a digital orig91 direct or indirect1 9 ! great body ( ! words exam9$4 ,b x is cle>ly %[n t su* a d]ivation _c be e/abli%$ = all num]als2 & evid5ce collect$ by ! mo/ rec5t rese>* fully sub/antiates ! position tak5 by ,dr4 ,trumbull4 ,ne>ly all ! d]ivations e/abli%$ are su* z to rem9d u ( ! mean+s we h already se5 recurr+ 9 "o =m or ano!r 9 language aft] language4 ,five is ! end ( ! f+] c\nt on "o h&--z1 ! ,micmac nan1 & ,mohegan nunon1 gone1 or sp5t2 ! ,pawnee sihuks1 h&s half2 ! ,dakota zaptan1 h& turn$ d[n2 & ! ,massa*usetts napanna1 on "o side4 ,t5 is ! end ( ! f+] c\nt1 b is n always express$ by ! bo? h&s =mula s commonly met )4 ,! ,cree t]m = ?is numb] is mitatat1 no fur!r2 & ! correspond+ ^w 9 ,delaw>e is m'tell51 no m4 ,! ,dakota #aj is1 l its #e1 a /raight5+ out ( ! f+]s :i* h be5 turn$ ov] 9 c\nt+1 or wick*emna1 spread out unb5t4 ,! same is true ( ! ,hidatsa pitika1 :i* signifies a smoo?+ out1 or /raight5+4 ,! ,pawnee #d1 skitiks1 is unusual1 signify+ z x does all ! f+]s1 or m prop]ly1 ! f+]s ( ! h&4 ,! same mean+ atta*es to ?is num]al 9 a few o!r languages also1 & rem9ds "o ( ! habit "s p h ( beg9n+ to c\nt on ! =ef+] & proce$+ f !re to ! little f+]4 ,c ?is h be5 ! habit ( ! tribes 9 "q8 ,a sugge/ion ( ! same nature is made by ! ,ill9ois & ,miami words = #h1 p>>e & polane1 :i* signify ne>ly end$4 ,six is almo/ always digital 9 orig91 ?\gh ! d]ivation may be indirect1 z 9 ! ,ill9ois kakat*ui1 pass+ beyond ! middle2 & ! ,dakota %akpe1 #a 9 addition4 ,"s ( ^! significations are well mat*$ by num]als f ! ,ewe scales ( we/]n ,africa1 :]e we f9d ! foll[+3#adh #a4 de a go+1 i4e4 a beg9n+4 7,cf4 ! ,zui tp9te1 tak5 to />t )47 #c4 eto ! fa!r 7f ! middle1 or longe/ f+]74 #f4 ade ! o!r go+4 #i4 asieke p>t+ ) ! h&s4 #aj4 ewo done4 ,9 /udy+ ! names = #b we are at once l$ away f a /rictly digital orig9 = ! t]ms by :i* ?is numb] is express$4 ,^! names seem to come f f\r diff]5t s\rces3 7#a7 roots d5ot+ sep>ation or di/9ction2 7#b7 lik5ess1 equality1 or opposition2 7#c7 addition1 i4e4 putt+ to1 or putt+ )2 7#d7 c\pl+1 pair+1 or mat*+4 ,!y are (t5 relat$ to1 & p]haps d]iv$ f1 names ( natural pairs1 z feet1 h&s1 eyes1 arms1 or w+s4 ,9 ! ,dakota & ,algonk9 dialects #b is almo/ always relat$ to arms or h&s1 & 9 ! ,a?apaskan to feet4 ,b ! relation%ip is t ( common orig91 r ?an ( d]ivation f ^! pair-names4 ,9 ! ,puri & ,hott5tot languages1 #b & h& are closely alli$2 :ile 9 ,sanskrit1 #b may be express$ by any "o ( ! words k>a1 h&1 bahu1 arm1 pak%a1 w+1 or netra1 eye4#adi ,/ill m remote f any?+ digital 9 _! d]ivation are ! foll[+1 tak5 at r&om f a v great numb] ( examples t might be cit$ to illu/rate ?is po9t4 ,! ,ass9ibo9es call #g1 %ak ko we1 or u %e nah1 ! odd numb]4#aej ,! ,cr[ #a1 hamat1 signifies ! lea/2#aea ! ,mississaga #a1 pecik1 a v small ?+4#aeb ,9 ,javanese1 ,malay1 & ,manadu1 ! words = #a1 :i* are respectively siji1 satu1 & sabuah1 signify #a se$1 #a pebble1 & #a fruit respectively#aec--words z natural & z mu* to be expect$ at ! beg9n+ ( a numb] scale z any f+] "n c\ld possibly be4 ,among almo/ all savage races "o =m or ano!r ( palpable ari?metic is f\nd1 su* z c\nt+ by se$s1 pebbles1 %ells1 not*es1 or knots2 & ! d]ivation ( numb] words f ^! s\rces c con/itute no gr\nd = surprise4 ,! ,m>quesan ^w = #d is pona1 knot1 f ! practice ( ty+ breadfruit 9 knots ( #d4 ,! ,maori #aj is tekau1 bun*1 or p>cel1 f ! c\nt+ ( yams & fi% by p>cels ( #aj4aed ,! ,javanese call #be1 lawe1 a ?read1 or /r+2 #ej1 ekat1 a ske9 ( ?read2 #djj1 samas1 a bit ( gold2 #hjj1 domas1 #b bits ( gold4#aee ,! ,macass> & ,butong t]m = #ajj is bilangan1 #a tale or reckon+4#aef ,! ,aztec #bj is cem pohualli1 #a c\nt2 #djj is c5tzontli1 #a hair ( ! head2 & #hjjj is xiquipilli1 sack4#aeg ,?is sack 0 ( su* a size z to conta9 #hjjj cacao nibs1 or gra9s1 h5ce ! d]ivation ( ! ^w 9 its num]al s5se is p]fectly natural4 ,9 ,japanese we f9d a l>ge numb] ( t]ms :i*1 z appli$ to ! diff]5t units ( ! numb] scale1 seem almo/ purely fanciful4 ,^! words1 ) _! mean+s z giv5 by a ,japanese lexicon1 are z foll[s3 #aj1jjj1 or #ajd1 mn enorm\s numb]4 #ajh1 oku a comp\nd ( ! words man & m9d4 #ajab1 *io indication1 or symptom4 #ajaf1 kei capital city4 #ajbj1 si a t]m ref]r+ to gra9s4 #ajbd1 owi ---- #ajbh1 jio ext5t ( l&4 #ajcb1 ko canal4 #ajcf1 kan "s k9d ( a body ( wat]4 #ajdj1 sai ju/ice4 #ajdd1 sa support4 #ajdh1 kioku limit1 or m /rictly1 ultimate4 4#jab1 r9 ---- 4#jac1 mo hair 7( "s animal74 4#jad1 %i ?read4 ,9 addition to ^!1 "s ( ! l[] fractional values are describ$ by words mean+ v small1 v f9e ?read1 s& gra91 du/1 & v vague4 ,tak5 altoge!r1 ! ,japanese numb] sy/em is ! mo/ rem>kable ,i h ev] exam9$1 9 ! ext5t & v>iety ( ! high] num]als ) well-def9$ descriptive names4 ,mo/ ( ! t]ms employ$ are su* z to defy any attempt to trace ! process ( reason+ :i* l$ to _! adoption4 ,x is n improbable t ! *oice 01 9 "s ( ^! cases at lea/1 ei!r accid5tal or arbitr>y2 b /ill1 ! *anges 9 ^w mean+s :i* occur ) ! lapse ( "t may h diff]5tiat$ significations orig9ally alike1 until no trace ( k9%ip w\ld appe> to ! casual obs]v]4 ,our num]als score & gross are nev] ?\ght ( z hav+ any orig9al relation to :at is convey$ by ! o!r mean+s :i* atta* to ^! words4 ,b ! orig9 ( ea*1 :i* is easily trac$1 %[s t1 9 ! beg9n+1 !re exi/$ a well-def9$ reason = ! selection ( ^!1 r ?an o!r t]ms1 = ! numb]s !y n[ describe4 ,possibly ^! rem>kable ,japanese t]ms may be acc\nt$ = 9 ! same way1 ?\gh ! supposition is1 = "s reasons1 q improbable4 ,! same may be said = ! ,malagasy #ajjj1 al9a1 :i* also means night1 & ! ,hebrew #f1 %e%1 :i* has ! additional signification :ite m>ble1 & ! /ray exceptions :i* n[ & !n come to ! light 9 ?is or t language4 ,su* t]ms z ^! may admit ( "s logical explanation1 b = ! great mass ( num]als ^: primitive mean+s c be trac$ at all1 no explanation :atev] is ne$$2 ! words are self-explanatory1 z ! examples already cit$ %[4 ,a few additional examples ( natural d]ivation may /ill fur!r emphasize ! po9t j discuss$4 ,9 ,bamb>ese ! ^w = #aj1 tank1 is d]iv$ directly f adang1 to c\nt4#aeh ,9 ! language ( ,mota1 "o ( ! isl&s ( ,melanesia1 #ajj is mel nol1 us$ & done )1 ref]r+ to ! leaves ( ! cycas tree1 ) :i* ! c\nt _h be5 c>ri$ on4#aei ,9 _m o!r ,melanesian dialects#afj #ajj is rau1 a bran* or leaf4 ,9 ! ,torres ,/raits we f9d ! same numb] express$ by na won1 ! close2 & 9 ,eromanga x is n>olim n>olim 7#b #e77b #e74afa ,?is comb9ation des]ves rem>k only because ( ! involv$ =m :i* seems to h be5 requir$ = ! expression ( s small a numb] z #ajj4 ,a comp\nd in/ead ( a simple t]m = any high] unit is nev] to be wond]$ at1 s rude are "s ( ! savage me?ods ( express+ numb]2 b two fives 7times7 two fives is c]ta9ly rem>kable4 ,"s =m l t employ$ by ! ,nusqually#afb ( ,puget ,s\nd = #ajjj1 i4e4 paduts-subqut*e1 t5 hundr$1 is m 9 accordance ) primitive me?od4 ,b we are equally likely to f9d su* descriptive phrases = ?is num]al z ! dor paka1 banyan roots1 ( ! ,torres ,isl&s2 rau na hai1 leaves ( a tree1 ( ,vaturana2 or udolu1 all1 ( ! ,fiji ,isl&s4 ,& two curi\s phrases = #ajjj are ^? ( ! ,banks' ,isl&s1 t> mataqelaqela1 eye bl9d ?\s&1 i4e4 _m beyond c\nt2 & ( ,malanta1 w>ehune huto1 opossum's hairs1 or idumie "o1 c\nt ! s&4#afc ,! native languages ( ,india1 ,?ibet1 & portions ( ! ,indian ar*ipelago furni% u ) abundant in/ances ( ! =mation ( second>y num]al scales1 :i* 7 us$ only = special purposes1 & )\t 9 any way int]f]+ ) ! use ( ! numb] words already 9 use4 ,?us ! s*ol>s ( ,india1 ages ago1 select$ a set ( words = a memoria te*nica1 9 ord] to record dates & numb]s4 ,^! words !y *ose = reasons :i* are /ill 9 great measure evid5t2 ?us 'moon' or 'e>?' express$ #a1 !re be+ b "o ( ea*2 #b might be call$ 'eye1' 'w+1' 'arm1' 'jaw1' z go+ 9 pairs2 = #c !y said ',rama1' 'fire1' or 'quality1' !re be+ consid]$ to be ?ree ,ramas1 ?ree k9ds ( fire1 ?ree qualities 7guna72 = #d 7 us$ 'v$a1' 'age1' or 'ocean1' !re be+ f\r ( ea* recogniz$2 'season' = #f1 because !y reckon$ six seasons2 'sage' or 'v[el1' = #g1 f ! sev5 sages & ! sev5 v[els2 & s on ) high] numb]s1 'sun' = #ab1 because ( 8 twelve annual d5om9ations1 or 'zodiac' f 8 twelve signs1 & 'nail' = #bj1 a ^w incid5tally br++ 9 f+] notation4 ,z ,sanskrit is v ri* 9 synonyms1 & z ev5 ! num]als !mselves might be us$1 x became v easy to draw up phrases or nons5se v]ses to record s]ies ( numb]s by ?is sy/em ( artificial memory4#afd ,m ?an en\gh has be5 said to %[ h[ baseless is ! claim t all num]al words are d]iv$1 ei!r directly or indirectly1 f ! names ( f+]s1 h&s1 or feet4 ,connect$ ) ! orig9 ( ea* numb] ^w !re may be "s metaphor1 :i* _c always be di/9ctly trac$2 & :]e ! metaphor 0 born ( ! h& or ( ! foot1 we inevitably associate x ) ! practice ( f+] c\nt+4 ,b races z fond ( metaphor & ( l+ui/ic embelli%m5t z are ^? ( ! ,ea/1 or z are our ,am]ican ,indians ev51 might readily resort to "s o!r s\rce ?an t furni%$ by ! memb]s ( ! human body1 :5 9 want ( a t]m ) :i* to describe ! #e1 #aj1 or any o!r numb] ( ! num]al scale !y 7 unconsci\sly =m+4 ,t ! fir/ numb]s ( a num]al scale are usually d]iv$ f o!r s\rces1 we h "s reason to believe2 b t all above #b1 #c1 or at mo/ #d1 are almo/ univ]sally ( digital orig9 we mu/ admit4 ,exception %\ld prop]ly be made ( high] units1 say #ajjj or any?+ great]1 :i* c\ld n be expect$ to con=m to any law ( d]ivation gov]n+ ! fir/ few units ( a sy/em4 ,collect+ toge!r & comp>+ ) "o ano!r ! great mass ( t]ms by :i* we f9d any numb] express$ 9 diff]5t languages1 &1 :ile admitt+ ! great div]sity ( me?od practis$ by diff]5t tribes1 we obs]ve c]ta9 resemblances :i* 7 n at fir/ suppos$ to exi/4 ,! v>i\s mean+s ( #a1 :]e !y c be trac$ at all1 clu/] into a little gr\p ( significations ) :i* at la/ we come to associate ! idea ( unity4 ,simil>ly ( #b1 or #e1 or #aj1 or any "o ( ! little b& :i* does picket duty = ! advance gu>d ( ! great ho/ ( numb] words :i* are to foll[4 ,a c>eful exam9ation ( ! fir/ decade w>rants ! ass]tion t ! probable mean+ ( any "o ( ! units w be f\nd 9 ! li/ giv5 bel[4 ,! words select$ are int5d$ m]ely to s]ve z indications ( ! ?\ght und]ly+ ! savage's *oice1 & n necess>ily z ! exact t]m by means ( :i* he describes 8 numb]4 ,only ! commone/ mean+s are includ$ 9 ! tabulation "h giv54 #a exi/5ce1 piece1 gr\p1 beg9n+4 #b repetition1 division1 natural pair4 #c collection1 _m1 two-"o4 #d two twos4 #e h&1 gr\p1 division1 #f five-"o1 two ?rees1 second "o4 #g five-two1 second two1 ?ree f t54 #h five-?ree1 second ?ree1 two f\rs1 two f t54 #i five-f\r1 ?ree ?rees1 "o f t54 #aj "o 7gr\p71 two fives 7h&s71 half a man1 "o man4 #ae t5-five1 "o foot1 ?ree fives4 #bj two t5s1 "o man1 two feet4#afe ,,*apt] ,v4 ,,miscellane\s ,,numb] ,,bases4 ,9 ! developm5t & ext5sion ( any s]ies ( numb]s into a sy/ematic arrangem5t to :i* ! t]m sy/em may be appli$1 ! fir/ & mo/ indisp5sable /ep is ! selection ( "s numb] :i* is to s]ve z a base4 ,:5 ! savage beg9s ! process ( c\nt+ he inv5ts1 "o aft] ano!r1 names ) :i* to designate ! successive /eps ( 8 num]ical j\rney4 ,at fir/ !re is no attempt at def9it5ess 9 ! description he gives ( any consid]able numb]4 ,if he _c %[ :at he means by ! use ( 8 f+]s1 or p]haps by ! f+]s ( a s+le h&1 he unhesitat+ly passes x by1 call+ x _m1 heap1 innum]able1 z _m z ! leaves on ! trees1 or some?+ else equally expressive & equally indef9ite4 ,b ! "t comes at la/ :5 a great] degree ( exactness is requir$4 ,p]haps ! numb] #aa is to be indicat$1 & indicat$ precisely4 ,a fre% m5tal ef=t is requir$ ( ! ignorant *ild ( nature2 & ! result is all ! f+]s & "o m1 bo? h&s & "o m1 "o on ano!r c\nt1 or "s equival5t circumlocution4 ,if he has an indep5d5t ^w = #aj1 ! result w be simply t5-"o4 ,:5 ?is /ep has be5 tak51 ! base is e/abli%$4 ,! savage has1 ) entire unconsci\sness1 made all 8 subsequ5t progress dep5d5t on ! numb] #aj1 or1 9 o!r words1 he has e/abli%$ #aj z ! base ( 8 numb] sy/em4 ,! process j indicat$ may be gone ?r\gh ) at #e1 or at #bj1 ?us giv+ u a qu9>y or a vigesimal1 or1 m probably1 a mix$ sy/em2 &1 9 r>e in/ances1 "s o!r numb] may s]ve z ! po9t ( dep>ture f simple into comp\nd num]al t]ms4 ,b ! g5]al idea is always ! same1 & only ! details ( =mation are f\nd to diff]4 ,)\t ! e/abli%m5t ( "s base any sy/em ( numb]s is impossible4 ,! savage has no means ( keep+ track ( 8 c\nt unless he c at ea* /ep ref] himself to "s well-def9$ mile/one 9 8 c\rse4 ,if1 z has be5 po9t$ out 9 ! =ego+ *apt]s1 confusion results :5ev] an attempt is made to c\nt any numb] :i* c>ries him above #aj1 x mu/ at once appe> t progress beyond t po9t w\ld be r5d]$ _m times m difficult if x 7 n = ! fact t1 at ea* new /ep1 he has only to indicate ! di/ance he has progress$ beyond 8 base1 & n ! di/ance f 8 orig9al />t+-po9t4 ,"s idea may1 p]haps1 be ga9$ ( ! nature ( ?is difficulty by imag9+ ! numb]s ( our ord9>y scale to be repres5t$1 ea* "o by a s+le symbol diff]5t f t us$ to d5ote any o!r numb]4 ,h[ long w\ld x take ! av]age intellect to ma/] ! fir/ #ej ev51 s t ea* numb] c\ld )\t hesitation be indicat$ by its appropriate symbol8 ,aft] ! fir/ #ej 7 once ma/]$1 :at ( ! next #ej8 & ! next8 & ! next8 & s on4 ,! acquisition ( a scale = :i* we _h no o!r means ( expression ?an t j describ$ w\ld be a matt] ( ! extreme/ difficulty1 & c\ld nev]1 save 9 ! mo/ exceptional circum/ances1 progress beyond ! atta9m5t ( a limit ( a few hundr$4 ,if ! v>i\s numb]s 9 "q 7 designat$ by words in/ead ( by symbols1 ! difficulty ( ! task w\ld be /ill fur!r increas$4 ,h5ce1 ! e/abli%m5t ( "s numb] z a base is n only a matt] ( ! v highe/ conv5i5ce1 b ( absolute necessity1 if any save ! fir/ few numb]s are ev] to be us$4 ,9 ! selection ( a base1--( a numb] f :i* he makes a fre% />t1 & to :i* he ref]s ! next /eps 9 8 c\nt1--! savage simply foll[s nature :5 he *ooses #aj1 or p]haps #e or #bj4 ,b x is a matt] ( ! greate/ int]e/ to f9d t o!r numb]s h1 9 exceptional cases1 be5 us$ = ?is purpose4 ,two c5turies ago ! di/+ui%$ philosoph] & ma!matician1 ,leibnitz1 propos$ a b9>y sy/em ( num]ation4 ,! only symbols ne$$ 9 su* a sy/em w\ld be #j & #a4 ,! numb] :i* is n[ symboliz$ by ! figure #b w\ld be repres5t$ by #aj2 :ile #c1 #d1 #e1 #f1 #g1 #h1 etc41 w\ld appe> 9 ! b9>y notation z #aa1 #ajj1 #aja1 #aaj1 #aaa1 #ajjj1 etc4 ,! difficulty ) su* a sy/em is t x rapidly gr[s cumb]some1 requir+ ! use ( s _m figures = indicat+ any numb]4 ,b ,leibnitz f\nd 9 ! repres5tation ( all numb]s by means ( ! two digits #j & #a a fitt+ symbolization ( ! creation out ( *aos1 or no?+1 ( ! entire univ]se by ! p[] ( ! ,deity4 ,9 commemoration ( ?is inv5tion a m$al 0 /ruck be>+ on ! obv]se ! words ,num]o ,deus imp>i gaudet1 & on ! rev]se1 ,omnibus ex nihilo duc5dis sufficit ,unum4#aff ,?is curi\s sy/em seems to h be5 reg>d$ ) ! greate/ affection by its inv5tor1 :o us$ e endeav\r 9 8 p[] to br+ x to ! notice ( s*ol>s & to urge its claims4 ,b x appe>s to h be5 receiv$ ) entire indiff]5ce1 & to h be5 reg>d$ m]ely z a ma!matical curiosity4 ,unkn[n to ,leibnitz1 h[ev]1 a b9>y me?od ( c\nt+ actually exi/$ dur+ t age2 & x is only at ! pres5t "t t x is becom+ ext9ct4 ,9 ,au/ralia1 ! cont95t t is unique 9 its flora1 its fauna1 & its g5]al topography1 we f9d also ?is anomaly among me?ods ( c\nt+4 ,! natives1 :o are to be class$ among ! l[e/ & ! lea/ intellig5t ( ! aborig9al races ( ! _w1 h numb] sy/ems ( ! mo/ rudim5t>y nature1 & ev9ce a decid$ t5d5cy to c\nt by twos4 ,?is peculi>ity1 :i* 0 to "s ext5t %>$ by ! ,tasmanians1 ! isl& tribes ( ! ,torres ,/raits1 & o!r aborig9al races ( t region1 has by "s writ]s be5 reg>d$ z peculi> to _! "p ( ! _w2 z ?\gh a b9>y numb] sy/em 7 n to be f\nd else:]e4 ,?is attempt to make out ( ! rude & unusual me?od ( c\nt+ :i* obta9$ among ! ,au/ralians a racial *>act]i/ic is h>dly ju/ifi$ by full] inve/igation4 ,b9>y numb] sy/ems1 :i* are giv5 9 full on ano!r page1 are f\nd 9 ,s\? ,am]ica4 ,"s ( ! ,dravidian scales are b9>y2#afg & ! m>k$ pref]5ce1 n infrequ5tly obs]v$ among savage races1 = c\nt+ by pairs1 is 9 itself a suffici5t refutation ( ?is !ory4 ,/ill x is an unque/ionable fact t ?is b9>y t5d5cy is m pron\nc$ among ! ,au/ralians ?an among any o!r ext5sive numb] ( k9dr$ races4 ,!y seldom c\nt 9 words above #d1 & almo/ nev] z high z #g4 ,"o ( ! mo/ c>eful obs]v]s among !m expresses 8 d\bt z to a native's ability to discov] ! loss ( two p9s1 if he 7 fir/ %[n sev5 p9s 9 a r[1 & !n two 7 remov$ )\t 8 k4#afh ,b he believes t if a s+le p9 7 remov$ f ! sev51 ! ,blackfell[ w\ld become consci\s ( its loss4 ,?is is due to 8 habit ( c\nt+ by pairs1 :i* enables him to discov] :e!r any numb] )9 reasonable limit is odd or ev54 ,"s ( ! negro tribes ( ,africa1 & ( ! ,indian tribes ( ,am]ica1 h ! same habit4 ,progression by pairs may seem to "s tribes z natural z progression by s+le units4 ,x c]ta9ly is n at all r>e2 & 9 ,au/ralia its influ5ce on spok5 numb] sy/ems is mo/ app>5t4 ,any numb] sy/em :i* passes ! limit #aj is reasonably sure to h ei!r a qu9>y1 a decimal1 or a vigesimal /ructure4 ,a b9>y scale c\ld1 z x is develop$ 9 primitive languages1 h>dly ext5d to #bj1 or ev5 to #aj1 )\t becom+ exce$+ly cumb]some4 ,a b9>y scale inevitably sugge/s a wret*$ly l[ degree ( m5tal developm5t1 :i* /&s 9 ! way ( ! =mation ( any numb] scale wor?y to be dignifi$ by ! "n ( sy/em4 ,take1 = example1 "o ( ! dialects f\nd among ! we/]n tribes ( ! ,torres ,/raits1 :]e1 9 g5]al1 b two num]als are f\nd to exi/4 ,9 ?is dialect ! me?od ( c\nt+ is3#afi #a4 urapun4 #b4 okosa4 #c4 okosa urapun #b-a4 #d4 okosa okosa #b-b4 #e4 okosa okosa urapun #b-b-a4 #f4 okosa okosa okosa #b-b-b4 ,any?+ above #f !y call ras1 a lot4 ,= ! sake ( uni=mity we may speak ( ?is z a sy/em4 ,b 9 s do+1 we give to ! legitimate mean+ ( ! ^w a sev]e /ra94 ,! cu/oms & modes ( life ( ^! p are n su* z to require ! use ( any save ! scanty li/ ( numb]s giv5 above2 & _! m5tal pov]ty prompts !m to call #c1 ! fir/ numb] above a s+le pair1 #b-a4 ,9 ! same way1 #d & #f are respectively #b pairs & #c pairs1 :ile #e is #a m ?an #b pairs4 ,five objects1 h[ev]1 !y sometimes d5ote by urapuni-getal1 #a h&4 ,a precisely simil> condition is f\nd to prevail respect+ ! ari?metic ( all ! ,au/ralian tribes4 ,9 "s cases only two num]als are f\nd1 & 9 o!rs ?ree4 ,b 9 a v great numb] ( ! native languages ( t cont95t ! c\nt proce$s by pairs1 if inde$ x proce$s at all4 ,h5ce we at once reject ! !ory t ,au/ralian ari?metic1 or ,au/ralian c\nt+1 is ess5tially peculi>4 ,x is simply a legitimate result1 su* z might be look$ = 9 any "p ( ! _w1 ( ! b>b>ism 9 :i* ! races ( t qu>t] ( ! _w 7 sunk1 & 9 :i* !y 7 cont5t to live4 ,! foll[+ examples ( ,au/ralian & ,tasmanian numb] sy/ems %[ h[ scanty 0 ! num]ical ability possess$ by ^! tribes1 & illu/rate fully _! t5d5cy to c\nt by twos or pairs4 ,,murray ,,riv]4#agj #a4 enea4 #b4 pet*eval4 #c4 pet*eval5ea #b-a4 #d4 pet*eval peteheval #b-b4 ,,m>\ra4 #a4 nukee4 #b4 b>kolo4 #c4 b>kolo nuke #b-a4 #d4 b>kolo b>kolo #b-b4 ,,lake ,,kopp]amana4 #a4 ng]na4 #b4 mondroo4 #c4 b>kooloo4 #d4 mondroo mondroo #b-b4 ,,mort ,,n\l>4 #a4 gambod54 #b4 b5g]oo4 #c4 b5g]oganmel #b-a4 #d4 b5g]oovor b5g]oo #b #b4 ,,wimm]a4 #a4 keyap4 #b4 pollit4 #c4 pollit keyap #b-a4 #d4 pollit pollit #b-b4 ,,popham ,,bay4 #a4 motu4 #b4 lawitb>i4 #c4 lawitb>i-motu #b-a4 ,,kamil>oi4#aga #a4 mal4 #b4 bul>r4 #c4 guliba4 #d4 bul>rbul>r #b-b4 #e4 bulaguliba #b-c4 #f4 gulibaguliba #c-c4 ,,port ,,ess+ton4#agb #a4 erad4 #b4 n>g>ik4 #c4 n>g>ikel]ad #b-a4 #d4 n>g>ikn>g>ik #b-b4 ,,w>rego4 #a4 t>l9a4 #b4 b>kalo4 #c4 t>l9a b>kalo #a-b4 ,,crock] ,,isl&4 #a4 roka4 #b4 orialk4 #c4 orialk]>oka #b-a4 ,,w>rior ,,isl&4#agc #a4 woorapoo4 #b4 ocas>a4 #c4 ocas>a woorapoo #b-a4 #d4 ocas>a ocas>a #b-b4 ,,dippil4#agd #a4 kalim4 #b4 bull]4 #c4 boppa4 #d4 bull] gira bull] #b #b4 #e4 bull] gira bull] kalim #b #b #a4 ,,fraz]',s ,,isl&4#age #a4 kalim4 #b4 bulla4 #c4 goorbunda4 #d4 bulla-bulla #b-b4 ,,moreton',s ,,bay4#agf #a4 kunn]4 #b4 budela4 #c4 muddan4 #d4 budela b]delu #b-b4 ,,enc\nt] ,,bay4#agg #a4 yamalaitye4 #b4 n+5k4 #c4 nepald>4 #d4 kuko kuko #b-b1 or pair pair4 #e4 kuko kuko ki #b-b-a4 #f4 kuko kuko kuko #b-b-b4 #g4 kuko kuko kuko ki #b-b-b-a4 ,,adelaide4#agh #a4 kuma4 #b4 purlaitye1 or bula4 #c4 m>nkutye4 #d4 y]a-bula pair #b4 #e4 y]a-bula kuma pair #b-a4 #f4 y]a-bula purlaitye pair #b4b4 ,,wiraduroi4#agi #a4 numbai4 #b4 bula4 #c4 bula-numbai #b-a4 #d4 bungu _m4 #e4 bungu-galan v _m4 ,,wirri-,,wirri4#ahj #a4 mooray4 #b4 booll>4 #c4 bel> mooray #b-a4 #d4 booll> booll> #b-b4 #e4 mongoonballa4 #f4 mongun mongun4 ,,coop]',s ,,creek4#aha #a4 goona4 #b4 b>koola4 #c4 b>koola goona #b-a4 #d4 b>koola b>koola #b-b4 ,,b\rke1 ,,d>l+ ,,riv]4#ahb #a4 nee*a4 #b4 boolla4 #d4 boolla nee*a #b-a4 #c4 boolla boolla #b-b4 ,,murray ,,riv]1 ,n4,w4 ,,b5d4#ahc #a4 mata4 #b4 rankool4 #c4 rankool mata #b-a4 #d4 rankool rankool #b-b4 ,,yit-,,?a4#ahd #a4 mo4 #b4 ?ral4 #c4 ?ral mo #b-a4 #d4 ?ral ?ral #b-b4 ,,port ,,d>w94#ahe #a4 kulagook4 #b4 kalletillick4 #c4 kalletillick kulagook #b-a4 #d4 kalletillick kalletillick #b-b4 ,,*ampion ,,bay4#ahf #a4 kootea4 #b4 woo!ra4 #c4 woo!ra kootea #b-a4 #d4 woo!ra woo!ra #b-b4 ,,bely&o ,,riv]4#ahg #a4 wog94 #b4 bool]oo4 #c4 bool]oo wog9 #b-a4 #d4 bool]oo bool]oo #b-b4 ,,w>rego ,,riv]4 #a4 onk]a4 #b4 paulludy4 #c4 paulludy onk]a #b-a4 #d4 paulludy paulludy #b-b4 ,,ri*mond ,,riv]4 #a4 yabra4 #b4 booroora4 #c4 booroora yabra #b-a4 #d4 booroora booroora #b-b4 ,,port ,,macqu>ie4 #a4 w>col4 #b4 bl>vo4 #c4 bl>vo w>col #b-a4 #d4 bl>vo bl>vo #b-b4 ,,hill ,,end4 #a4 miko4 #b4 bullagut4 #c4 bullagut miko #b-a4 #d4 bullagut bullagut #b-b4 ,,mon]oo #a4 boor4 #b4 wajala1 blala4 #c4 blala boor #b-a4 #d4 wajala wajala4 ,,gonn ,,/ation4 #a4 k>p4 #b4 pellige4 #c4 pellige k>p #b-a4 #d4 pellige pellige #b-b4 ,,upp] ,,y>ra4 #a4 kaambo4 #b4 b5j]o4 #c4 b5j]o kaambo #b-b4 #d4 b5j]o on b5j]o #b-b4 ,,omeo4 #a4 bore4 #b4 w>kolala4 #c4 w>kolala bore #b-a4 #d4 w>kolala w>kolala #b-b4 ,,sn[y ,,riv]4 #a4 kootook4 #b4 boolong4 #c4 booloom ca?a kootook #b #a4 #d4 booloom ca?a booloom #b #b4 ,,ng>rim[ro4 #a4 w>rang54 #b4 platir4 #c4 platir w>rang5 #b-a4 #d4 platir platir #b-b4 ,?is ,au/ralian li/ might be greatly ext5d$1 b ! scales select$ may be tak5 z repres5tative examples ( ,au/ralian b9>y scales4 ,ne>ly all ( !m %[ a /ructure too cle>ly m>k$ to require comm5t4 ,9 a few cases1 h[ev]1 ! sy/ems are to be reg>d$ r z %[+ a trace ( b9>y /ructure1 ?an z p]fect examples ( c\nt+ by twos4 ,examples ( ?is nature are especially num]\s 9 ,curr's ext5sive li/--! mo/ complete collection ( ,au/ralian vocabul>ies ev] made4 ,a few b9>y scales h be5 f\nd 9 ,s\? ,am]ica1 b !y %[ no important v>iation on ! ,au/ralian sy/ems cit$ above4 ,! only ones ,i h be5 able to collect are ! foll[+3 ,,bakairi4#ahh #a4 tokalole4 #b4 asage4 #c4 asage tokalo #b-a4 #d4 asage asage #b-b4 ,,zap>a4#ahi #a4 nuquaqui4 #b4 namisc9iqui4 #c4 haimuckum>a*i4 #d4 namisc9iqui ck>a maitacka #b #b4 #e4 namisc9iqui ck>a maitacka nuquaqui #b pairs #a4 #f4 haimuckum>acki ck>amsitacka #c pairs4 ,,ap9ages4#aij #a4 p\*i4 #b4 at cr\d\4 #c4 at cr\di-p%i #b-a4 #d4 agontad-acr\do #b-b4 ,,cotoxo4#aia #a4 ihueto4 #b4 ize4 #c4 ize-te-hueto #b-a4 #d4 ize-te-seze #b-b4 #e4 ize-te-seze-hue #b-b-a4 ,,mbayi4#aib #a4 un9itegui4 #b4 iniguata4 #c4 iniguata dugani #b ov]4 #d4 iniguata dr9iguata #b-b4 #e4 oguidi _m4 ,,tama4#aic #a4 teyo4 #b4 cayapa4 #c4 *o-teyo #b #a4 #d4 cayapa-ria #b aga94 #e4 cia-j5te h&4 ,,curetu4#aid #a4 t*udyu4 #b4 ap-adyu4 #c4 arayu4 #d4 apa$yi #b #b4 #e4 t*umupa4 ,if ! exi/5ce ( numb] sy/ems l ! above are to be acc\nt$ = simply on ! gr\nd ( l[ civilization1 "o might reasonably expect to f9d t]n>y & & quat]n>y scales1 z well z b9>y4 ,su* scales actually exi/1 ?\gh n 9 su* numb]s z ! b9>y4 ,an example ( ! =m] is ! ,betoya scale1#aie :i* runs ?us3 #a4 edoyoyoi4 #b4 edoi ano!r4 #c4 ibutu beyond4 #d4 ibutu-edoyoyoi beyond #a1 or #c-a4 #e4 ru-mocoso h&4 ,! ,kamil>oi scale1 giv5 z an example ( b9>y =mation1 is p>tly t]n>y2 & its ^w = #f1 guliba guliba1 #c-c1 is purely t]n>y4 ,an occasional t]n>y trace is also f\nd 9 numb] sy/ems o!rwise decimal or qu9>y vigesimal2 z ! dlkun\tl1 second #c1 ( ! ,haida ,indians ( ,briti% ,columbia4 ,! ,k>5s ( ,india#aif 9 a sy/em o!rwise /rictly decimal1 exhibit ! foll[+ b9>y-t]n>y-quat]n>y vag>y3 #f4 !n ?o #c #b4 #g4 !n ?o ta #c #b-a4 #h4 lwie ?o #d #b4 #i4 lwie ?o ta #d #b-a4 ,9 ! ,wokka dialect1#aig f\nd on ! ,burnett ,riv]1 ,au/ralia1 a s+le t]n>y num]al is f\nd1 ?us3 #a4 k>boon4 #b4 wombura4 #c4 *rommunda4 #d4 *rommuda k>boon #c-a4 ,in/ances ( quat]n>y num]ation are less r>e ?an are ^? ( t]n>y1 & !re is reason to believe t ?is me?od ( c\nt+ has be5 practis$ m ext5sively ?an any o!r1 except ! b9>y & ! ?ree natural me?ods1 ! qu9>y1 ! decimal1 & ! vigesimal4 ,! numb] ( f+]s on "o h& is1 exclud+ ! ?umb1 f\r4 ,possibly !re h be5 tribes among :i* c\nt+ by f\rs arose z a legitimate1 ?\gh unusual1 result ( f+] c\nt+2 j z !re are1 n[ & !n1 individuals :o c\nt on _! f+]s ) ! =ef+] z a />t+-po9t4 ,b no su* practice has ev] be5 obs]v$ among savages1 & su* !oriz+ is ! m]e/ guess-"w4 ,/ill a def9ite t5d5cy to c\nt by f\rs is sometimes met )1 :atev] be its orig94 ,quat]n>y traces are repeat$ly to be f\nd among ! ,indian languages ( ,briti% ,columbia4 ,9 describ+ ! ,columbians1 ,bancr(t says3 ,sy/ems ( num]ation are simple1 proce$+ by f\rs1 fives1 or t5s1 accord+ to ! diff]5t languages4444#aih ,! same pref]5ce = f\r is said to h exi/$ 9 primitive times 9 ! languages ( ,c5tral ,asia1 & t ?is =m ( num]ation1 result+ 9 scores ( #af & #fd1 0 a developm5t ( f+] c\nt+4#aii ,9 ! ,hawaiian & a few o!r languages ( ! isl&s ( ! c5tral ,pacific1 :]e 9 g5]al ! numb] sy/ems employ$ are decimal1 we f9d a mo/ int]e/+ case ( ! developm5t1 )9 numb] scales already well e/abli%$1 ( bo? b9>y & quat]n>y sy/ems4 ,_! orig9 seems to h be5 p]fectly natural1 b ! sy/ems !mselves mu/ h be5 p]fect$ v sl[ly4 ,9 ,tahitian1 ,r>otongan1 ,mang>evan1 & o!r dialects f\nd 9 ! neighb\r+ isl&s ( ^? s\!rn latitudes1 c]ta9 ( ! high] units1 tekau1 rau1 mano1 :i* orig9ally signifi$ #aj1 #ajj1 #ajjj1 h become d\bl$ 9 value1 & n[ /& = #bj1 #bjj1 #bjjj4 ,9 ,hawaiian & o!r dialects !y h aga9 be5 d\bl$1 & !re !y /& = #dj1 #djj1 #djjj4bjj ,9 ! ,m>quesas gr\p bo? =ms are f\nd1 ! =m] 9 ! s\!rn1 ! latt] 9 ! nor!rn1 "p ( ! ar*ipelago2 & x seems probable t "o or bo? ( ^! me?ods ( num]ation are scatt]$ some:at widely ?r\gh\t t region4 ,! orig9 ( ^! me?ods is probably to be f\nd 9 ! fact t1 aft] ! migration f ! we/ t[>d ! ea/1 ne>ly all ! objects ! natives w\ld ev] c\nt 9 any great numb]s 7 small1--z yams1 cocoanuts1 fi%1 etc41--& w\ld be mo/ conv5i5tly c\nt$ by pairs4 ,h5ce ! native1 z he c\nt$ "o pair1 two pairs1 etc41 might readily say "o1 two1 & s on1 omitt+ ! ^w pair altoge!r4 ,hav+ mu* m frequ5t occasion to employ ?is second>y ?an ! prim>y mean+ ( 8 num]als1 ! native w\ld easily all[ ! orig9al significations to fall into disuse1 & 9 ! lapse ( "t to be entirely =gott54 ,) a subsequ5t migration to ! nor?w>d a second duplication might take place1 & s produce ! s+ul> effect ( giv+ to ! same num]al ^w ?ree diff]5t mean+s 9 diff]5t p>ts ( ,oceania4 ,to illu/rate ! =m] or b9>y me?od ( num]ation1 ! ,tahuatan1 "o ( ! s\!rn dialects ( ! ,m>quesas gr\p1 may be employ$4#bja ,"h ! ord9>y num]als are3 #a4 tahi1 #aj4 onohuu4 #bj4 takau4 #bjj4 au4 #b1jjj4 mano4 #bj1jjj4 t9i4 #bj1jjj4 tufa4 #b1jjj1jjj4 pohi4 ,9 c\nt+ fi%1 & all k9ds ( fruit1 except breadfruit1 ! scale beg9s ) tauna1 pair1 & !n1 omitt+ onohuu1 !y employ ! same words aga91 b 9 a modifi$ s5se4 ,takau becomes #aj1 au #ajj1 etc42 b z ! ^w pair is und]/ood 9 ea* case1 ! value is ! same z be=e4 ,! table =m$ on ?is basis w\ld be3 #b 7units7 #a tauna #b4 #aj tauna #a takau #bj4 #aj takau #a au #bjj4 #aj au #a mano #bjjj4 #aj mano #a t9i #bj1jjj4 #aj t9i #a tufa #bjj1jjj4 #aj tufa #a pohi #b1jjj1jjj4 ,= c\nt+ breadfruit !y use pona1 knot1 z _! unit1 breadfruit usually be+ ti$ up 9 knots ( f\r4 ,takau n[ takes its ?ird signification1 #dj1 & becomes ! base ( _! breadfruit sy/em1 s to speak4 ,= "s unkn[n reason ! next unit1 #djj1 is express$ by tauau1 :ile au1 :i* is ! t]m t w\ld regul>ly /& = t numb]1 has1 by a second duplication1 come to signify #hjj4 ,! next unit1 mano1 has 9 a simil> mann] be5 twi/$ out ( its orig9al s5se1 & 9 c\nt+ breadfruit is made to s]ve = #hjjj4 ,9 ! nor!rn1 or ,nukuhivan ,isl&s1 ! decimal-quat]n>y sy/em is m regul>4 ,x is 9 ! c\nt+ ( breadfruit only1#bjb #d breadfruits #a pona #d4 #aj pona #a toha #dj4 #aj toha #a au #djj4 #aj au #a mano #djjj4 #aj mano #a t9i #dj1jjj4 #aj t9i #a tufa #djj1jjj4 #aj tufa #a pohi #d1jjj1jjj4 ,9 ! ,hawaiian dialect ?is scale is1 ) slight modification1 ! univ]sal scale1 us$ n only 9 c\nt+ breadfruit1 b any o!r objects z well4 ,! result is a complete decimal-quat]n>y sy/em1 su* z is f\nd n[h]e else 9 ! _w except 9 ?is & a few ( ! neighb\r+ dialects ( ! ,pacific4 ,?is scale1 :i* is almo/ id5tical ) ! ,nukuhivan1 is#bjc #d units #a ha or tauna #d4 #aj tauna #a tanaha #dj4 #aj tanaha #a lau #djj4 #aj lau #a mano #djjj4 #aj mano #a t9i #dj1jjj4 #aj t9i #a lehu #djj1jjj4 ,! quat]n>y elem5t ?us introduc$ has modifi$ ! entire /ructure ( ! ,hawaiian numb] sy/em4 ,fifty is tanaha me ta umi1 #dj #aj2 #gf is #dj #bj #aj #f2 #ajj is ua tanaha ma tekau1 #b #dj #aj2 #bjj is lima tanaha1 #e #dj2 & #hfd1hie is #b #djj1jjj #dj1jjj #f #djjj #b #djj #b #dj #aj #e4bjd ,su* examples %[ t ?is second>y influ5ce1 ent]+ & incorporat+ itself z a "p ( a well-develop$ decimal sy/em1 has radically *ang$ x by ! e/abli%m5t ( #d z ! prim>y numb] base4 ,! role :i* #aj n[ plays is peculi>4 ,9 ! natural =mation ( a quat]n>y scale new units w\ld be introduc$ at #af1 #fd1 #bef1 etc42 t is1 at ! squ>e1 ! cube1 & ea* successive p[] ( ! base4 ,b1 in/ead ( ?is1 ! new units are introduc$ at #aj #d1 #ajj #d1 #ajjj #d1 etc42 t is1 at ! products ( #d by ea* successive p[] ( ! old base4 ,?is leaves ! scale a decimal scale /ill1 ev5 :ile x may ju/ly be call$ quat]n>y2 & produces "o ( ! mo/ s+ul> & int]e/+ in/ances ( numb]-sy/em =mation t has ev] be5 obs]v$4 ,9 ?is connection x is wor? not+ t ^! ,pacific isl& numb] scales h be5 develop$ to v high limits--9 "s cases into ! millions4 ,! num]als = ^! l>ge numb]s d n seem 9 any way indef9ite1 b r to convey to ! m9d ( ! native an idea z cle> z c well be convey$ by numb]s ( su* magnitude4 ,beyond ! limits giv51 ! isl&]s h indef9ite expressions1 b z f> z c be asc]ta9$ ^! are only us$ :5 ! limits giv5 above h actually be5 pass$4 ,to quote "o m example1 ! ,h]vey ,isl&]s1 :o h a b9>y-decimal scale1 c\nt z foll[s3 #e kaviri 7bun*es ( cocoanuts7 #a takau #bj4 #aj takau #a rau #bjj4 #aj rau #a mano #bjjj4 #aj mano #a kiu #bj1jjj4 #aj kiu #a t9i #bjj1jjj4 ,any?+ above ?is !y speak ( 9 an unc]ta9 way1 z mano mano or t9i t9i1 :i* may1 p]haps1 be p>allel$ by our ,engli% phrases myriads ^u myriads1 & millions ( millions4#bje ,x is mo/ rem>kable t ! same qu>t] ( ! globe %\ld pres5t u ) ! /unt$ numb] s5se ( ! ,au/ralians1 &1 side by side ) x1 s ext5d$ & intellig5t an appreciation ( num]ical values z t possess$ by _m ( ! less] tribes ( ,polynesia4 ,! ,luli ( ,p>aguay#bjf %[ a decid$ pref]5ce = ! base #d4 ,?is pref]5ce gives way only :5 !y rea* ! numb] #aj1 :i* is an ord9>y digit num]al4 ,all numb]s above t po9t belong r to decimal ?an to quat]n>y num]ation4 ,_! num]als are3 #a4 alapea4 #b4 tamop4 #c4 tamlip4 #d4 lokep4 #e4 lokep moile alapea #d ) #a1 or is-alapea h& #a4 #f4 lokep moile tamop #d ) #b4 #g4 lokep moile tamlip #d ) #c4 #h4 lokep moile lokep #d ) #d4 #i4 lokep moile lokep alapea #d ) #d-a4 #aj4 is ya\m all ! f+]s ( h&4 #aa4 is ya\m moile alapea all ! f+]s ( h& ) #a4 #bj4 is elu ya\m all ! f+]s ( h& & foot4 #cj4 is elu ya\m moile is-ya\m all ! f+]s ( h& & foot ) all ! f+]s ( h&4 ,/ill ano!r in/ance ( quat]n>y c\nt+1 ?is "t c>ry+ ) x a sugge/ion ( b9>y influ5ce1 is furni%$ by ! ,mocobi#bjg ( ! ,p>ana region4 ,_! scale is exce$+ly rude1 & !y use ! f+]s & toes almo/ exclusively 9 c\nt+2 only us+ _! spok5 num]als :51 = any reason1 !y wi% to disp5se ) ! aid ( _! h&s & feet4 ,_! fir/ eight num]als are3 #a4 iniat$a4 #b4 inabaca4 #c4 inabacao ca9i #b above4 #d4 inabacao ca9iba #b above #b2 or natolatata4 #e4 inibacao ca9iba iniat$a #b above #b-a2 or natolatata iniat$a #d-a4 #f4 natolatatata inibaca #d-b4 #g4 natolata inibacao-ca9i #d-b above4 #h4 natolata-natolata #d-d4 ,!re is probably no record$ in/ance ( a numb] sy/em =m$ on #f1 #g1 #h1 or #i z a base4 ,no natural reason exi/s = ! *oice ( any ( ^! numb]s = su* a purpose2 & x is h>dly conceivable t any race %\ld proce$ beyond ! un9tellig5t b9>y or quat]n>y /age1 & !n beg9 ! =mation ( a scale = c\nt+ ) any o!r base ?an "o ( ! ?ree natural bases to :i* allusion has already be5 made4 ,n[ & !n "s anomal\s fragm5t is f\nd imb$d$ 9 an o!rwise regul> sy/em1 :i* c>ries u back to ! "t :5 ! savage 0 grop+ 8 way onw>d 9 8 attempt to give expression to "s numb] great] ?an any he _h ev] us$ be=e2 & n[ & !n "o ( ^! fragm5ts is su* z to lead u to ! bord] l& ( ! might-h-be51 & to cause u to speculate on ! possibility ( s great a num]ical curiosity z a s5>y or a sept5>y scale4 ,! ,bretons call #ah tri\ec'h1 #c-f1 b o!rwise _! language conta9s no h9t ( c\nt+ by sixes2 & we are left at p]fect lib]ty to !orize at w on ! exi/5ce ( s unusual a numb] ^w4 ,pott rem>ks#bjh t ! ,bolans1 ( we/]n ,africa1 appe> to make "s use ( #f z _! numb] base1 b _! sy/em1 tak5 z a :ole1 is really a qu9>y-decimal4 ,! language ( ! ,sundas1#bji or m\nta9e]s ( ,java1 conta9s traces ( s5>y c\nt+4 ,! ,akra words = #g & #h1 paggu & paniu1 appe> to mean #f-a & #g-a1 respectively2 & ! same is true ( ! correspond+ ,tambi words pagu & panjo4#baj ,! ,watji tribe#baa call #f &ee1 & #g &]ee1 :i* probably means #f-a4 ,^! words are to be reg>d$ z accid5tal v>iations on ! ord9>y laws ( =mation1 & are no m significant ( a desire to c\nt by sixes ?an is ! ,walla*ian t]m deu-maw1 :i* expresses #ah z #b-i1 indicates ! exi/5ce ( a scale ( :i* #i is ! base4 ,"o rem>kably int]e/+ numb] sy/em is t exhibit$ by ! ,mosquito tribe#bab ( ,c5tral ,am]ica1 :o possess an ext5sive qu9>y-vigesimal scale conta9+ "o b9>y & ?ree s5>y comp\nds4 ,! fir/ t5 words ( ?is s+ul> scale1 :i* has already be5 quot$1 are3 #a4 kumi4 #b4 wal4 #c4 niupa4 #d4 wal-wal #b-b4 #e4 mata-sip f+]s ( "o h&4 #f4 matlalkabe4 #g4 matlalkabe pura kumi #f #a4 #h4 matlalkabe pura wal #f #b4 #i4 matlalkabe pura niupa #f #c4 #aj4 mata-wal-sip f+]s ( ! second h&4 ,9 pass+ f #f to #g1 ?is tribe1 also1 has v>i$ ! almo/ univ]sal law ( progression1 & has call$ #g #f-a4 ,_! #h & #i are =m$ 9 a simil> mann]2 b at #aj ! ord9>y me?od is resum$1 & is cont9u$ f t po9t onw>d4 ,few numb] sy/ems conta9 z _m z ?ree num]als :i* are associat$ ) #f z _! base4 ,9 ne>ly all in/ances we f9d su* num]als s+ly1 or at mo/ 9 pairs2 & 9 ! /ructure ( any sy/em z a :ole1 !y are ( no importance :atev]4 ,= example1 9 ! ,pawnee1 a pure decimal scale1 we f9d ! foll[+ odd sequ5ce3#bac #f4 %ek%abi%4 #g4 petko%ek%abi% #b-f1 i4e4 #b;d #f4 #h4 t\wet%abi% #c-f1 i4e4 #c;d #f4 #i4 lok%]ewa #aj - #a4 ,9 ! ,ua9uma scale ! expressions = #g & #h are obvi\sly ref]r$ to #f1 ?\gh ! mean+ ( #g is n giv51 & x is impossible to guess :at x really does signify4 ,! num]als 9 "q are3#bad #f4 aira-ettagapi4 #g4 aira-ettagapi-hairiwigani-apecapecapsi4 #h4 aira-ettagapi-mats*ahma #f #b4 ,9 ! dialect ( ! ,mille tribe a s+le trace ( s5>y c\nt+ appe>s1 z ! num]als giv5 bel[ %[3#bae #f4 dildjidji4 #g4 dildjidji me djuun #f #a4 ,f9ally1 9 ! num]als us$ by ! natives ( ! ,m>%all ,isl&s1 ! foll[+ curi\sly irregul> sequ5ce also conta9s a s+le s5>y num]al3#baf #f4 ?il ?9o #c #c4 #g4 ?il?ilim-?uon #f #a4 #h4 rua-li-dok #aj - #b4 #i4 rua?im-?uon #aj - #b #a4 ,_m ye>s ago a /atem5t appe>$ :i* at once attract$ att5tion & awak5$ curiosity4 ,x 0 to ! effect t ! ,maoris1 ! aborig9al inhabitants ( ,new ,zeal&1 us$ z ! basis ( _! num]al sy/em ! numb] #aa2 & t ! sy/em 0 q ext5sively develop$1 hav+ simple words = #aba & #acca1 i4e4 = ! squ>e & cube ( #aa4 ,no app>5t reason exi/$ = ?is anomaly1 & ! ,maori scale 0 = a long "t look$ ^u z some?+ q exceptional & outside all ord9>y rules ( numb]-sy/em =mation4 ,b a clos] & m accurate k ( ! ,maori language & cu/oms s]v$ to correct ! mi/ake1 & to %[ t ?is sy/em 0 a simple decimal sy/em1 & t ! error arose f ! foll[+ habit4 ,sometimes :5 c\nt+ a numb] ( objects ! ,maoris w\ld put aside #a to repres5t ea* #aj1 & !n ^? s set aside w\ld aft]w>d be c\nt$ to asc]ta9 ! numb] ( t5s 9 ! heap4 ,e>ly obs]v]s among ?is p1 see+ !m c\nt #aj & !n set aside #a1 at ! same "t pron\nc+ ! ^w tekau1 imag9$ t ?is ^w meant #aa1 & t ! ignorant savage 0 mak+ use ( ?is numb] z 8 base4 ,?is misconception f\nd its way into ! e>ly ,new ,zeal& diction>y1 b 0 correct$ 9 lat] editions4 ,x is "h m5tion$ only because ( ! wide diffusion ( ! error1 & ! int]e/ x has always excit$4#bag ,aside f our common decimal scale1 !re exi/ 9 ! ,engli% language o!r me?ods ( c\nt+1 "s ( !m =mal en\gh to be dignifi$ by ! t]m sy/em--z ! sexagesimal me?od ( measur+ "t & angul> magnitude2 & ! duodecimal sy/em ( reckon+1 s ext5sively us$ 9 buy+ & sell+4 ,( ^! sy/ems1 o!r ?an decimal1 two are notic$ by ,tylor1#bah & comm5t$ on at "s l5g?1 z foll[s3 ,"o is ! well-kn[n dic+ set1 ace1 deuce1 tray1 cat]1 c9que1 size2 ?us size-ace is #f-a1 c9ques or s9ks1 d\ble #e4 ,^! came to u f ,france1 & correspond ) ! common ,fr5* num]als1 except ace1 :i* is ,lat9 z1 a ^w ( great philological int]e/1 mean+ '"o4' ,! o!r borr[$ set is to be f\nd 9 ! ,slang ,diction>y4 ,x appe>s t ! ,engli% /reet-folk h adopt$ z a means ( secret communication a set ( ,italian num]als f ! organ-gr9d]s & image-sell]s1 or by o!r ways ?r\gh :i* ,italian or ,l+ua ,franca is br\ght into ! l[ neighb\rhoods ( ,london4 ,9 s do+ !y h p]=m$ a philological op]ation n only curi\s b in/ructive4 ,by copy+ su* expressions z due soldi1 tre soldi1 z equival5t to 'twop5ce1' '?reep5ce1' ! ^w saltee became a recogniz$ slang t]m = 'p5ny'2 & p5ce are reckon$ z foll[s3 oney saltee #a;d4 uno soldo4 dooe saltee #b;d4 due soldi4 tray saltee #c;d4 tre soldi4 qu>t]] saltee #d;d4 quattro soldi4 *9k] saltee #e;d4 c9que soldi4 say saltee #f;d4 sei soldi4 say oney saltee1 or sett] saltee #g;d4 sette soldi4 say dooe saltee1 or ott] saltee #h;d4 otto soldi4 say tray saltee1 or nobba saltee #i;d4 nove soldi4 say qu>t]] saltee1 or da*a saltee #aj;d4 dieci soldi4 say *9k] saltee or da*a oney saltee #aa;d4 undici soldi4 oney beong #as4 a beong say saltee #as4 #f;d4 dooe beong say saltee1 or madza c>oon #bs4 #f;d4 7half-cr[n1 mezza corona74 ,"o ( ^! s]ies simply adopts ,italian num]als decimally4 ,b ! o!r1 :5 x has rea*$ #f1 hav+ _h en\gh ( novelty1 makes #g by #f-a1 & s =?4 ,x is = no ab/ract reason t #f is ?us made ! turn+-po9t1 b simply because ! co/]mong] is add+ p5ce up to ! silv] sixp5ce1 & !n add+ p5ce aga9 up to ! %ill+4 ,?us our duodecimal co9age has l$ to ! practice ( c\nt+ by sixes1 & produc$ a philological curiosity1 a real s5>y notation4 ,9 addition to ! two me?ods ( c\nt+ "h allud$ to1 ano!r may be m5tion$1 :i* is equally in/ructive z %[+ h[ readily any special me?od ( reckon+ may be develop$ out ( ! ne$s aris+ 9 connection ) any special l9e ( "w4 ,z is well kn[n1 x is ! cu/om 9 ocean1 lake1 & riv] navigation to measure s\nd+s by ! fa?om4 ,on ! ,mississippi ,riv]1 :]e con/ant vigilance is ne$$ because ( ! rapid %ift+ ( s&-b>s1 a special s\nd+ nom5clature has come into vogue1#bai :i* ! foll[+ t]ms w illu/rate3 #e ft4 five feet4 #f ft4 six feet4 #i ft4 n9e feet4 #aj-a_/b ft4 a qu>t] less twa92 i4e4 a qu>t] ( a fa?om less ?an #b4 #ab ft4 m>k twa94 #ac-a_/b ft4 a qu>t] twa94 #af-a_/b ft4 a qu>t] less ?ree4 #ah ft4 m>k ?ree4 #ai-a_/b ft4 a qu>t] ?ree4 #bd ft4 deep f\r4 ,z ! s\nd+s are tak51 ! read+s are call$ (f 9 ! mann] indicat$ 9 ! table2 #aj-a_/b feet be+ a qu>t] less twa91 #ab feet m>k twa91 etc4 ,any s\nd+ above deep f\r is report$ z no bottom4 ,9 ! ,atlantic & ,gulf wat]s on ! coa/ ( ?is c\ntry ! same sy/em prevails1 only x is ext5d$ to meet ! requirem5ts ( ! deep] s\nd+s !re f\nd1 & in/ead ( six feet1 m>k twa91 etc41 we f9d ! full] expressions1 by ! m>k "o1 by ! m>k two1 & s on1 z f> z ! dep? requires4 ,?is example also sugge/s ! old] & f> m widely diffus$ me?od ( reckon+ "t at sea by bells2 a sy/em 9 :i* "o bell1 two bells1 ?ree bells1 etc41 m>k ! passage ( "t = ! sailor z di/9ctly z ! h&s ( ! clock c\ld d x4 ,o!r examples ( a simil> nature w readily sugge/ !mselves to ! m9d4 ,two possible numb] sy/ems t h1 = purely !oretical reasons1 attract$ mu* att5tion1 are ! octon>y & ! duodecimal sy/ems4 ,9 fav\r ( ! octon>y sy/em x is urg$ t #h is an exact p[] ( #b2 or 9 o!r words1 a l>ge numb] ( repeat$ halves c be tak5 ) #h z a />t+-po9t1 )\t produc+ a fractional result4 ,) #h z a base we %\ld obta9 by successive halv+s1 #d1 #b1 #a4 ,a simil> process 9 our decimal scale gives #e1 #b-a_/b1 #a-a_/d4 ,all ?is is und5iably true1 b1 grant+ ! argum5t up to ?is po9t1 "o is !n tempt$ to ask ,:at ( x8 ,a c]ta9 degree ( simplicity w\ld !reby be introduc$ into ! ,!ory ( ,numb]s2 b ! only p]sons suffici5tly int]e/$ 9 ?is bran* ( ma!matics to appreciate ! b5efit ?us obta9$ are already tra9$ ma!maticians1 :o are conc]n$ r ) ! pure sci5ce involv$1 ?an ) reckon+ on any special base4 ,a slightly increas$ simplicity w\ld appe> 9 ! "w ( /ockbrok]s1 & o!rs :o reckon ext5sively by qu>t]s1 eigh?s1 & sixte5?s4 ,b su* m5 exp]i5ce no difficulty :atev] 9 p]=m+ _! m5tal computations 9 ! decimal sy/em2 & !y acquire ?r\gh con/ant practice su* quickness & accuracy ( calculation1 t x is difficult to see h[ octon>y reckon+ w\ld mat]ially assi/ !m4 ,altoge!r1 ! reasons t h 9 ! pa/ be5 adduc$ 9 fav\r ( ?is =m ( ari?metic seem trivial4 ,!re is no record ( any tribe t ev] c\nt$ by eights1 nor is !re ! slighte/ likelihood t su* a sy/em c\ld ev] meet ) any g5]al fav\r4 ,x is said t ! anci5t ,saxons us$ ! octon>y sy/em1#bbj b h[1 or = :at purposes1 is n /at$4 ,x is n to be suppos$ t ?is 0 ! common sy/em ( c\nt+1 = x is well kn[n t ! decimal scale 0 9 use z f> back z ! evid5ce ( language w take u4 ,b ! field ( speculation into :i* "o is l$ by ! octon>y scale has prov$ mo/ attractive to "s1 & ! conclusion has be5 sob]ly rea*$1 t 9 ! hi/ory ( ! ,aryan race ! octon>y 0 to be reg>d$ z ! pr$ecessor ( ! decimal scale4 ,9 support ( ?is !ory no direct evid5ce is br\ght =w>d1 b c]ta9 v]bal resemblances4 ,^? ignes fatuii ( ! philologi/ are made to p]=m ! duty ( support+ an hypo!sis :i* w\ld nev] h exi/$ b = _! own trea*]\s sugge/ions4 ,"h is "o ( ! mo/ attractive ( !m3 ,betwe5 ! ,lat9 words novus1 new1 & novem1 n9e1 !re exi/s a resemblance s close t x may well be m ?an accid5tal4 ,n9e is1 !n1 ! new numb]2 t is1 ! fir/ numb] on a new c\nt1 ( :i* #h mu/ orig9ally h be5 ! base4 ,pursu+ ?is ?\ght by inve/igation into diff]5t languages1 ! same resemblance is f\nd !re4 ,h5ce ! !ory is /r5g!n$ by corroborative evid5ce4 ,9 language aft] language ! same resemblance is f\nd1 until x seems impossible to d\bt1 t 9 prehi/oric times1 #i 0 ! new numb]--! beg9n+ ( a second tale4 ,! foll[+ table w %[ h[ widely spread is ?is co9cid5ce3 ,sanskrit1 navan #i4 nava new4 ,p]sian1 nuh #i4 nau new4 ,greek1 ,greek3 ennea #i4 ,greek3 neos new4 ,lat91 novem #i4 novus new4 ,g]man1 neun #i4 neu new4 ,sw$i%1 nio #i4 ny new4 ,dut*1 neg5 #i4 nieuw new4 ,dani%1 ni #i4 ny new4 ,icel&ic1 nyr #i4 niu new4 ,engli%1 n9e #i4 new new4 ,fr5*1 neuf #i4 n\veau new4 ,spani%1 nueve #i4 neuvo new4 ,italian1 nove #i4 nuovo new4 ,portuguese1 nove #i4 novo new4 ,iri%1 naoi #i4 nus new4 ,wel%1 naw #i4 newydd new4 ,breton1 nevez #i4 nuhue new4#bba ,?is table might be ext5d$ /ill fur!r1 b ! above examples %[ h[ widely diffus$ ?r\gh\t ! ,aryan languages is ?is resemblance4 ,! li/ c]ta9ly is an impressive "o1 & ! /ud5t is at fir/ ?\ght tempt$ to ask :e!r all ^! resemblances c possibly h be5 accid5tal4 ,b a s+le consid]ation sweeps away ! entire argum5t z ?\gh x 7 a cobweb4 ,all ! languages ?r\gh :i* ?is v]bal lik5ess runs are d]iv$ directly or indirectly f "o common /ock2 & ! common e-day words1 n9e & new1 h be5 transmitt$ f t primitive tongue into all ^! l+ui/ic (fspr+ ) b little *ange4 ,n only are ! two words 9 "q ak9 9 ea* individual language1 b !y are ak9 9 all ! languages4 ,h5ce all ^! resemblances r$uce to a s+le resemblance1 or p]haps id5tity1 t betwe5 ! ,aryan words = n9e & new4 ,?is 0 probably an accid5tal resemblance1 no m significant ?an any "o ( ! scores ( o!r simil> cases occurr+ 9 e language4 ,if !re 7 any fur!r evid5ce ( ! =m] exi/5ce ( an ,aryan octon>y scale1 ! co9cid5ce w\ld possess a c]ta9 degree ( significance2 b n a %r$ has ev] be5 produc$ :i* is wor?y ( consid]ation4 ,if our remote ance/ors ev] c\nt$ by eights1 we are entirely ignorant ( ! fact1 & mu/ rema9 s until mu* m is kn[n ( _! language ?an s*ol>s n[ h at _! comm&4 ,! ^w resemblances not$ above are h>dly m significant ?an ^? occurr+ 9 two ,polynesian languages1 ! ,fatuhivan & ! ,nakuhivan1#bbb :]e new is associat$ ) ! numb] #g4 ,9 ! =m] case #g is fitu1 & new is f\2 9 ! latt] #g is hitu1 & new is h\4 ,b no "o has1 because ( ?is lik5ess1 ev] sugge/$ t ^! tribes ev] c\nt$ by ! s5>y me?od4 ,ano!r equally trivial resemblance occurs 9 ! ,tawgy & ! ,kamass9 languages1#bbc ?us3 ,,tawgy4 ,,kamass94 #h4 siti-data #b #d4 #h4 s9-!'de #b #d4 #i4 nameaitjuma ano!r4 #i4 ami?un ano!r4 ,b x w\ld be *ildi% to argue1 f ?is fact alone1 t ei!r #d or #h 0 ! numb] base us$4 ,9 a rec5t antiqu>ian "w ( consid]able int]e/1 ! au?or exam9es into ! "q ( a =m] octon>y sy/em ( c\nt+ among ! v>i\s races ( ! _w1 p>ticul>ly ^? ( ,asia1 & br+s to light mu* curi\s & ent]ta9+ mat]ial respect+ ! use ( ?is numb]4 ,its use & importance 9 ,*9a1 ,india1 & c5tral ,asia1 z well z among "s ( ! isl&s ( ! ,pacific1 & 9 ,c5tral ,am]ica1 leads him to ! conclusion t !re 0 a "t1 long be=e ! beg9n+ ( record$ hi/ory1 :5 #h 0 ! common numb] base ( ! _w4 ,b 8 conclusion has no basis 9 8 own mat]ial ev54 ,! argum5t _c be exam9$ "h1 b any "o :o c>es to inve/igate x c f9d !re an excell5t illu/ration ( ! fact t a pet !ory may take complete possession ( its orig9ator1 & r$uce him f9ally to a /ate ( infantile subjugation4#bbd ,( all numb]s ^u :i* a sy/em c\ld be bas$1 #ab seems to comb9e 9 itself ! greate/ numb] ( advantages4 ,x is capable ( division by #b1 #c1 #d1 & #f1 & h5ce admits ( ! tak+ ( halves1 ?irds1 qu>t]s1 & six?s ( itself )\t ! introduction ( fractions 9 ! result4 ,f a comm]cial /&-po9t ?is advantage is v great2 s great t _m h s]i\sly advocat$ ! entire abolition ( ! decimal scale1 & ! sub/itution ( ! duodecimal 9 its /ead4 ,x is said t ,*>les ,,xii4 ( ,sw$5 0 actually contemplat+ su* a *ange 9 8 dom9ions at ! "t ( 8 dea?4 ,9 pursuance ( ?is idea1 "s writ]s h gone s f> z to sugge/ symbols = #aj & #aa1 & to reca/ our entire num]al nom5clature to con=m to ! duodecimal base4#bbe ,7 su* a *ange made1 we %\ld express ! fir/ n9e numb]s z at pres5t1 #aj & #aa by new1 s+le symbols1 & #ab by #aj4 ,f ?is po9t ! progression w\ld be regul>1 z 9 ! decimal scale--only ! same comb9ation ( figures 9 ! diff]5t scales w\ld mean v diff]5t ?+s4 ,?us1 #ag 9 ! decimal scale w\ld become #ae 9 ! duodecimal2 #add 9 ! decimal w\ld become #ajj 9 ! duodecimal2 & #agbh1 ! cube ( ! new base1 w\ld ( c\rse be repres5t$ by ! figures #ajjj4 ,x is impossible t any su* *ange c ev] meet ) g5]al or ev5 p>tial fav\r1 s firmly has ! decimal scale become intr5*$ 9 its position4 ,b x is m ?an probable t a l>ge "p ( ! _w ( trade & comm]ce w cont9ue to buy & sell by ! doz51 ! gross1 or "s multiple or fraction ( ! "o or ! o!r1 z long z buy+ & sell+ %all cont9ue4 ,su* has be5 its cu/om = c5turies1 & su* w d\btless be its cu/om = c5turies to come4 ,! duodecimal is n a natural scale 9 ! same s5se z are ! qu9>y1 ! decimal1 & ! vigesimal2 b x is a sy/em :i* is call$ into be+ long aft] ! complete developm5t ( "o ( ! natural sy/ems1 solely because ( ! simple & famili> fractions into :i* its base is divid$4 ,x is ! scale ( civilization1 j z ! ?ree common scales are ! scales ( nature4 ,b an example ( its use 0 long s\ght = 9 va9 among ! primitive races ( ! _w4 ,humboldt1 9 comm5t+ on ! numb] sy/ems ( ! v>i\s peoples he _h visit$ dur+ 8 travels1 rem>k$ t no race _h ev] us$ exclusively t be/ ( bases1 #ab4 ,b x has rec5tly be5 ann\nc$#bbf t ! discov]y ( su* a tribe _h actually be5 made1 & t ! ,aphos ( ,b5u1 an ,african tribe1 c\nt to #ab by simple words1 & !n = #ac say #ab-a1 = #ad1 #ab-b1 etc4 ,?is report has yet to be v]ifi$1 b if true x w con/itute a mo/ int]e/+ addition to an?ropological k4 ,,*apt] ,,vi4 ,,! ,,qu9>y ,,sy/em4 ,! orig9 ( ! qu9>y mode ( c\nt+ has be5 discuss$ ) "s fulness 9 a prec$+ *apt]1 & ^u t "q b little m ne$ be said4 ,x is ! fir/ ( ! natural sy/ems4 ,:5 ! savage has f9i%$ 8 c\nt ( ! f+]s ( a s+le h&1 he has rea*$ ?is natural numb] base4 ,at ?is po9t he ceases to use simple numb]s1 & beg9s ! process ( comp\nd+4 ,by "s "o ( ! num]\s me?ods illu/rat$ 9 e>li] *apt]s1 he passes f #e to #aj1 us+ "h ! f+]s ( 8 second h&4 ,he n[ has two fives2 &1 j z we say tw5ty1 i4e4 two t5s1 he says two h&s1 ! second h& f9i%$1 all ! f+]s1 ! f+]s ( bo? h&s1 all ! f+]s come to an end1 or1 mu* m r>ely1 "o man4 ,t is1 he is1 9 "o ( ! _m ways at 8 comm&1 say+ two fives4 ,at #ae he has ?ree h&s or "o foot2 & at #bj he pauses ) f\r h&s1 h&s & feet1 bo? feet1 all ! f+]s ( h&s & feet1 h&s & feet f9i%$1 or1 m probably1 "o man4 ,all ^! modes ( expression are /rictly natural1 & all h be5 f\nd 9 ! numb] scales :i* 71 & 9 _m cases /ill are1 9 daily use among ! unciviliz$ races ( mank9d4 ,9 its /ructure ! qu9>y is ! simple/1 ! mo/ primitive1 ( ! natural sy/ems4 ,its base is almo/ always express$ by a ^w mean+ h&1 or by "s equival5t circumlocution1 & its digital orig9 is usually trac$ )\t difficulty4 ,a consi/5t =mation w\ld require ! expression ( #aj by "s phrase mean+ two fives1 #ae by ?ree fives1 etc4 ,su* a scale is ! "o obta9$ f ! ,betoya language1 already m5tion$ 9 ,*apt] ,,iii41 :]e ! =mation ( ! num]als is purely qu9>y1 z ! foll[+ indicate3#bbg #e4 te5te #a h&4 #aj4 caya5te1 or caya hu5a #b h&s4 #ae4 toazumba-ente #c h&s4 #bj4 caesa-ente #d h&s4 ,! same =mation appe>s1 ) great] or less di/9ctness1 9 _m ( ! qu9>y scales already quot$1 & 9 _m m ( :i* m5tion might be made4 ,collect+ ! significant num]als f a few su* scales1 & tabulat+ !m = ! sake ( conv5i5ce ( comp>ison1 we see ?is po9t cle>ly illu/rat$ by ! foll[+3 ,,tamanac4 #e4 amnaitone #a h&4 #aj4 amna atse pon>e #b h&s4 ,,arawak1 ,,guiana4 #e4 abba tekkabe #a h&4 #aj4 biamantekkabe #b h&s4 ,,jiviro4 #e4 alactegladu #a h&4 #aj4 catgladu #b h&s4 ,,niam ,,niam #e4 biswe #aj4 bauwe #b;d #e4 ,,n5gones #e4 se dono ! end 7( ! f+]s ( #a h&74 #aj4 rewe tub59e #b s]ies 7( f+]s74 ,,sesake4#bbh #e4 lima h&4 #aj4 dua lima #b h&s4 ,,ambrym4#bbi #e4 lim h&4 #aj4 ra-lim #b h&s4 ,,pama4#bbi #e4 e-lime h&4 #aj4 ha-lua-lim ! #b h&s4 ,,d9ka4#bcj #e4 wdyets4 #aj4 wty]1 or wty> #e #b4 ,,b>i #e4 kanat #aj4 puk #e #e8 ,,kanuri #e4 ugu4 #aj4 megu #b #e4 ,,rio ,,norte ,,& ,,san ,,antonio4#bca #e4 juyopamauj4 #aj4 juyopamauj ajte #e #b4 ,,api4#bcb #e4 lima4 #aj4 lua-lima #b #e4 ,,erromango #e4 suku-rim4 #aj4 nduru-lim #b #e4 ,,tl+it1 ,,briti% ,,columbia4#bcc #e4 k$j9 7f dj9 h&74 #aj4 dj9kat bo? h&s8 ,?us f> ! qu9>y =mation is simple & regul>2 & 9 view ( ! evid5ce ) :i* ^! & simil> illu/rations furni% u1 x is mo/ surpris+ to f9d an em95t au?ority mak+ ! unequivocal /atem5t t ! numb] #aj is n[h]e express$ by #b fives#bcd--t all tribes :i* beg9 _! c\nt on a qu9>y base express #aj by a simple ^w4 ,x is a fact1 z w be fully illu/rat$ 9 ! foll[+ pages1 t qu9>y numb] sy/ems1 :5 ext5d$1 usually m]ge into ei!r ! decimal or ! vigesimal4 ,! result is1 ( c\rse1 a comp\nd ( two1 & sometimes ( ?ree1 sy/ems 9 "o scale4 ,a pure qu9>y or vigesimal numb] sy/em is exce$+ly r>e2 b qu9>y scales c]ta9ly d exi/ 9 :i*1 z f> z we possess ! num]als1 no trace ( any o!r influ5ce appe>s4 ,x is also to be notic$ t "s tribes1 l ! ,eskimos ( ,po9t ,b>r[1 ?\gh _! sy/ems may prop]ly be class$ z mix$ sy/ems1 exhibit a decid$ pref]5ce = #e z a base1 & 9 c\nt+ objects1 divid$ into gr\ps ( #e1 obta9+ ! sum 9 ?is way4#bce ,b ! savage1 aft] c\nt+ up to #aj1 (t5 f9ds himself unconsci\sly impell$ to dep>t f 8 /rict reckon+ by fives1 & to assume a new basis ( ref]5ce4 ,take1 = example1 ! ,zui sy/em1 9 :i* ! fir/ #b fives are3 #e4 pte ! not*$ (f4 #aj4 a/em'?la all ! f+]s4 ,x w be notic$ t ! ,zui does n say two h&s1 or ! f+]s ( bo? h&s1 b simply all ! f+]s4 ,! #e is no long] prom95t1 b in/ead ! m]e notion ( "o entire c\nt ( ! f+]s has tak5 its place4 ,! division ( ! f+]s into two sets ( five ea* is /ill 9 8 m9d1 b x is no long] ! lead+ idea4 ,z ! c\nt proce$s fur!r1 ! qu9>y base may be reta9$1 or x may be supplant$ by a decimal or a vigesimal base4 ,h[ readily ! "o or ! o!r may pr$om9ate is se5 by a glance at ! foll[+ num]als3 ,,galibi4#bcf #e4 atoneigne oietona #a h&4 #aj4 oia bat\e ! o!r h&4 #bj4 p\p\patoret oup\me feet & h&s4 #dj4 op\p\me twice ! feet & h&s4 ,,gu>ani4#bcg #e4 ace popetei #a h&4 #aj4 ace pomocoi #b h&s4 #bj4 acepo acepiabe h&s & feet4 ,,fate4#bch #e4 lima h&4 #aj4 relima #b h&s4 #bj4 relima rua 7#b #e7 #b4 ,,kiriri #e4 mibika misa #a h&4 #aj4 mikriba misa sai bo? h&s4 #bj4 mikriba nusa ideko ibi sai bo? h&s toge!r ) ! feet4 ,,zamuco #e4 tsu5a yimana-ite end$ #a h&4 #aj4 tsu5a yimana-die end$ bo? h&s4 #bj4 tsu5a yiri-die end$ bo? feet4 ,,pikumbul #e4 mulanbu4 #aj4 bul>9 murra belong+ to ! two h&s4 #ae4 mulanba d9na #e toes add$ on 7to ! #aj f+]s74 #bj4 bul>9 d9na belong+ to ! #b feet4 ,,y>uros4#bci #e4 kani-iktsi-mo #a h& alone4 #aj4 y[a-iktsi-bo all ! h&s4 #ae4 kani-tao-mo #a foot alone4 #bj4 kani-pume #a man4 ,by ! "t #bj is rea*$ ! savage has probably all[$ 8 conception ( any aggregate to be s f> modifi$ t ?is numb] does n pres5t itself to 8 m9d z #d fives4 ,x may f9d expression 9 "s phraseology su* z ! ,kiriris employ--bo? h&s toge!r ) ! feet--or 9 ! %ort] end$ bo? feet ( ! ,zamucos1 9 :i* case we may presume t he is consci\s t 8 c\nt has be5 complet$ by means ( ! f\r sets ( fives :i* are furni%$ by 8 h&s & feet4 ,b x is at lea/ equally probable t he in/9ctively divides 8 total into #b t5s1 & ?us passes unconsci\sly f ! qu9>y into ! decimal scale4 ,aga91 ! summ+ up ( ! #aj f+]s & #aj toes (t5 results 9 ! concept ( a s+le :ole1 a lump sum1 s to speak1 & ! savage !n says "o man1 or some?+ t gives utt]ance to ?is ?\ght ( a new unit4 ,?is leads ! qu9>y into ! vigesimal scale1 & produces ! comb9ation s (t5 f\nd 9 c]ta9 p>ts ( ! _w4 ,?us ! inevitable t5d5cy ( any numb] sy/em ( qu9>y orig9 is t[>d ! e/abli%m5t ( ano!r & l>g] base1 & ! =mation ( a numb] sy/em 9 :i* bo? are us$4 ,:]ev] ?is is done1 ! great] ( ! two bases is always to be reg>d$ z ! pr9cipal numb] base ( ! language1 & ! #e z entirely subord9ate to x4 ,x is h>dly correct to say t1 z a numb] sy/em is ext5d$1 ! qu9>y elem5t disappe>s & gives place to ! decimal or vigesimal1 b r t x becomes a factor ( q second>y importance 9 ! developm5t ( ! scale4 ,if1 = example1 #h is express$ by #e-c 9 a qu9>y decimal sy/em1 #ih w be #i #aj #e-c4 ,! qu9>y elem5t does n disappe>1 b m]ely s9ks into a relatively unimportant position4 ,"o ( ! pure/ examples ( qu9>y num]ation is t furni%$ by ! ,betoya scale1 already giv5 9 full 9 ,*apt] ,,iii41 & briefly m5tion$ at ! beg9n+ ( ?is *apt]4 ,9 ! simplicity & regul>ity ( its con/ruction x is s notewor?y t x is wor? repeat+1 z ! fir/ ( ! long li/ ( qu9>y sy/ems giv5 9 ! foll[+ pages4 ,no fur!r comm5t is ne$$ on x ?an t already made 9 connection ) its digital significance4 ,z f> z giv5 by ,dr4 ,br9ton ! scale is3 #a4 tey4 #b4 cayapa4 #c4 toazumba4 #d4 cajezea #b ) plural t]m9ation4 #e4 te5te h&4 #f4 tey5te tey h& #a4 #g4 tey5te cayapa h& #b4 #h4 tey5te toazumba h& #c4 #i4 tey5te caesea h& #d4 #aj4 caya ente1 or caya hu5a #b h&s4 #aa4 caya ente-tey #b h&s #a4 #ae4 toazumba-ente #c h&s4 #af4 toazumba-ente-tey #c h&s #a4 #bj4 caesea ente #d h&s4 ,a f> m common me?od ( progression is furni%$ by languages :i* int]rupt ! qu9>y =mation at #aj1 & express t numb] by a s+le ^w4 ,any scale 9 :i* ?is takes place c1 f ?is po9t onw>d1 be qu9>y only 9 ! subord9ate s5se to :i* allusion has j be5 made4 ,examples ( ?is are furni%$ 9 a m or less p]fect mann] by ne>ly all s-call$ qu9>y-vigesimal & qu9>y-decimal scales4 ,z fairly repres5t+ ?is phase ( numb]-sy/em /ructure1 ,i h select$ ! fir/ #bj num]als f ! foll[+ languages3 ,,wel%4#bdj #a4 un4 #b4 dau4 #c4 tri4 #d4 p$w>4 #e4 pump4 #f4 *we*4 #g4 sai?4 #h4 wy?4 #i4 naw4 #aj4 deg4 #aa4 un ar ddeg #a #aj4 #ab4 deuddeg #b #aj4 #ac4 tri ar ddeg #c #aj4 #ad4 p$w> ar ddeg #d #aj4 #ae4 pym!g #e #aj4 #af4 un ar bym!g #a #e #aj4 #ag4 dau ar bym!g #b #e #aj4 #ah4 tri ar bym!g #c #e #aj4 #ai4 p$w> ar bym!g #d #e #aj4 #bj4 uga94 ,,nahuatl4#bda #a4 ce4 #b4 ome4 #c4 yei4 #d4 naui4 #e4 macuilli4 #f4 *iquac5 #e #a4 #g4 *icome #e #b4 #h4 *icuey #e #c4 #i4 *iucnaui #e #d4 #aj4 matlactli4 #aa4 matlactli oce #aj #a4 #ab4 matlactli omome #aj #b4 #ac4 matlactli omey #aj #c4 #ad4 matlactli onnaui #aj #d4 #ae4 caxtolli4 #af4 caxtolli oce #ae #a4 #ag4 caxtolli omome #ae #b4 #ah4 caxtolli omey #ae #c4 #ai4 caxtolli onnaui #ae #d4 #bj4 cempualli #a acc\nt4 ,,canaque#bdb ,,new ,,cal$onia4 #a4 *agu94 #b4 c>\4 #c4 c>]i4 #d4 cab\e #e4 cani4 #f4 cani-mon-*agu9 #e #a4 #g4 cani-mon-c>\ #e #b4 #h4 cani-mon-c>]i #e #c4 #i4 cani-mon-cab\e #e #d4 #aj4 panr]e4 #aa4 panr]e-mon-*agu9 #aj #a4 #ab4 panr]e-mon-c>\ #aj #b4 #ac4 panr]e-mon-c>]i #aj #c4 #ad4 panr]e-mon-cab\e #aj #d4 #ae4 panr]e-mon-cani #aj #e4 #af4 panr]e-mon-cani-mon-*agu9 #aj #e #a4 #ag4 panr]e-mon-cani-mon-c>\ #aj #e #b4 #ah4 panr]e-mon-cani-mon-c>]i #aj #e #c4 #ai4 panr]e-mon-cani-mon-cab\e #aj #e #d4 #bj4 jaquemo #a p]son4 ,,guato4#bdc #a4 c5ai4 #b4 d\\ni4 #c4 c\m4 #d4 dekai4 #e4 qu9\i4 #f4 c5ai-caicaira #a on ! o!r8 #g4 d\\ni-caicaira #b on ! o!r8 #h4 c\m-caicaira #c on ! o!r8 #i4 dekai-caicaira #d on ! o!r8 #aj4 qu9oi-da #e #b4 #aa4 c5ai-ai-caibo #a 7!7 h&s4 #ab4 d\\ni-ai-caibo #b #aj4 #ac4 c\m-ai-caibo #c #aj4 #ad4 dekai-ai-caibo #d #aj4 #ae4 qu9-oibo #e #c4 #af4 c5ai-ai-quacoibo #a #ae4 #ag4 d\\ni-ai-quacoibo #b #ae4 #ah4 c\m-ai-quacoibo #c #ae4 #ai4 dekai-ai-quacoibo #d #ae4 #bj4 qu9\i-ai-quacoibo #e #ae4 ,! mean+s assign$ to ! num]als #f to #i are entirely conjectural4 ,!y obvi\sly mean #a1 #b1 #c1 #d1 tak5 a second "t1 & z ! mean+s ,i h giv5 are (t5 f\nd 9 primitive sy/ems1 !y h1 at a v5ture1 be5 giv5 "h4 ,,lifu1 ,,loyalty ,,isl&s4#bdd #a4 ca4 #b4 lue4 #c4 ko5i4 #d4 eke4 #e4 tji pi4 #f4 ca ngem5 #a above4 #g4 lue ngem5 #b above4 #h4 ko5i ngem5 #c above4 #i4 eke ngem5 #d above4 #aj4 lue pi #b #e4 #aa4 ca ko4 #ab4 lue ko4 #ac4 ko5i ko4 #ad4 eke ko4 #ae4 ko5i pi #c #e4 #af4 ca huai ano4 #ag4 lua huai ano4 #ah4 ko5i huai ano4 #ai4 eke huai ano4 #bj4 ca atj #a man4 ,,bongo4#bde #a4 kotu4 #b4 ngorr4 #c4 motta4 #d4 neheo4 #e4 mui4 #f4 dokotu #e #a4 #g4 dongorr #e #b4 #h4 domotta #e #c4 #i4 doheo #e #d4 #aj4 kih4 #aa4 ki dokpo kotu #aj #a4 #ab4 ki dokpo ngorr #aj #b4 #ac4 ki dokpo motta #aj #c4 #ad4 ki dokpo neheo #aj #d4 #ae4 ki dokpo mui #aj #e4 #af4 ki dokpo mui d mui okpo kotu #aj #e m1 to #e1 #a m4 #ag4 ki dokpo mui d mui okpo ngorr #aj #e m1 to #e1 #b m4 #ah4 ki dokpo mui d mui okpo motta #aj #e m1 to #e1 #c m4 #ai4 ki dokpo mui d mui okpo nehea #aj #e m1 to #e1 #d m4 #bj4 mbaba kotu4 ,above #bj1 ! ,lufu & ! ,bongo sy/ems are vigesimal1 s t !y are1 z a :ole1 mix$ sy/ems4 ,! ,wel% scale beg9s z ?\gh x 7 to pres5t a pure decimal /ructure1 & no h9t ( ! qu9>y elem5t appe>s until x has pass$ #ae4 ,! ,nahuatl1 on ! o!r h&1 c\nts f #e to #aj by ! ord9>y qu9>y me?od1 & !n appe>s to pass into ! decimal =m4 ,b :5 #af is rea*$1 we f9d ! qu9>y influ5ce /ill p]si/5t2 & f ?is po9t to #bj1 ! num]al words 9 bo? scales are su* z to %[ t ! notion ( c\nt+ by fives is q z prom95t z ! notion ( ref]r+ to #aj z a base4 ,above #bj ! sy/ems become vigesimal1 ) a qu9>y or decimal /ructure appe>+ 9 all num]als except multiples ( #bj4 ,?us1 9 ,wel%1 #cf is un>bym!g ar uga91 #a #e #aj #bj2 & 9 ,nahuatl ! same numb] is cempualli caxtolli oce1 #bj #ae #a4 ,h5ce ^! & simil> numb] sy/ems1 ?\gh commonly allud$ to z vigesimal1 are really mix$ scales1 ) #bj z _! prim>y base4 ,! ,canaque scale diff]s f ! ,nahuatl only 9 =m+ a comp\nd ^w = #ae1 in/ead ( introduc+ a new & simple t]m4 ,9 ! examples :i* foll[1 x is n ?\ght be/ to ext5d ! li/s ( num]als beyond #aj1 except 9 special in/ances :]e ! illu/ration ( "s p>ticul> po9t may dem& x4 ,! usual qu9>y scale w be f\nd1 ) a few exceptions l ^? j in/anc$1 to h ! foll[+ /ructure or "o simil> to x 9 all ess5tial details3 #a1 #b1 #c1 #d1 #e1 #e-a1 #e-b1 #e-c1 #e-d1 #aj1 #aj-a1 #aj-b1 #aj-c1 #aj-d1 #aj-e1 #aj-e-a1 #aj-e-b1 #aj-e-c1 #aj-e-d1 #bj4 ,f ^! =ms ! entire sy/em c readily be con/ruct$ z soon z x is kn[n :e!r its pr9cipal base is to be #aj or #bj4 ,turn+ fir/ to ! native ,african languages1 ,i h select$ ! foll[+ qu9>y scales f ! abundant mat]ial t has be5 collect$ by ! v>i\s explor]s ( ! ,d>k ,cont95t4 ,9 "s cases ! num]als ( c]ta9 tribes1 z giv5 by "o writ]1 are f\nd to diff] widely f ! same num]als z report$ by ano!r4 ,no attempt has be5 made at comp>ison ( ^! v>y+ =ms ( or?ography1 :i* are usually to be ascrib$ to diff]5ce ( nationality on ! "p ( ! collectors4 ,,feloops4#bdf #a4 enory4 #b4 sickaba1 or cookaba4 #c4 sisajee4 #d4 sibake]4 #e4 footuck4 #f4 footuck-enory #e-a4 #g4 footuck-cookaba #e-b4 #h4 footuck-sisajee #e-c4 #i4 footuck-sibake] #e-d4 #aj4 sibankony54 ,,kissi4#bdg #a4 pili4 #b4 miu4 #c4 nga4 #d4 iol4 #e4 ngu5u4 #f4 ngom-pum #e-a4 #g4 ngom-miu #e-b4 #h4 ngommag #e-c4 #i4 ngu5u-iol #e-d4 #aj4 to4 ,,a%antee4#bdh #a4 tah4 #b4 noo4 #c4 sah4 #d4 nah4 #e4 taw4 #f4 torata #e #a4 #g4 toorife5oo #e #b4 #h4 toorifeessa #e #c4 #i4 toorife5a #e #d4 #aj4 nopnoo4 ,,basa4#bdi #a4 d4 #b4 s4 #c4 ta4 #d4 h9ye4 #e4 hum4 #f4 hum-le-d #e #a4 #g4 hum-le-s #e #b4 #h4 hum-le-ta #e #c4 #i4 hum-le-h9yo #e #d4 #aj4 bla-bue4 ,,jallonkas4#bej #a4 kidd+4 #b4 fidd+4 #c4 s>ra4 #d4 nani4 #e4 soolo4 #f4 s5i4 #g4 soolo ma fidd+ #e #b4 #h4 soolo ma s>ra #e #c4 #i4 soolo ma nani #e #d4 #aj4 nuff4 ,,kru4 #a4 da-d4 #b4 de-son4 #c4 de-tan4 #d4 de-nie4 #e4 de-mu4 #f4 dme-du #e-a4 #g4 ne-son #e #b4 #h4 ne-tan #e #c4 #i4 sepadu #aj - #a8 #aj4 pua4 ,,jal(fs4#bea #a4 wean4 #b4 y>4 #c4 yat4 #d4 yanet4 #e4 judom4 #f4 judom-wean #e-a4 #g4 judom-y> #e-b4 #h4 judom-yat #e-c4 #i4 judom yanet #e-d4 #aj4 fook4 ,,golo4#beb #a4 mbali4 #b4 bisi4 #c4 bitta4 #d4 b&a4 #e4 zonno4 #f4 tsimmi tongbali #e #a4 #g4 tsimmi tobisi #e #b4 #h4 tsimmi tobitta #e #c4 #i4 tsimmi to b&a #e #d4 #aj4 nifo4 ,,f\lah4#bec #a4 g4 #b4 de$dee4 #c4 tettee4 #d4 nee4 #e4 j\ee4 #f4 jego #e-a4 #g4 j$e$dee #e-b4 #h4 je-tettee #e-c4 #i4 je-nee #e-d4 #aj4 sappo4 ,,s\ss\4#bed #a4 k]54 #b4 fir+4 #c4 s>kan4 #d4 nani4 #e4 s\li4 #f4 s5i4 #g4 solo-f]e #e-b4 #h4 solo-maz>kan #e #c4 #i4 solo-manani #e #d4 #aj4 fu4 ,,bullom4#bee #a4 bul4 #b4 t94 #c4 ra4 #d4 hyul4 #e4 m54 #f4 m5-bul #e-a4 #g4 m5-t9 #e-b4 #h4 m5-ra #e-c4 #i4 m5-hyul #e-d4 #aj4 won4 ,,vei4#bef #a4 dondo4 #b4 f]a4 #c4 sagba4 #d4 nani4 #e4 soru4 #f4 sun-dondo #e-a4 #g4 sum-f]a #e-b4 #h4 sun-sagba #e-c4 #i4 sun-nani #e-d4 #aj4 tan4 ,,d9ka4#beg #a4 tok4 #b4 r\4 #c4 dyak4 #d4 nuan4 #e4 wdyets4 #f4 wdetem #e-a4 #g4 wd]\ #e-b4 #h4 bet1 b$ #e-c4 #i4 wd5uan #e-d4 #aj4 wty] #e #b4 ,,temne4 #a4 94 #b4 ran4 #c4 sas4 #d4 anle4 #e4 tr-amat4 #f4 tr-amat rok-9 #e #a4 #g4 tr-amat de ran #e #b4 #h4 tr-amat re sas #e #c4 #i4 tr-amat ro n-anle #e #d4 #aj4 tr-(atr4 ,,abak]4#beh #a4 kili4 #b4 bore4 #c4 dotla4 #d4 a%e4 #e4 ini4 #f4 im kili #e-a4 #g4 im-bone #e-b4 #h4 ini-dotta #e-c4 #i4 t9 a%e #e-d4 #aj4 *ica4 ,,bagrimma4#bei #a4 k$e4 #b4 sab4 #c4 muta4 #d4 s4 #e4 mi4 #f4 mi-ga #e #a4 #g4 tsidi4 #h4 m>ta #e #b4 #i4 d-s #e #c #aj4 duk-keme4 ,,papaa4#bfj #a4 depoo4 #b4 auwi4 #c4 ottong4 #d4 enne4 #e4 attong4 #f4 attugo4 #g4 atjuwe #e #b4 #h4 attiatong #e #c4 #i4 atje5ne #e #d4 #aj4 awo4 ,,efik4#bfa #a4 kiet4 #b4 iba4 #c4 ita4 #d4 inan4 #e4 itiun4 #f4 itio-kiet #e-a4 #g4 itia-ba #e-b4 #h4 itia-eta #e-c4 #i4 osu-kiet #aj - #a8 #aj4 duup4 ,,nupe4#bfb #a4 n9i4 #b4 gu-ba4 #c4 gu-ta4 #d4 gu-ni4 #e4 gu-tsun4 #f4 gu-sua-y9 #e #a4 #g4 gu-tua-ba #e #b4 #h4 gu-tu-ta #e #c4 #i4 gu-tua-ni #e #d4 #aj4 gu-wo4 ,,mokko4#bfc #a4 ki4 #b4 iba4 #c4 itta4 #d4 inan4 #e4 tt94 #f4 itjekee #e #a4 #g4 ittiaba #e #b4 #h4 itteiata #e #c4 #i4 hus*ukiet4 #aj4 bb4 ,,kanuri4#bfd #a4 tilo4 #b4 ndi4 #c4 yasge4 #d4 dege4 #e4 ugu4 #f4 arasge #e #a4 #g4 tulur4 #h4 wusge #e #c4 #i4 leg>4 #aj4 megu #b #e4 ,,b994#bfe #a4 bo4 #b4 be4 #c4 la4 #d4 n94 #e4 tang4 #f4 tahu #e #a8 #g4 tabi #e #b4 #h4 t>a #e #c4 #i4 ian9 7tan987 #e #d8 #aj4 te4 ,,kr$y4#bff #a4 baia4 #b4 rommu4 #c4 totto4 #d4 sosso4 #e4 saya4 #f4 yembobaia #e #a4 #g4 yemborommu #e #b4 #h4 yembototto #e #c4 #i4 yembososso #e #d4 #aj4 puh4 ,,h]]o4#bfg #a4 mue4 #b4 v>i4 #c4 tatu4 #d4 ne4 #e4 tano4 #f4 hamb\-mue #e #a4 #g4 hamb\-v>i #e #b4 #h4 hamb\-tatu #e #c4 #i4 hamb\-ne #e #d4 #aj4 ,,ki-,,yau4#bfh #a4 jumo4 #b4 wawiri4 #c4 watatu4 #d4 m*e*e4 #e4 msano4 #f4 musano na jumo #e #a4 #g4 musano na wiri #e #b4 #h4 musano na watatu #e #c4 #i4 musano na m*e*e #e #d4 #aj4 ikumi4 ,,f]n&o ,,po4#bfi #a4 muli4 #b4 mempa4 #c4 meta4 #d4 mi5e4 #e4 mimito4 #f4 mimito na muli #e #a4 #g4 mimito na mempa #e #b4 #h4 mimito na meta #e #c4 #i4 mimito na mi5e #e #d4 #aj4 miemieu #e-e8 ,,ki-,,nyassa #a4 kimodzi4 #b4 vi-wiri4 #c4 vi-tatu4 #d4 v9ye4 #e4 visano4 #f4 visano na kimodzi #e #a4 #g4 visano na vi-wiri #e #b4 #h4 visano na vitatu #e #c4 #i4 visano na v9ye #e #d4 #aj4 *ikumi4 ,,bal5gue4#bgj #a4 guevoho4 #b4 ib>e4 #c4 r>o4 #d4 ina4 #e4 itano4 #f4 itano na guevoho #e #a4 #g4 itano na ib>e #e #b4 #h4 itano na r>o #e #c4 #i4 itano na ina #e #d4 #aj4 ndi\m1 or nai-h9a4 ,,kunama4#bga #a4 ella4 #b4 b>e4 #c4 sadde4 #d4 salle4 #e4 kussume4 #f4 kon-t'-ella h& #a4 #g4 kon-te-b>e h& #b4 #h4 kon-te-sadde h& #c4 #i4 kon-te-salle h& #d4 #aj4 kol-lakada4 ,,gola4#bgb #a4 ng\m\4 #b4 ntie4 #c4 nta4 #d4 t9a4 #e4 nonon4 #f4 dieg\m #e #a4 #g4 di5tie #e #b4 #h4 dietai #e #c4 #i4 dect9a #e #d4 #aj4 esia4 ,,b>ea4#bgc #a4 doko #b4 arega4 #c4 sane4 #d4 sone4 #e4 oita4 #f4 data4 #g4 dz-ariga #e #b4 #h4 dis-s5a #e #c4 #i4 lefete-mada )\t #aj4 #aj4 lefek4 ,,matibani4#bgd #a4 mosa4 #b4 pili4 #c4 t>u4 #d4 teje4 #e4 t>u4 #f4 tana mosa #e-a4 #g4 tana pili #e-b4 #h4 tana t>u #e-c4 #i4 loco4 #aj4 loco nakege4 ,,bonz4#bge #a4 tan4 #b4 vele4 #c4 daba4 #d4 nani4 #e4 lol\4 #f4 mada #e #a4 #g4 mafile #e #b4 #h4 ma%aba #e #c4 #i4 manan #e #d4 #aj4 b\4 ,,mpovi #a4 m\eta4 #b4 bevali4 #c4 betata4 #d4 b5a4 #e4 betani4 #f4 betani m\eta #e-a4 #g4 betani bevali #e-b4 #h4 betani betata #e-c4 #i4 betani b5ai #e-d4 #aj4 n*9ia4 ,,triton',s ,,bay1 ,,new ,,qu9ea4#bgf #a4 samosi4 #b4 r\eti4 #c4 t\r\4 #d4 faat4 #e4 rimi4 #f4 rim-samosi #e-a4 #g4 rim-r\eti #e-b4 #h4 rim-t\r\ #e-c4 #i4 rim-faat #e-d4 #aj4 outsia4 ,,ende1 ,,or ,,flores4#bgg #a4 sa4 #b4 zua4 #c4 telu4 #d4 wutu4 #e4 lima h&4 #f4 lima-sa #e-a1 or h& #a4 #g4 lima-zua #e-b4 #h4 rua-butu #b #d8 #i4 trasa #aj - #a8 #aj4 sabulu4 ,,mallicolo4#bgh #a4 tseekaee4 #b4 ery4 #c4 erei4 #d4 ebats4 #e4 ereem4 #f4 tsookaee #e #a4 #g4 gooy #e #b4 #h4 hoorey #e #c4 #i4 goodbats #e #d4 #aj4 s5e>n4 ,,ebon1 ,,m>%all ,,isl&s4#bgi #a4 iuwun4 #b4 drud4 #c4 *ilu4 #d4 em]4 #e4 lailem4 #f4 *il*9u #e #a4 #g4 *il*ime #e #b4 #h4 twali?uk #aj - #b4 #i4 twahmejuw\ #aj - #a4 #aj4 iung\4 ,,uea1 ,,loyalty ,,isl&4#bhj #a4 tahi4 #b4 lua4 #c4 tolu4 #d4 fa4 #e4 lima4 #f4 tahi4 #g4 lua4 #h4 tolu4 #i4 fa4 #aj4 lima4 ,,uea4#bhj--;ano!r dialect4 #a4 ha*a4 #b4 lo4 #c4 kuun4 #d4 ?ack4 #e4 ?abumb4 #f4 lo-a*a #b;d #a4 #g4 lo-alo #b;d #b4 #h4 lo-kuun #b;d #c4 #i4 lo-?ack #b;d #d4 #aj4 leb5etee4 ,,isle ,,( ,,p9es4#bha #a4 ta4 #b4 bo4 #c4 beti4 #d4 beu4 #e4 ta-hue4 #f4 no-ta #b;d #a4 #g4 no-bo #b;d #b4 #h4 no-beti #b;d #c4 #i4 no-beu #b;d #d4 #aj4 de-kau4 ,,urep>ap>a1 ,,banks ,,isl&s4#bhb #a4 vo t[a4 #b4 vo ro4 #c4 vo tol4 #d4 vo vet4 #e4 teveliem #a h&4 #f4 leve jea o!r #a4 #g4 leve ro o!r #b4 #h4 leve tol o!r #c4 #i4 leve vet o!r #d4 #aj4 san[ul #b sets4 ,,mota1 ,,banks ,,isl&s4#bhb #a4 tuwale4 #b4 nirua4 #c4 nitol4 #d4 nivat4 #e4 tavelima #a h&4 #f4 laveatea o!r #a4 #g4 lave>ua o!r #b4 #h4 laveatol o!r #c4 #i4 laveavat o!r #d4 #aj4 sanavul #b sets4 ,,new ,,cal$onia4#bhc #a4 p>ai4 #b4 p>oo4 #c4 p>gh54 #d4 p>bai4 #e4 panim4 #f4 panim-gha #e-a4 #g4 panim-roo #e-b4 #h4 panim-gh5 #e-c4 #i4 panim-bai #e-d4 #aj4 p>ooneek4 ,,y5g51 ,,new ,,cal4#bhd #a4 hets4 #b4 heluk4 #c4 hey54 #d4 pobits4 #e4 nim h&4 #f4 nim-wet #e-a4 #g4 nim-weluk #e-b4 #h4 nim-wey5 #e-c4 #i4 nim-pobit #e-d4 #aj4 pa9-duk4 ,,aneiteum4#bhe #a4 e?i4 #b4 ero4 #c4 eseik4 #d4 manohwan4 #e4 nikman4 #f4 nikman cl$ et e?i #e #a4 #g4 nikman cl$ et oro #e #b4 #h4 nikman cl$ et eseik #e #c4 #i4 nikman cl$ et manohwan #e #d4 #aj4 nikman lep ikman #e #e4 ,,tanna #a4 riti4 #b4 k>u4 #c4 kah>4 #d4 kefa4 #e4 krirum4 #f4 krirum riti #e-a4 #g4 krirum k>u #e-b4 #h4 krirum kah>8 #e-c4 #i4 krirum kefa8 #e-d4 #aj4 ---- ,,eromanga #a4 sai4 #b4 duru4 #c4 disil4 #d4 divat4 #e4 siklim #a h&4 #f4 misikai o!r #a8 #g4 siklim n>u #e-b4 #h4 siklim disil #e-c4 #i4 siklim m9divat #e #d4 #aj4 n>olim #b h&s4 ,,fate1 ,,new ,,heb4#bhf #a4 iskei4 #b4 rua4 #c4 tolu4 #d4 bate4 #e4 lima h&4 #f4 la tesa o!r #a4 #g4 la rua o!r #b4 #h4 la tolu o!r #c4 #i4 la fiti o!r #d4 #aj4 relima #b h&s4 ,,api1 ,,new ,,heb4 #a4 tai4 #b4 lua4 #c4 tolu4 #d4 v>i4 #e4 lima h&4 #f4 o rai o!r #a4 #g4 o lua o!r #b4 #h4 o tolo o!r #c4 #i4 o v>i o!r #d4 #aj4 lua lima #b h&s4 ,,sesake1 ,,new ,,heb4 #a4 sikai4 #b4 dua4 #c4 dolu4 #d4 pati4 #e4 lima h&4 #f4 la tesa o!r #a4 #g4 la dua o!r #b4 #h4 la dolu o!r #c4 #i4 lo veti o!r #d4 #aj4 dua lima #b h&s4 ,,pama1 ,,new ,,heb4 #a4 tai4 #b4 e lua4 #c4 e tolu4 #d4 e hati4 #e4 e lime h&4 #f4 a hitai o!r #a4 #g4 o lu o!r #b4 #h4 o tolu o!r #c4 #i4 o hati o!r #d4 #aj4 ha lua lim #b h&s ,,aurora1 ,,new ,,heb4 #a4 tewa4 #b4 i rua4 #c4 i tol4 #d4 i vat4 #e4 tavalima #a h&4 #f4 lava tea o!r #a4 #g4 lava rua o!r #b4 #h4 lava tol o!r #c4 #i4 la vat o!r #d4 #aj4 sanwulu two sets4 ,,tobi4#bhg #a4 yat4 #b4 glu4 #c4 ya4 #d4 uan4 #e4 yanim #a h&4 #f4 yawor o!r #a4 #g4 yavic o!r #b4 #h4 yawa o!r #c4 #i4 yatu o!r #d4 #aj4 yasec4 ,,palm ,,isl&4#bhh #a4 yonkol4 #b4 yakka4 #c4 tetjora4 #d4 t>ko4 #e4 yonkol mala #a h&4 ,,jaj[]ong1 ,,victoria4#bhh #a4 ki>p4 #b4 bulaits4 #c4 bulaits ki>p #b-a4 #d4 bulaits bulaits #b-b4 #e4 ki>p munn> #a h&4 #f4 bulaits bulaits bulaits #b-b-b4 #aj4 bulaits munn> #b h&s4 ,! la/ two scales des]ve special notice4 ,!y are ,au/ralian scales1 & ! =m] is /rongly b9>y1 z are s _m o!rs ( t cont95t4 ,b bo? %[ an incipi5t qu9>y t5d5cy 9 _! names = #e & #aj4 ,,cambodia4#bhi #a4 muy4 #b4 pir4 #c4 bey4 #d4 buon4 #e4 pram4 #f4 pram muy #e-a4 #g4 pram pil #e-b4 #h4 pram bey #e-c4 #i4 pram buon #e-d4 #aj4 dap4 ,,ts*uks*i4#bij #a4 in54 #b4 nira*4 #c4 n'ro*4 #d4 n'ra*4 #e4 milig5 h&4 #f4 in5 milig5 #a-e4 #g4 nira* milig5 #b-e4 #h4 anwrotk94 #i4 *ona ts9ki4 #aj4 migitk5 bo? h&s4 ,,kottis*#bia #a4 hutsa4 #b4 ina4 #c4 tona4 #d4 sega4 #e4 *ega4 #f4 *elutsa #e #a4 #g4 *el9a #e #b4 #h4 *altona #e #c4 #i4 tsumnaga #aj - #a4 #aj4 haga4 ,,eskimo ,,( ,n4-,w4 ,,alaska4#bib #a4 a t[%ek4 #b4 hipah1 or malho4 #c4 p+i%ute4 #d4 sesaimat4 #e4 talema4 #f4 okv9ile1 or ah*eg>et ano!r #a8 #g4 talema-malronik #e-two ( !m4 #h4 p+i%u-okv+ile #b;d #c8 #i4 kol+otalia #aj - #a8 #aj4 koleet4 ,,kamts*atka1 ,,s\?4#bic #a4 dis*ak4 #b4 kas*a4 #c4 ts*ook4 #d4 ts*aaka4 #e4 kumnaka4 #f4 ky'lkoka4 #g4 itatyk #b #e4 #h4 ts*ookotuk #c #e4 #i4 ts*uaktuk #d #e4 #aj4 kume*tuk #e #e4 ,,aleuts#bid #a4 ataqan4 #b4 aljak4 #c4 qankun4 #d4 sits94 #e4 tsan my h&4 #f4 atun #a #e4 #g4 ulun #b #e4 #h4 qamts9 #c #e4 #i4 sits9 #d #e4 #aj4 hatsiq4 ,,t*iglit1 ,,mack5zie ,r4#bie #a4 ataotirkr4 #b4 aypak1 or mallo]ok4 #c4 illaak1 or piatcut4 #d4 titamat4 #e4 tallemat4 #f4 arv5elo]it4 #g4 arv5elo]it-aypak #e #b4 #h4 arv5elo]it-illaak #e #c4 #i4 arv5elo]it-titamat #e #d4 #aj4 krolit4 ,,sahapt9 7,,nez ,,p]ces74#bif #a4 naks4 #b4 lapit4 #c4 mitat4 #d4 pi-lapt #b #b4 #e4 pa*at4 #f4 oi-laks #e #a4 #g4 oi-napt #e #b4 #h4 oi-matat #e #c4 #i4 koits4 #aj4 putimpt4 ,,gre5l&4#big #a4 atauseq4 #b4 ma*dluq4 #c4 p9asut4 #d4 sisamat #e4 tadlimat4 #f4 a*f9eq-atauseq o!r h& #a4 #g4 a*f9eq-ma*dluq o!r h& #b4 #h4 a*f9eq-p9asut o!r h& #c4 #i4 a*f9eq-sisamat o!r h& #d4 #aj4 qulit4 #aa4 a*qaneq-atauseq fir/ foot #a4 #ab4 a*qaneq-ma*dluq fir/ foot #b4 #ac4 a*qaneq-p9asut fir/ foot #c4 #ad4 a*qaneq-sisamat fir/ foot #d4 #ae4 a*fe*saneq8 #af4 a*fe*saneq-atauseq o!r foot #a4 #ag4 a*fe*saneq-ma*dlup o!r foot #b4 #ah4 a*fe*saneq-p9asut o!r foot #c4 #ai4 a*fe*saneq-sisamat o!r foot #d4 #bj4 inuk navdlu*o a man end$4 ,up to ?is po9t ! ,gre5l&]'s scale is almo/ purely qu9>y4 ,l ^? ( :i* m5tion 0 made at ! beg9n+ ( ?is *apt]1 x p]si/s 9 progress+ by fives until x rea*es #bj1 :5 x ann\nces a new base1 :i* %[s t ! sy/em w f n[ on be vigesimal4 ,?is scale is "o ( ! mo/ int]e/+ ( :i* we h any record1 & w be notic$ aga9 9 ! next *apt]4 ,9 _m respects x is l ! scale ( ! ,po9t ,b>r[ ,eskimo1 :i* 0 giv5 e>ly 9 ,*apt] ,,iii4 ,! ,eskimo languages are *>act]i/ically qu9>y-vigesimal 9 _! numb] sy/ems1 b few ( !m pres5t su* p]fect examples ( t me?od ( c\nt+ z d ! two j m5tion$4 ,,*ippeway4#bih #a4 bejig4 #b4 nij4 #c4 nisswi4 #d4 niw94 #e4 nanun4 #f4 n+otwasswi #a aga98 #g4 nijwasswi #b aga98 #h4 ni%wasswi #c aga98 #i4 jangasswi #d aga98 #aj4 midasswi #e aga94 ,,massa*usetts4#bii #a4 nequt4 #b4 neese4 #c4 ni%4 #d4 yaw4 #e4 napanna on "o side1 i4e4 #a h&4 #f4 nequttata% #a add$4 #g4 nesausuk #b aga98 #h4 %awosuk #c aga98 #i4 pa%oogun x comes ne>1 i4e4 to #aj4 #aj4 puik4 ,,ojibwa ,,( ,,*egoimegon4#cjj #a4 ba%ik4 #b4 ne5%4 #c4 niswe4 #d4 new94 #e4 nanun4 #f4 n+odwaswe #a aga98 #g4 ni%waswe #b aga98 #h4 %\swe #c aga98 #i4 %angaswe #d aga98 #aj4 m$aswe #e aga98 ,,ottawa4 #a4 n+ot*au4 #b4 n9jwa4 #c4 niswa4 #d4 niw94 #e4 nanau4 #f4 n+otwaswi #a aga98 #g4 n9jwaswi #b aga98 #h4 ni*waswi #c aga98 #i4 %ang4 #aj4 kwet*4 ,,delaw>e4 #a4 n'gutti4 #b4 niskha4 #c4 nakha4 #d4 newa4 #e4 nalan ak9 to pal5a*1 h&4 #f4 gutta% #a on ! o!r side4 #g4 ni%a% #b on ! o!r side4 #h4 khaa% #c on ! o!r side4 #i4 pe%gonk com+ ne>4 #aj4 tell5 no m4 ,,%awnoe4 #a4 negote4 #b4 ne%wa4 #c4 ni?uie4 #d4 newe4 #e4 nial9we gone4 #f4 negotewa?we #a fur!r4 #g4 ne%wa?we #b fur!r4 #h4 sa%ekswa #c fur!r8 #i4 *akatswe ak9 to *agisse1 us$ up4 #aj4 meta?we no fur!r4 ,,micmac4#cja #a4 naiookt4 #b4 tahboo4 #c4 see/4 #d4 naioo4 #e4 nahn4 #f4 usoo-cum4 #g4 eloo-igunuk4 #h4 oo-gumool*94 #i4 pescoonaduk4 #aj4 mtl94 ,"o peculi>ity ( ! ,micmac num]als is mo/ notewor?y4 ,! num]als are real v]bs1 in/ead ( adjectives1 or1 z is sometimes ! case1 n\ns4 ,!y are conjugat$ ?r\gh all ! v>iations ( mood1 t5se1 p]son1 & numb]4 ,! =ms giv5 above are n ^? t w\ld be us$ 9 c\nt+1 b are = specific use1 be+ v>i$ accord+ to ! ?\ght x 0 int5d$ to express4 ,= example1 naiooktai* !re is #a1 is pres5t t5se2 naiooktai*cus1 !re 0 #a1 is imp]fect2 & encoodai*d$\1 !re w be #a1 is future4 ,! v>iation 9 p]son is %[n by ! foll[+ inflection3 ,,pres5t ,,t5se4 #a/ p]s4 tahboosee-ek !re are #b ( u4 #b;d p]s4 tahboosee-yok !re are #b ( y4 #c;d p]s4 tahboo-sijik !re are #b ( !m4 ,,imp]fect ,,t5se4 #a/ p]s4 tahboosee-egup !re 7 #b ( u4 #b;d p]s4 tahboosee-yogup !re 7 #b ( y4 #c;d p]s4 tahboosee-sibunik !re 7 #b ( !m4 ,,future ,,t5se4 #c;d p]s4 tahboosee-dak !re w be #b ( !m1 etc4 ,! negative =m is also compreh5d$ 9 ! li/ ( possible v>iations4 ,?us1 tahboo-seekw1 !re are n #b ( !m2 mah tahboo-seekw1 !re w n be #b ( !m2 & s on1 ?r\gh all ! *anges :i* ! conjugation ( ! v]b p]mits4 ,,old ,,algonqu94 #a4 peygik4 #b4 n9%4 #c4 nisswey4 #d4 neyoo4 #e4 nahran gone4 #f4 n+ootwassoo #a on ! o!r side4 #g4 n9%wassoo #b on ! o!r side4 #h4 nisswasso #c on ! o!r side4 #i4 %angassoo ak9 to *agisse1 us$ up4 #aj4 mitassoo no fur!r4 ,,omaha4 #a4 meea**ee4 #b4 nomba4 #c4 rabe5ee4 #d4 tooba4 #e4 satta h&1 i4e4 all ! f+]s turn$ d[n4 #f4 %appai #a m4 #g4 pa9umba f+]s #b4 #h4 pairabe5ee f+]s #c4 #i4 %onka only #a f+] 7rema9s74 #aj4 kraibaira unb5t4#cjb ,,*octaw4 #a4 a*(ee4 #b4 tuklo4 #c4 tu*9a4 #d4 u%ta4 #e4 tahlape ! fir/ h& ends4 #f4 hanali4 #g4 untuklo aga9 #b4 #h4 untu*9a aga9 #c4 #i4 *okali soon ! end2 i4e4 next ! la/4 #aj4 pokoli4 ,,caddoe4 #a4 k\anigh4 #b4 behit4 #c4 daho4 #d4 hehweh4 #e4 dihsehkon4 #f4 dunkeh4 #g4 bisekah #e #b4 #h4 d\sehka #e #c4 #i4 hehwehsehka #d h&4 #aj4 behnehaugh4 ,,*ippeway4 #a4 pay%ik4 #b4 nee%4 #c4 neeswoy4 #d4 neon4 #e4 naman gone4 #f4 nequtwosswoy #a on ! o!r side4 #g4 nee%swosswoy #b on ! o!r side4 #h4 swoswoy #c on ! o!r side8 #i4 %angosswoy ak9 to *agissi1 us$ up4 #aj4 metosswoy no fur!r4 ,,adaize4 #a4 nancas4 #b4 nass4 #c4 colle4 #d4 taca*e4 #e4 seppacan4 #f4 pacanancus #e #a4 #g4 pacaness #e #b4 #h4 pacalcon #e #c4 #i4 sick9i% h&s m9us8 #aj4 neusne4 ,,pawnee4 #a4 askoo4 #b4 peetkoo4 #c4 t\weet4 #d4 %keetik%4 #e4 %eeook% h&s half4 #f4 %eek%abi% #e #a4 #g4 peetkoo%ee%abi% #b #e4 #h4 t\weet%abi% #c #e4 #i4 look%e]eewa #aj - #a4 #aj4 look%e]ee #b;d #e8 ,,m9si4 #a4 gutti4 #b4 niskha4 #c4 nakba4 #d4 newa4 #e4 nulan gone8 #f4 gutta% #a add$4 #g4 ni%oa% #b add$4 #h4 khaa% #c add$4 #i4 n[eli4 #aj4 wimbat4 ,,konlis*54 #a4 tlek4 #b4 te*4 #c4 nezk4 #d4 taakun4 #e4 kejets*94 #f4 klet us*u #e #a4 #g4 ta*ate us*u #e #b4 #h4 nesket us*u #e #c4 #i4 kus*ok #aj - #a8 #aj4 ts*9kat4 ,,tl+it4#cjc #a4 tlek4 #b4 deq4 #c4 natsk4 #d4 dak'on #b;d #b4 #e4 k$j9 h&4 #f4 tle durcu o!r #a4 #g4 daqa durcu o!r #b4 #h4 natska durcu o!r #c4 #i4 gocuk4 #aj4 dj9kat bo? h&s4 ,,rapid1 ,,or ,,fall1 ,,indians4 #a4 k>ci4 #b4 neece4 #c4 n>ce4 #d4 nean4 #e4 yautune4 #f4 nete>tuce #a ov]8 #g4 nes>tuce #b ov]8 #h4 n>sw>tuce #c ov]8 #i4 anh>betw>tuce #d ov]8 #aj4 mett>tuce no fur!r8 ,,heiltsuk4#cjd #a4 m54 #b4 matl4 #c4 yutq4 #d4 mu4 #e4 sky'a4 #f4 katla4 #g4 matlaaus o!r #b8 #h4 yutquaus o!r #c8 #i4 mam5e #aj - #a4 #aj4 aiky'z4 ,,nootka4#cje #a4 nup4 #b4 atla4 #c4 kat/sa4 #d4 mo4 #e4 sutca4 #f4 nopo o!r #a8 #g4 atlpo o!r #b8 #h4 atlakutl #aj - #b4 #i4 ts'owakutl #aj - #a4 #aj4 haiu4 ,,tsim%ian4#cjf #a4 gyak4 #b4 tepqat4 #c4 guant4 #d4 tqalpq4 #e4 kctonc 7f anon1 h&74 #f4 kalt #b;d #a4 #g4 t'epqalt #b;d #b4 #h4 gu&alt #b;d #c8 #i4 kctemac4 #aj4 gy'ap4 ,,bilqula4#cjf #a4 7s7maotl4 #b4 tlnos4 #c4 asmo/4 #d4 mos4 #e4 tse*4 #f4 tqotl #b;d #a8 #g4 nu/lnos #b;d #b8 #h4 k'etlnos #b #d4 #i4 k'esman4 #aj4 tsk*lak*t4 ,,molele4#cjg #a4 mangu4 #b4 lapku4 #c4 mutka4 #d4 pipa4 #e4 pika4 #f4 napitka #a #e4 #g4 lapitka #b #e4 #h4 mutpitka #c #e4 #i4 lag9/%iatkus4 #aj4 nawitspu4 ,,waiilatpu4#cjh #a4 na4 #b4 lepl94 #c4 matn94 #d4 pip+4 #e4 tawit4 #f4 no9a #e #a4 #g4 noilip #e #b4 #h4 noimat #e #c4 #i4 tanauiai%im%im4 #aj4 n+itelp4 ,,lutuami4#cjg #a4 nat%ik4 #b4 lapit4 #c4 ntani4 #d4 wonip4 #e4 tonapni4 #f4 nakski%uptane #a #e4 #g4 tapki%uptane #b #e4 #h4 ndaneki%uptane #c #e4 #i4 natskaiaki% #aj - #a4 #aj4 taunip4 ,,sa/e 7,,%a/a74#cji #a4 t%iamu4 #b4 hoka4 #c4 hatski4 #d4 irahaia4 #e4 et%a4 #f4 tahaia4 #g4 hokaik9is #b #e4 #h4 hatsikikiri #c #e4 #i4 kirih>iki-ikiriu4 #aj4 etsehewi4 ,,cahuillo4#caj #a4 supli4 #b4 mewi4 #c4 mepai4 #d4 mewittsu4 #e4 nomekadnun4 #f4 kadnun-supli #e-a4 #g4 kan-munwi #e-b4 #h4 kan-munpa #e-c4 #i4 kan-munwitsu #e-d4 #aj4 nomatsumi4 ,,timukua4#caa #a4 yaha4 #b4 yutsa4 #c4 hapu4 #d4 tseketa4 #e4 m>ua4 #f4 m>eka #e #a #g4 pikitsa #e #b #h4 pik9ahu #e #c #i4 peke-tsaketa #e #d #aj4 tuma4 ,,otomi#cab #a4 n>a4 #b4 yo*o4 #c4 *iu4 #d4 go*o4 #e4 kuto4 #f4 rato #a #e4 #g4 yoto #b #e4 #h4 *iato #c #e4 #i4 guto #d #e4 #aj4 reta4 ,,t>asco4#cac #a4 ma4 #b4 dziman4 #c4 tanimo4 #d4 tamu4 #e4 yumu4 #f4 kuimu4 #g4 yun-dziman #e #b4 #h4 yun-tanimo #e #c4 #i4 yun-tamu #e #d4 #aj4 temb54 ,,matlaltz9can4#cad #a4 indawi4 #b4 inawi4 #c4 inyuhu4 #d4 inkun[i4 #e4 inkutaa4 #f4 inda-t[i #a #e4 #g4 ine-t[i #b #e4 #h4 ine-ukun[i #b-d4 #i4 imuratadahata #aj - #a8 #aj4 inda-hata4 ,,cora4#cae #a4 ceaut4 #b4 huapoa4 #c4 huaeica4 #d4 moacua4 #e4 anxuvi4 #f4 a-cevi #e #a4 #g4 a-huapoa #e #b4 #h4 a-huaeica #e #c4 #i4 a-moacua #e #d4 #aj4 tamoamata 7ak9 to moamati1 h&74 ,,aym>a4#caf #a4 maya4 #b4 paya4 #c4 kimsa4 #d4 pusi4 #e4 piska4 #f4 tsokta4 #g4 pa-kalko #b #e4 #h4 kimsa-kalko #c #e4 #i4 pusi-kalko #d #e4 #aj4 tunka4 ,,c>ibs ,,( ,,essequibo1 ,,guiana4#cag #a4 owe54 #b4 oko4 #c4 oro[a4 #d4 oko-baimema4 #e4 w9eetanee #a h&4 #f4 owee-puimapo #a aga98 #g4 oko-puimapo #b aga98 #h4 oro[a-puimapo #c aga98 #i4 oko-baimema-puimapo #d aga98 #aj4 owe5-abatoro4 ,,c>ib4#cah 7,,r\c\y5ne87 #a4 aban1 amo94 #b4 biama4 #c4 ele\a4 #d4 biam-b\ri #b aga98 #e4 ouacabo-ap\rc\-aban-tibateli4 #f4 aban laoyagone-ouacabo-ap\rc\4 #g4 biama laoyagone-ouacabo-ap\rc\4 #h4 ele\a laoyagone-ouacabo-ap\rc\4 #i4 ---- #aj4 *on n\cabo4 ,x is un=tunate t ! mean+s ( ^! rem>kable num]als _c be giv54 ,! c\nt+ is evid5tly qu9>y1 b ! t]ms us$ mu/ h be5 purely descriptive expressions1 hav+ _! orig9 und\bt$ly 9 c]ta9 ge/ures or f+] motions4 ,! num]als obta9$ f ?is region1 & f ! tribes to ! s\? & ea/ ( ! ,c>ib c\ntry1 are especially ri* 9 digital t]ms1 & an analysis ( ! above num]als w\ld probably %[ cle>ly ! m5tal /eps ?r\gh :i* ?is p pass$ 9 con/ruct+ ! rude scale :i* s]v$ = ! expression ( _! ideas ( numb]4 ,,kiriri4#cai #a4 bi*e4 #b4 watsani4 #c4 watsani dikie4 #d4 sum>a oroba4 #e4 mi bi*e misa #a h&4 #f4 mirepri bu-bi*e misa sai4 #g4 mirepri watsani misa sai4 #h4 mirepri wats&ikie misa sai4 #i4 mirepri sum>a oraba sai4 #aj4 mikriba misa sai bo? h&s4 ,,cayubaba#cbj #a4 pebi4 #b4 mbeta4 #c4 kimisa4 #d4 pusi4 #e4 pisika4 #f4 sukuta4 #g4 pa-kaluku #b aga98 #h4 kimisa-kaluku #c aga98 #i4 pusu-kaluku #d aga98 #aj4 tunka4 ,,sapibocona#cbj #a4 k>ata4 #b4 mitia4 #c4 kurapa4 #d4 tsada4 #e4 maid>a 7f arue1 h&74 #f4 k>ata-rirobo #a h& )4 #g4 mitia-rirobo #b h& )4 #h4 kurapa-rirobo #c h& )4 #i4 tsada-rirobo #d h& )4 #aj4 bururutse h& h&4 ,,ticuna4#cba #a4 hueih4 #b4 t>epueh4 #c4 tomepueh4 #d4 aguem\jih #e4 hueamepueh4 #f4 namehueapueh #e #a4 #g4 namehueat>eh #e #b4 #h4 namehueatameapueh #e #c4 #i4 gomeapueh #aj - #a4 #aj4 gomeh4 ,,yanua4#cbb #a4 tck9i4 #b4 nanojui4 #c4 munua4 #d4 naroju9o #b;d #b4 #e4 t5aja4 #f4 teki-natea #a aga98 #g4 nanojui-natea #b aga98 #h4 munua-natea #c aga98 #i4 naroju9o-natea #d aga98 #aj4 huijeju9o #b #e8 ,! =ego+ examples w %[ ) consid]able fulness ! wide disp]sion ( ! qu9>y scale4 ,e "p ( ! _w contributes its %>e except ,europe1 :]e ! only exceptions to ! univ]sal use ( ! decimal sy/em are ! half-doz5 languages1 :i* /ill l+] on its conf9es1 ^: numb] base is ! vigesimal4 ,n only is !re no liv+ ,european tongue possess+ a qu9>y numb] sy/em1 b no trace ( ?is me?od ( c\nt+ is f\nd 9 any ( ! num]als ( ! e>li] =ms ( spee*1 :i* h n[ become obsolete4 ,! only possible exceptions ( :i* ,i c ?9k are ! ,greek ,greek3 pempaze91 to c\nt by fives1 & a few k9dr$ words :i* c]ta9ly d h9t at a remote antiquity 9 :i* ! ance/ors ( ! ,greeks c\nt$ on _! f+]s1 & s gr\p$ _! units into fives4 ,! ,roman notation1 ! famili> ,i41 ,,ii41 ,,iii41 ,,iv4 7orig9ally ,,iiii471 ,v41 ,,vi41 etc41 ) equal c]ta9ty sugge/s qu9>y c\nt+1 b ! ,lat9 language conta9s no ve/ige ( any?+ ( ! k9d1 & ! :ole range ( ,lat9 lit]ature is sil5t on ?is po9t1 ?\gh x conta9s num]\s ref]5ces to f+] c\nt+4 ,x is q )9 ! b\nds ( possibility t ! prehi/oric nations ( ,europe possess$ & us$ a qu9>y num]ation4 ,b ( ^! races ! mod]n _w kn[s no?+ save ! few scanty facts t c be ga!r$ f ! /one implem5ts :i* h n[ & !n be5 br\ght to light4 ,_! languages h p]i%$ z utt]ly z h ! races !mselves1 & speculation conc]n+ !m is useless4 ,:atev] _! =m ( num]ation may h be51 x has left no p]ceptible trace on ! languages by :i* !y 7 succe$$4 ,ev5 ! languages ( nor!rn & c5tral ,europe :i* 7 contempor>y ) ! ,greek & ,lat9 ( classical times h1 ) ! exception ( ! ,celtic tongues ( ! extreme ,nor?-we/1 left beh9d !m b meagre traces = ! mod]n /ud5t to "w on4 ,we presume t ! anci5t ,gauls & ,go?s1 ,huns & ,scy?ians1 & o!r b>b>ian tribes _h ! same me?od ( num]ation t _! desc5dants n[ h2 & x is a matt] ( c]ta9ty t ! decimal scale 01 at t "t1 n us$ ) ! univ]sality :i* n[ obta9s2 b :]ev] ! decimal 0 n us$1 ! univ]sal me?od 0 vigesimal2 & t ! qu9>y ev] _h any?+ ( a foo?old 9 ,europe is only to be guess$ f its pres5ce to-day 9 almo/ all ( ! o!r corn]s ( ! _w4 ,f ! fact t ! qu9>y is t "o ( ! ?ree natural scales ) ! smalle/ base1 x has be5 conjectur$ t all tribes possess1 at "s "t 9 _! hi/ory1 a qu9>y num]ation1 :i* at a lat] p]iod m]ges into ei!r ! decimal or ! vigesimal1 & ?us disappe>s or =ms ) "o ( ! latt] a mix$ sy/em4#cbc ,9 support ( ?is !ory x is urg$ t ext5sive regions :i* n[ %[ no?+ b decimal c\nt+ 71 beyond all reasonable d\bt1 qu9>y4 ,x is well kn[n1 = example1 t ! decimal sy/em ( ! ,malays has spread ov] almo/ ! entire ,polynesian region1 displac+ :atev] native scales x enc\nt]$4 ,! same ph5om5on has be5 obs]v$ 9 ,africa1 :]e ! ,arab trad]s h dissem9at$ _! own num]al sy/em v widely1 ! native tribes adopt+ x or modify+ _! own scales 9 su* a mann] t ! ,arab influ5ce is detect$ )\t difficulty4 ,9 view ( ^! facts1 & ( ! extreme read9ess ) :i* a tribe w\ld ?r\gh its f+] c\nt+ fall into ! use ( ! qu9>y me?od1 x does n at fir/ seem improbable t ! qu9>y 0 ! orig9al sy/em4 ,b an ext5d$ /udy ( ! me?ods ( c\nt+ 9 vogue among ! unciviliz$ races ( all p>ts ( ! _w has %[n t ?is !ory is entirely unt5able4 ,! decimal scale is no less simple 9 its /ructure ?an ! qu9>y2 & ! savage1 z he ext5ds ! limit ( 8 scale f #e to #f1 may call 8 new numb] #e-a1 or1 ) equal probability1 give x an entirely new "n1 indep5d5t 9 all respects ( any t h prec$$ x4 ,) ! use ( ?is new "n !re may be associat$ ! conception ( #e & #a m2 b 9 su* multitudes ( in/ances ! words employ$ %[ no trace ( any su* mean+1 t x is impossible = any "o to draw1 ) any degree ( safety1 ! inf]5ce t ! signification 0 orig9ally !re1 b t ! *anges ( "t _h wr\ght *anges 9 v]bal =m s great z to bury x pa/ ! p[] ( recov]y4 ,a full discussion ( ?is "q ne$ n be ent]$ ^u "h4 ,b x w be ( int]e/ to notice two or ?ree num]al scales 9 :i* ! qu9>y influ5ce is s fa9t z to be h>dly disc]nible4 ,!y are f\nd 9 consid]able numb]s among ! ,nor? ,am]ican ,indian languages1 z may be se5 by consult+ ! vocabul>ies t h be5 prep>$ & publi%$ dur+ ! la/ half c5tury4#cbd ,f ^! ,i h select$ ! foll[+1 :i* are suffici5t to illu/rate ! po9t 9 "q3 ,,quappa4 #a4 mil*tih4 #b4 nonnepah4 #c4 dahgh5ih4 #d4 tuah4 #e4 satt\4 #f4 s*appeh4 #g4 p5napah4 #h4 pehdagh5ih4 #i4 s*unkkah4 #aj4 g$eh bonah4 ,,t]raba4#cbe #a4 kr>a4 #b4 kr[4 #c4 krom miah4 #d4 krob k+4 #e4 kras* k+de4 #f4 t]deh4 #g4 kogodeh4 #h4 kwongdeh4 #i4 s*kawdeh4 #aj4 dw[deh4 ,,mohican #a4 ngwitloh4 #b4 neesoh4 #c4 noghhoh4 #d4 nauwoh4 #e4 nunon4 #f4 ngwittus4 #g4 tup\wus4 #h4 ghusooh4 #i4 nauneeweh4 #aj4 mtannit4 ,9 ! ,quappa scale #g & #h appe> to be d]iv$ f #b & #c1 :ile #f & #i %[ no visible trace ( k9%ip ) #a & #d4 ,9 ,mohican1 on ! o!r h&1 #f & #i seem to be d]iv$ f #a & #d1 :ile #g & #h h little or no claim to relation%ip ) #b & #c4 ,9 "s scales a s+le ^w only is f\nd 9 ! second qu9ate to indicate t #e 0 orig9ally ! base on :i* ! sy/em re/$4 ,x is h>dly to be d\bt$1 ev51 t *ange might affect ea* & e "o ( ! num]als f #e to #aj or #f to #i1 s t a dep5d5ce :i* might once h be5 easily detect$ is n[ unrecognizable4 ,b if ?is is s1 ! natural & inevitable "q foll[s--might n ?is h be5 ! hi/ory ( all num]al scales n[ purely decimal8 ,may n ! *anges ( "t h alt]$ ! comp\nds :i* 7 once a cle> indication ( qu9>y c\nt+1 until no trace rema9s by :i* !y c be foll[$ back to _! true orig98 ,p]haps s4 ,x is n 9 ! lea/ degree probable1 b its possibility may1 ( c\rse1 be admitt$4 ,b ev5 !n ! univ]sality ( qu9>y c\nt+ = primitive peoples is by no means e/abli%$4 ,9 ,*apt] ,,ii1 examples 7 giv5 ( races :i* _h no numb] base4 ,lat] on x 0 obs]v$ t 9 ,au/ralia & ,s\? ,am]ica _m tribes us$ #b z _! numb] base2 9 "s cases c\nt+ on pa/ #e )\t %[+ any t5d5cy to use t z a new unit4 ,aga91 ?r\gh ! habit ( c\nt+ ^u ! f+] jo9ts1 in/ead ( ! f+]s !mselves1 ! use ( #c z a base is br\ght into prom95ce1 & #f & #i become #b ?rees & #c ?rees1 respectively1 in/ead ( #e #a & #e #d4 ,! same may be notic$ ( #d4 ,c\nt+ by means ( 8 f+]s1 )\t includ+ ! ?umbs1 ! savage beg9s by divid+ into f\rs in/ead ( fives4 ,traces ( ?is =m ( c\nt+ are some:at num]\s1 especially among ! ,nor? ,am]ican aborig9al tribes4 ,h5ce ! qu9>y =m ( c\nt+1 h[ev] widespread its use may be %[n to be1 c 9 no way be claim$ z ! univ]sal me?od ( any /age ( developm5t 9 ! hi/ory ( mank9d4 ,9 ! va/ majority ( cases1 ! passage f ! base to ! next succe$+ numb] 9 any scale1 is cle>ly def9$4 ,b among races ^: intellig5ce is ( a l[ ord]1 or--if x be p]missible to express x 9 ?is way--among races ^: numb] s5se is feeble1 progression f "o numb] to ! next is n always 9 accordance ) any well-def9$ law4 ,aft] "o or two di/9ct num]als ! c\nt may1 z 9 ! case ( ! ,v$das & ! ,&amans1 proce$ by f+] pantomime & by ! repetition ( ! same ^w4 ,occasionally ! same ^w is us$ = two successive numb]s1 "s ge/ure und\bt$ly s]v+ to di/+ui% ! "o f ! o!r 9 ! savage's m9d4 ,examples ( ?is are n infrequ5t among ! =e/ tribes ( ,s\? ,am]ica4 ,9 ! ,t>iana dialect #i & #aj are express$ by ! same ^w1 paihipawalianuda2 9 ,cobeu1 #h & #i by pepelicoloblic\il9i2 9 ,b>re1 #d1 #e1 & #i by ualibucubi4#cbf ,9 o!r languages ! *ange f "o num]al to ! next is s slight t "o in/9ctively concludes t ! savage is =m+ 9 8 own m9d ano!r1 to him new1 num]al imm$iately f ! la/4 ,9 su* cases ! entire numb] sy/em is scanty1 & ! creep+ hesitancy ) :i* progress is made is visible 9 ! =ms :i* ! num]als are made to take4 ,a s+le illu/ration or two ( ?is mu/ suffice2 b ! ones *os5 are n isolat$ cases4 ,! scale ( ! ,macunis1#cbg "o ( ! num]\s tribes ( ,brazil1 is #a4 poc*a5ang4 #b4 haihg4 #c4 haigunhgnill4 #d4 haihgts*at+4 #e4 haihgts*ihat+ ano!r #d8 #f4 ha?ig-/*iha?+ #b-d8 #g4 ha?9k-ts*iha?+ #b-e8 #h4 ha?9k-ts*ihat+ #b #d8 ,! complete abs5ce (--"o is tempt$ to say--any rhyme or reason f ?is scale is m ?an en\gh to refute any argum5t :i* might t5d to %[ t ! qu9>y1 or any o!r scale1 0 ev] ! sole numb] scale ( primitive man4 ,irregul> z ?is is1 ! sy/em ( ! ,montagnais fully mat*es x1 z ! subjo9$ num]als %[3#cbh #a4 inl'are4 #b4 nak'e4 #c4 t'are4 #d4 d9ri4 #e4 se-sunl>e4 #f4 elkke-t'are #b #c4 #g4 t'a-ye-oy]tan #aj - #c1 or inl'z d9ri #d #c8 #h4 elkke-d9ri #b #d4 #i4 inl'a-ye-oy]tan #aj - #a4 #aj4 on]nan4 ,,*apt] ,,vii4 ,,! ,,vigesimal ,,sy/em4 ,9 its ord9>y developm5t ! qu9>y sy/em is almo/ sure to m]ge into ei!r ! decimal or ! vigesimal sy/em1 & to =m1 ) "o or ! o!r or bo? ( ^!1 a mix$ sy/em ( c\nt+4 ,9 ,africa1 ,oceanica1 & p>ts ( ,nor? ,am]ica1 ! union is almo/ always ) ! decimal scale2 :ile 9 o!r p>ts ( ! _w ! qu9>y & ! vigesimal sy/ems h %[n a decid$ aff9ity = ea* o!r4 ,x is n to be und]/ood t any geographical law ( di/ribution has ev] be5 obs]v$ :i* gov]ns ?is1 b m]ely t c]ta9 families ( races h %[n a pref]5ce = ! "o or ! o!r me?od ( c\nt+4 ,^! families1 dissem9at+ _! *>act]i/ics ?r\gh _! v>i\s bran*es1 h produc$ c]ta9 gr\ps ( races :i* exhibit a well-m>k$ t5d5cy1 "h t[>d ! decimal1 & !re t[>d ! vigesimal =m ( num]ation4 ,z f> z c be asc]ta9$1 ! *oice ( ! "o or ! o!r scale is det]m9$ by no ext]nal circum/ances1 b dep5ds solely on ! m5tal *>act]i/ics ( ! tribes !mselves4 ,environm5t does n ex]t any appreciable influ5ce ei!r4 ,bo? decimal & vigesimal num]ation are f\nd indiff]5tly 9 w>m & 9 cold c\ntries2 9 fruitful & 9 b>r5 l&s2 9 m>itime & 9 inl& regions2 & among highly civiliz$ or deeply degrad$ peoples4 ,:e!r or n ! pr9cipal numb] base ( any tribe is to be #bj seems to dep5d entirely ^u a s+le consid]ation2 are ! f+]s alone us$ z an aid to c\nt+1 or are bo? f+]s & toes us$8 ,if only ! f+]s are employ$1 ! result+ scale mu/ become decimal if suffici5tly ext5d$4 ,if use is made ( ! toes 9 addition to ! f+]s1 ! outcome mu/ inevitably be a vigesimal sy/em4 ,subord9ate to ei!r "o ( ^! ! qu9>y may & (t5 does appe>4 ,x is nev] ! pr9cipal base 9 any ext5d$ sy/em4 ,to ! /atem5t j made respect+ ! orig9 ( vigesimal c\nt+1 exception may1 ( c\rse1 be tak54 ,9 ! case ( num]al scales l ! ,wel%1 ! ,nahuatl1 & _m o!rs :]e ! exact mean+s ( ! num]als _c be asc]ta9$1 no pro( exi/s t ! ance/ors ( ^! peoples ev] us$ ei!r f+] or toe c\nt+2 & ! sweep+ /atem5t t any vigesimal scale is ! outgr[? ( ! use ( ^! natural c\nt]s is n susceptible ( pro(4 ,b s _m examples are met ) 9 :i* ! orig9 is cle>ly ( ?is nature1 t no hesitation is felt 9 putt+ ! above =w>d z a g5]al explanation = ! exi/5ce ( ?is k9d ( c\nt+4 ,any o!r orig9 is difficult to reconcile ) obs]v$ facts1 & /ill m difficult to reconcile ) any rational !ory ( numb] sy/em developm5t4 ,dismiss+ f consid]ation ! qu9>y scale1 let u briefly exam9e once m ! natural process ( evolution ?r\gh :i* ! decimal & ! vigesimal scales come into be+4 ,aft] ! completion ( "o c\nt ( ! f+]s ! savage ann\nces 8 result 9 "s =m :i* def9itely /ates to 8 m9d ! fact t ! end ( a well-m>k$ s]ies has be5 rea*$4 ,beg9n+ aga91 he n[ repeats 8 c\nt ( #aj1 ei!r on 8 own f+]s or on ! f+]s ( ano!r4 ,) ! completion ( ! second #aj ! result is ann\nc$1 n 9 a new unit1 b by means ( a duplication ( ! t]m already us$4 ,x is sc>cely cr$ible t ! unit unconsci\sly adopt$ at ! t]m9ation ( ! fir/ c\nt %\ld n[ be dropp$1 & a new "o sub/itut$ 9 its place4 ,:5 ! me?od "h describ$ is employ$1 #bj is n a natural unit to :i* high] numb]s may be ref]r$4 ,x is :olly artificial2 & x w\ld be mo/ surpris+ if x 7 adopt$4 ,b if ! c\nt ( ! second #aj is made on ! toes 9 place ( ! f+]s1 ! elem5t ( repetition :i* ent]$ into ! previ\s me?od is n[ want+4 ,in/ead ( ref]r+ ea* new numb] to ! #aj already complet$1 ! savage is /ill feel+ 8 way along1 designat+ 8 new t]ms by su* phrases z #a on ! foot1 #b on ! o!r foot1 etc4 ,& n[1 :5 #bj is rea*$1 a s+le s]ies is f9i%$ in/ead ( a d\ble s]ies z be=e2 & ! result is express$ 9 "o ( ! _m me?ods already notic$--"o man1 h&s & feet1 ! feet f9i%$1 all ! f+]s ( h&s & feet1 or "s equival5t =mula4 ,t5 is no long] ! natural base4 ,! numb] f :i* ! new />t is made is #bj1 & ! result+ scale is inevitably vigesimal4 ,if pebbles or /icks are us$ in/ead ( f+]s1 ! sy/em w probably be decimal4 ,b back ( ! /ick & pebble c\nt+ ! #aj natural c\nt]s always exi/1 & to !m we mu/ always look = ! orig9 ( ?is scale4 ,9 any collection ( ! pr9cipal vigesimal numb] sy/ems ( ! _w1 "o w\ld naturally beg9 ) ^? possess$ by ! ,celtic races ( ,europe4 ,^! races1 ! e>lie/ ,european peoples ( :om we h any exact k1 %[ a pref]5ce = c\nt+ by tw5ties1 :i* is almo/ z decid$ z t manife/$ by ,teutonic races = c\nt+ by t5s4 ,x has be5 conjectur$ by "s writ]s t ! explanation = ?is 0 to be f\nd 9 ! anci5t comm]cial int]c\rse :i* exi/$ betwe5 ! ,britons & ! ,c>?ag9ians & ,pho5icians1 ^: numb] sy/ems %[$ traces ( a vigesimal t5d5cy4 ,consid]+ ! fact t ! use ( vigesimal c\nt+ 0 univ]sal among ,celtic races1 ?is explanation is q gratuit\s4 ,! reason :y ! ,celts us$ ?is me?od is entirely unkn[n1 & ne$ n conc]n inve/igators 9 ! lea/4 ,b ! fact t !y did use x is important1 & comm&s att5tion4 ,! five ,celtic languages1 ,breton1 ,iri%1 ,wel%1 ,manx1 & ,gaelic1 conta9 ! foll[+ well-def9$ vigesimal scales4 ,only ! pr9cipal or *>act]i/ic num]als are giv51 ^? be+ suffici5t to enable ! read] to foll[ intellig5tly ! gr[? ( ! sy/ems4 ,ea* conta9s ! decimal elem5t also1 & is1 !re=e1 to be reg>d$ z a mix$ decimal-vigesimal sy/em4 ,,iri%4#cbi #aj4 deic4 #bj4 fice4 #cj4 triocad #c-aj #dj4 da ficid #b-bj4 #ej4 caogad #e-aj4 #fj4 tri ficid #c-bj4 #gj4 reactmoga #g-aj4 #hj4 ceitqe ficid #d-bj4 #ij4 nocad #i-aj4 #ajj4 cead4 #ajjj4 mile4 ,,gaelic4#ccj #aj4 dei*4 #bj4 fi*ead4 #cj4 dei* ar fi*ead #aj #bj4 #dj4 da fhi*ead #b-bj4 #ej4 da fhi*ead is dei* #dj #aj4 #fj4 tri fi*ead #c-bj4 #gj4 tri fi*ead is dei* #fj #aj4 #hj4 cei?ir fi*ead #d-bj4 #ij4 cei?ir fi*ead is dei* #hj #aj4 #ajj4 ceud4 #ajjj4 mile4 ,,wel%4#cca #aj4 deg4 #bj4 uga94 #cj4 deg ar huga9 #aj #bj4 #dj4 deuga9 #b-bj4 #ej4 deg a deuga9 #aj #dj4 #fj4 triga9 #c-bj4 #gj4 deg a ?riga9 #aj #fj4 #hj4 p$w> uga9 #d-bj4 #ij4 deg a p$w> uga9 #hj #aj4 #ajj4 cant4 ,,manx4#ccb #aj4 jeih4 #bj4 fe$4 #cj4 yn jeih z fe$ #aj #bj4 #dj4 dae$ #b-bj4 #ej4 jeih z dae$ #aj #dj4 #fj4 ?ree-fe$ #c-bj4 #gj4 ?ree-fe$ z jeih #fj #aj4 #hj4 ki>e-fe$ #d-bj4 #ajj4 keead4 #ajjj4 ?\sane1 or jeih *eead4 ,,breton4#ccc #aj4 dec4 #bj4 uegu5d4 #cj4 tregond #c-aj4 #dj4 deu uegu5d #b-bj4 #ej4 hant] h& half hundr$4 #fj4 tri uegu5d #c-bj4 #gj4 dec ha tri uegu5d #aj #fj4 #hj4 pi> uegu5d #d-bj4 #ij4 dec ha pi> uegu5d #aj #hj4 #ajj4 c&4 #abj4 hueh uegu5d #f-bj4 #adj4 seih uegu5d #g-bj4 #afj4 eih uegu5d #h-bj4 #ahj4 nau uegu5d #i-bj4 #bjj4 deu g& #b-ajj4 #bdj4 deuzec uegu5d #ab-bj4 #bhj4 pi>zec uegu5d #ad-bj4 #cjj4 tri h&1 or pembzec uegu5d4 #djj4 pi> h& #d-ajj4 #ajjj4 mil4 ,^! li/s %[ t ! native developm5t ( ! ,celtic numb] sy/ems1 orig9ally %[+ a /rong pref]5ce = ! vigesimal me?od ( progression1 has be5 greatly modifi$ by int]c\rse ) ,teutonic & ,lat9 races4 ,! high] num]als 9 all ^! languages1 & 9 ,iri% _m ( ! l[] also1 are se5 at a glance to be decimal4 ,among ! scales "h giv5 ! ,breton1 ! legitimate desc5dant ( ! anci5t ,gallic1 is especially int]e/+2 b "h1 j z 9 ! o!r ,celtic tongues1 :5 we rea* #ajjj1 ! famili> ,lat9 t]m = t numb] appe>s 9 ! v>i\s corruptions ( mille1 #ajjj1 :i* 0 c>ri$ into ! ,celtic c\ntries by mission>y & milit>y influ5ces4 ,9 connection ) ! ,celtic language1 m5tion mu/ be made ( ! p]si/5t vigesimal elem5t :i* has held its place 9 ,fr5*4 ,! anci5t ,gauls1 :ile adopt+ ! language ( _! conqu]ors1 s f> modifi$ ! decimal sy/em ( ,lat9 z to replace ! natural septante1 #gj1 octante1 #hj1 nonante1 #ij1 by soixante-dix1 #fj-aj1 quatre-v+t1 #d-bj1 & quatrev+t-dix1 #d-bj-aj4 ,f #fa to #ii ! ,fr5* me?od ( c\nt+ is :olly vigesimal1 except = ! pres5ce ( ! "o ^w soixante4 ,9 old ,fr5* ?is elem5t 0 /ill m pron\nc$4 ,soixante _h n yet appe>$2 & #fj & #gj 7 treis v9z1 #c-bj1 & treis v9z et dis1 #c-bj & #aj respectively4 ,also1 #abj 0 six v9z1 #f-bj1 #adj 0 sept-v9z1 etc4#ccd ,h[ f> ?is me?od ev] ext5d$ 9 ! ,fr5* language prop]1 x is1 p]haps1 impossible to say2 b f ! "n ( an alm%\se1 les qu9ze-v+ts1#cce :i* =m]ly exi/$ 9 ,p>is1 & 0 design$ z a home = #cjj bl9d p]sons1 & f ! pembzek-uegu5t1 #ae-bj1 ( ! ,breton1 :i* /ill survives1 we may inf] t x 0 f> en\gh to make x ! curr5t sy/em ( common life4 ,europe yields "o o!r example ( vigesimal c\nt+1 9 ! numb] sy/em ( ! ,basques4 ,l mo/ ( ! ,celtic scales1 ! ,basque seems to become decimal above #ajj4 ,x does n appe> to be relat$ to any o!r ,european sy/em1 b to be q isolat$ philologically4 ,! high] units1 z mila1 #ajjj1 are probably borr[$1 & n native4 ,! t5s 9 ! ,basque scale are3#ccf #aj4 ham>4 #bj4 hogei4 #cj4 hogei eta ham> #bj #aj4 #dj4 b]rogei #b-bj4 #ej4 b]rogei eta ham> #b-bj #aj4 #fj4 hirurogei #c-bj4 #gj4 hirurogei eta ham> #c-bj #aj4 #hj4 laurogei #d-bj4 #ij4 laurogei eta ham> #d-bj #aj4 #ajj4 ehun4 #ajjj4 milla4 ,besides ^! we f9d two or ?ree num]al scales 9 ,europe :i* conta9 di/9ct traces ( vigesimal c\nt+1 ?\gh ! scales are1 z a :ole1 decid$ly decimal4 ,! ,dani%1 "o ( ! ess5tially ,g]manic languages1 conta9s ! foll[+ num]als3 #cj4 tr$ive #c-aj4 #dj4 fyrretyve #d-aj4 #ej4 halvtr$s9d/yve half 7( #bj7 f #c-bj4 #fj4 tres9d/yve #c-bj4 #gj4 halvfi]ds9d/yve half f #d-bj4 #hj4 fiirs9d/yve #d-bj4 #ij4 halvfems9d/yve half f #e-bj4 #ajj4 hundr$e4 ,g]manic numb] sy/ems are1 z a rule1 pure decimal sy/ems2 & ! ,dani% exception is q rem>kable4 ,we h1 to be sure1 su* expressions 9 ,engli% z ?ree score1 f\r score1 etc41 & ! ,sw$i%1 ,icel&ic1 & o!r languages ( ?is gr\p h simil> t]ms4 ,/ill1 ^! are n pure num]als1 b auxili>y words r1 :i* belong to ! same category z pair1 doz51 diza9e1 etc41 :ile ! ,dani% words j giv5 are ! ord9>y num]als :i* =m a "p ( ! e-day vocabul>y ( t language4 ,! me?od by :i* ?is scale expresses #ej1 #gj1 & #ij is especially noticeable4 ,x w be met ) aga91 & fur!r examples ( its occurr5ce giv54 ,9 ,albania !re exi/s "o s+le fragm5t ( vigesimal num]ation1 :i* is probably an accid5tal comp\nd r ?an ! remnant ( a =m] vigesimal numb] sy/em4 ,) ?is s+le exception ! ,albanian scale is ( regul> decimal =mation4 ,a few ( ! num]als are giv5 = ! sake ( comp>ison3#ccg #cj4 tridgiete #c-aj4 #dj4 dizet #b-bj4 #ej4 pes$giete #e-aj4 #fj4 gia/$giete #f-aj1 etc4 ,among ! almo/ c\ntless dialects ( ,africa we f9d a comp>atively small numb] ( vigesimal numb] sy/ems4 ,! p[]s ( ! negro tribes are n /rongly develop$ 9 c\nt+1 & :]ev] _! num]al scales h be5 tak5 d[n by explor]s !y h almo/ always be5 f\nd to be decimal or qu9>y-decimal4 ,! small numb] ,i h be5 able to collect are "h giv54 ,!y are some:at fragm5t>y1 b are z complete z x 0 possible to make !m4 ,,affadeh4#cch #aj4 dekang4 #bj4 degumm4 #cj4 piaske4 #dj4 tikkumgassih #bj #b4 #ej4 tikkumgassigokang #bj #b #aj4 #fj4 tikkumgakro #bj #c4 #gj4 dungokrogokang #bj #c #aj4 #hj4 dukumgade #bj #d4 #ij4 dukumgadegokang #bj #d #aj4 #ajj4 miah 7borr[$ f ! ,arabs74 ,,ibo4#cci #aj4 iri4 #bj4 ogu4 #cj4 ogu n-iri #bj #aj1 or iri ato #aj #c4 #dj4 ogu abuo #bj #b1 or iri anno #aj #d4 #ajj4 ogu ise #bj #e4 ,,vei4#cdj #aj4 tan4 #bj4 mo b&e a p]son f9i%$4 #cj4 mo b&e ako tan #bj #aj4 #dj4 mo f]a b&e #b #bj4 #ajj4 mo soru b&e #e p]sons f9i%$4 ,,yoruba4#cda #aj4 duup4 #bj4 ogu4 #cj4 ogbo4 #dj4 ogo-dzi #bj #b4 #fj4 ogo-ta #bj #c4 #hj4 ogo-ri #bj #d4 #ajj4 ogo-ru #bj #e4 #abj4 ogo-fa #bj #f4 #adj4 ogo-dze #bj #g4 #afj4 ogo-dzo #bj #h1 etc4 ,,efik4#cdb #aj4 duup4 #bj4 edip4 #cj4 edip-ye-duup #bj #aj4 #dj4 aba #bj #b4 #fj4 ata #bj #c4 #hj4 anan #bj #d4 #ajj4 ikie4 ,! ,yoruba scale1 to :i* ref]5ce has already be5 made1 p4 #gj1 aga9 %[s its peculi> /ructure1 by cont9u+ its vigesimal =mation pa/ #ajj ) no int]ruption 9 its me?od ( num]al build+4 ,x w be rememb]$ t none ( ! ,european scales %[$ ?is p]si/5cy1 b pass$ at t po9t into decimal num]ation4 ,?is w (t5 be f\nd to be ! case2 b n[ & !n a scale w come to our notice ^: vigesimal /ructure is cont9u$1 )\t any break1 on into ! hundr$s & sometimes into ! ?\s&s4 ,,bongo4#cdc #aj4 kih4 #bj4 mbaba kotu #bj #a4 #dj4 mbaba gnorr #bj #b4 #ajj4 mbaba mui #bj #e4 ,,m5de4#cdd #aj4 pu4 #bj4 nu yela gboyongo mai a man f9i%$4 #cj4 nu yela gboyongo mahu pu #bj #aj4 #dj4 nu fele gboyongo #b m5 f9i%$4 #ajj4 nu lolu gboyongo #e m5 f9i%$4 ,,nupe4#cde #aj4 gu-wo4 #bj4 es94 #cj4 gbonwo4 #dj4 si-ba #b #bj4 #ej4 arota4 #fj4 sita #c #bj4 #gj4 adoni4 #hj4 s9i #d #bj4 #ij4 s9i be-guwo #hj #aj4 #ajj4 sisun #e #bj4 ,,logone4#cdf #aj4 *kan4 #bj4 tkam4 #cj4 tkam ka *kan #bj #aj4 #dj4 tkam ksde #bj #b4 #ej4 tkam ksde ka *kan #dj #aj4 #fj4 tkam ga*kir #bj #c4 #ajj4 mia 7f ,arabic74 #ajjj4 debu4 ,,mundo4#cdg #aj4 nujorquoi4 #bj4 tiki b]e4 #cj4 tiki bire nujorquoi #bj #aj4 #dj4 tiki borsa #bj #b4 #ej4 tike borsa nujorquoi #dj #aj4 ,,m&+o4#cdh #aj4 tang4 #bj4 mulu4 #cj4 mulu n9tang #bj #aj4 #dj4 mulu foola #bj #b4 #ej4 mulu foola n9tang #dj #aj4 #fj4 mulu sabba #bj #c4 #gj4 mulu sabba n9tang #fj #aj4 #hj4 mulu nani #bj #d4 #ij4 mulu nani n9tang #hj #aj4 #ajj4 kemi4 ,?is completes ! scanty li/ ( ,african vigesimal numb] sy/ems t a pati5t & some:at ext5d$ se>* has yield$4 ,x is rem>kable t ! numb] is no great]4 ,qu9>y c\nt+ is n uncommon 9 ! ,d>k ,cont95t1 & !re is no app>5t reason :y vigesimal reckon+ %\ld be any less common ?an qu9>y4 ,any "o inve/igat+ ,african modes ( c\nt+ ) ! mat]ial at pres5t accessible1 w f9d himself hamp]$ by ! fact t few explor]s h collect$ any except ! fir/ t5 num]als4 ,?is leaves ! =mation ( high] t]ms entirely unkn[n1 & %[s no?+ beyond ! qu9>y or non-qu9>y "* ( ! sy/em4 ,/ill1 among ^? :i* ,/anley1 ,s*we9fur?1 ,salt1 & o!rs h collect$1 by f> ! greate/ numb] are decimal4 ,z our k ( ,african languages is ext5d$1 new examples ( ! vigesimal me?od may be br\ght to light4 ,b our pres5t in=mation leads u to believe t !y w be few 9 numb]4 ,9 ,asia ! vigesimal sy/em is to be f\nd ) great] frequ5cy ?an 9 ,europe or ,africa1 b x is /ill ! exception4 ,z ,asiatic languages are mu* bett] kn[n ?an ,african1 x is probable t ! future w add b little to our /ock ( k on ?is po9t4 ,new in/ances ( c\nt+ by tw5ties may /ill be f\nd 9 nor!rn ,sib]ia1 :]e mu* e?nological "w yet rema9s to be done1 & :]e a t5d5cy t[>d ?is =m ( num]ation has be5 obs]v$ to exi/4 ,b ! total numb] ( ,asiatic vigesimal scales mu/ always rema9 small--q insignificant 9 comp>ison ) ^? ( decimal =mation4 ,9 ! ,caucasus region a gr\p ( languages is f\nd1 9 :i* all b ?ree or f\r conta9 vigesimal sy/ems4 ,^! sy/ems are z foll[s3 ,,abkhasia4#cdi #aj4 zpha-ba4 #bj4 gphozpha #b #aj4 #cj4 gphozphei zphaba #bj #aj4 #dj4 gph9-gphozpha #b #bj4 #fj4 *9-gphozpha #c #bj4 #hj4 phs9-gphozpha #d #bj4 #ajj4 sphki4 ,,av>i #aj4 ant%-g4 #bj4 qo-g4 #cj4 leb]go4 #dj4 khi-qogo #b #bj4 #ej4 khiqojalda ant%go #dj #aj4 #fj4 lab-qogo #c #bj4 #gj4 labqojalda ant%go #fj #aj4 #hj4 un-qogo #d #bj4 #ajj4 nusgo4 ,,kuri #aj4 t%ud4 #bj4 *ad4 #cj4 *anni t%ud #bj #aj4 #dj4 ja*t%ur4 #ej4 ja*t%urni t%ud #dj #aj4 #fj4 put *ad #c #bj4 #gj4 put*anni t%ud #fj #aj4 #hj4 kud-*ad #d #bj4 #ij4 kud*anni t%ud #hj #aj4 #ajj4 wis4 ,,udi #aj4 wit%4 #bj4 qa4 #cj4 sa-qo-wit% #bj #aj4 #dj4 pha-qo #b #bj4 #ej4 pha-qo-wit% #dj #aj4 #fj4 *ib-qo #c #bj4 #gj4 *ib-qo-wit% #fj #aj4 #hj4 bip-qo #d #bj4 #ij4 bip-qo-wit% #hj #aj4 #ajj4 bats4 #ajjj4 haz> 7,p]sian74 ,,t*et*nia #aj4 i?4 #bj4 tqa4 #cj4 tqe i? #bj #aj4 #dj4 sauz-tqa #b #bj4 #ej4 sauz-tqe i? #dj #aj4 #fj4 *uz-tqa #c #bj4 #gj4 *uz-tqe i? #fj #aj4 #hj4 w-iez-tqa #d #bj4 #ij4 w-iez-tqe i? #hj #aj4 #ajj4 b'e4 #ajjj4 ezir 7ak9 to ,p]sian74 ,,?us* #aj4 itt4 #bj4 tqa4 #cj4 tqa-itt #bj #aj4 #dj4 sauz-tq #b #bj4 #ej4 sauz-tqa-itt #dj #aj4 #fj4 *\z-tq #c #bj4 #gj4 *\z-tqa-itt #fj #aj4 #hj4 dhewuz-tq #d #bj4 #ij4 dhewuz-tqa-itt #hj #aj4 #ajj4 ph*auz-tq #e #bj4 #bjj4 it%a-tq #aj #bj4 #cjj4 phehiit%a-tq #ae #bj4 #ajjj4 sat% tqauz-tqa it%atqa #b #bj #bj #bjj4 ,,georgia #aj4 a?i4 #bj4 otsi4 #cj4 ots da a?i #bj #aj4 #dj4 or-m-otsi #b #bj4 #ej4 ormots da a?i #dj #aj4 #fj4 sam-otsi #c #bj4 #gj4 samots da a?i #fj #aj4 #hj4 o?*-m-otsi #d #bj4 #ij4 o?mots da a?i #hj #aj4 #ajj4 asi4 #ajjj4 a?-asi #aj #ajj4 ,,lazi #aj4 wit4 #bj4 ts4 #cj4 ts d wit #bj #aj4 #dj4 dzur en ts #b #bj4 #ej4 dzur en ts d wit #dj #aj4 #fj4 dzum en ts #c #bj4 #gj4 dzum en ts d wit #fj #aj4 #hj4 ot*-an-ts #d #bj4 #ajj4 os4 #ajjj4 silia 7ak9 to ,greek74 ,,*unsag4#cej #aj4 ants-g4 #bj4 *ogo4 #cj4 *ogela antsgo #bj #aj4 #dj4 ki*ogo #b #bj4 #ej4 ki*elda antsgo #dj #aj4 #fj4 taw *ago #c #bj4 #gj4 taw *ogelda antsgo #fj #aj4 #hj4 u*' *ogo #d #bj4 #ij4 u*' *ogelda antsgo4 #ajj4 nusgo4 #ajjj4 as>go 7ak9 to ,p]sian74 ,,dido4#cea #aj4 z9o4 #bj4 ku4 #cj4 kunoz9o4 #dj4 ka5o ku #b #bj4 #ej4 ka5o kuno z9o #dj #aj4 #fj4 sonno ku #c #bj4 #gj4 sonno kuno z9o #fj #aj4 #hj4 u9o ku #d #bj4 #ij4 u9o huno z9o #hj #aj4 #ajj4 bis*on4 #djj4 ka5o kuno z9o #dj #aj4 ,,ak>i #aj4 entzelgu4 #bj4 kobbeggu4 #cj4 l[]gu4 #dj4 kokawu #b #bj4 #ej4 kikaldanske #dj #aj4 #fj4 secikagu4 #gj4 kawalkaldansku #c #bj #aj4 #hj4 onkuku #d #bj4 #ij4 onkordansku #d #bj #aj4 #ajj4 nosku4 #ajjj4 ask]gu 7f ,p]sian74 ,,circassia #aj4 ps*e4 #bj4 to-ts*4 #cj4 tots*-era-ps*irre #bj #aj4 #dj4 ptl'i-s* #d #aj4 #ej4 ptl'is*-era-ps*irre #dj #aj4 #fj4 *i-ts* #f #aj4 #gj4 *its*-era-ps*irre #fj #aj4 #hj4 to%itl #bj #d8 #ij4 to%itl-era-ps*irre #hj #aj4 #ajj4 s*eh4 #ajjj4 m9 7,t>t>7 or s*i-ps*e #ajj #aj4 ,! la/ ( ^! scales is an unusual comb9ation ( decimal & vigesimal4 ,9 ! ev5 t5s x is q regul>ly decimal1 unless #hj is ( ! /ructure sugge/$ above4 ,on ! o!r h&1 ! odd t5s are =m$ 9 ! ord9>y vigesimal mann]4 ,! reason = ?is anomaly is n obvi\s4 ,i "k ( no o!r numb] sy/em t pres5ts ! same peculi>ity1 & _c give any hypo!sis :i* w satisfactorily acc\nt = its pres5ce "h4 ,9 ne>ly all ! examples giv5 ! decimal becomes ! lead+ elem5t 9 ! =mation ( all units above #ajj1 j z 0 ! case 9 ! ,celtic scales already notic$4 ,among ! nor!rn tribes ( ,sib]ia ! num]al scales appe> to be rud] & less simple ?an ^? j exam9$1 & ! c\nt+ to be m consi/5tly vigesimal ?an 9 any scale we h ?us f> met )4 ,! two foll[+ examples are exce$+ly int]e/+1 z be+ among ! be/ illu/rations ( c\nt+ by tw5ties t are to be f\nd any:]e 9 ! ,old ,_w4 ,,ts*uks*i4#ceb #aj4 migitk5 bo? h&s4 #bj4 *lik-k9 a :ole man4 #cj4 *likk9 m+itk9 p>ol #bj #aj4 #dj4 nira* *likk9 #b #bj4 #ajj4 mil9 *likk9 #e #bj4 #bjj4 m+it *likk9 #aj #bj1 i4e4 #aj m54 #ajjj4 milig5 *l9-*likk9 #e #bjj1 i4e4 five 7times7 #aj m54 ,,a9o4#cec #aj4 wambi4 #bj4 *oz4 #cj4 wambi i-doehoz #aj f #dj4 #dj4 to*oz #b #bj4 #ej4 wambi i-ri*oz #aj f #fj4 #fj4 re*oz #c #bj4 #gj4 wambi i8 ini*oz #aj f #hj4 #hj4 ini*oz #d #bj4 #ij4 wambi as*ik9i*oz #aj f #ajj4 #ajj4 as*ik9i*oz #e #bj4 #aaj4 wambi juwano*oz #aj f #abj4 #abj4 juwano *oz #f #bj4 #acj4 wambi aruwano*oz #aj f #adj4 #adj4 aruwano *oz #g #bj4 #aej4 wambi tubis*ano *oz #aj f #afj4 #afj4 tubis*ano *oz #h #bj4 #agj4 wambi s*nebis*ano *oz #aj f #ahj4 #ahj4 s*nebis*ano *oz #i #bj4 #aij4 wambi s*newano *oz #aj f #bjj4 #bjj4 s*newano *oz #aj #bj4 #cjj4 as*ik9i*oz i gas*ima *newano *oz #e #bj #aj #bj4 #djj4 tos*newano *oz #b 7#aj #bj74 #ejj4 as*ik9i*oz i gas*ima tos*newano *oz #ajj #djj4 #fjj4 res*9iwano *oz #c #bjj4 #gjj4 as*ik9i*oz i gas*ima res*9iwano *oz #ajj #fjj4 #hjj4 inis*9iwano *oz #d #bjj4 #ijj4 as*ik9i*oz i gas*ima inis*9iwano *oz #ajj #hjj4 #ajjj4 as*ik9i s*9ewano *oz #e #bjj4 #bjjj4 wanu s*9ewano *oz #aj 7#aj #bj74 ,?is scale is 9 "o s5se :olly vigesimal1 & 9 ano!r way x is n to be reg>d$ z pure1 b z mix$4 ,bel[ #bj x is qu9>y1 &1 h[ev] f> x might be ext5d$1 ?is qu9>y elem5t w\ld rema91 mak+ ! scale qu9>y-vigesimal4 ,b 9 ano!r s5se1 also1 ! ,a9o sy/em is n pure4 ,9 any unmix$ vigesimal scale ! ^w = #djj mu/ be a simple ^w1 & t numb] mu/ be tak5 z ! vigesimal unit correspond+ to #ajj 9 ! decimal scale4 ,b ! ,a9os h no simple num]al ^w = any numb] above #bj1 =m+ all high] numb]s by comb9ations ?r\gh "o or m ( ! processes ( addition1 subtraction1 & multiplication4 ,! only numb] above #bj :i* is us$ z a unit is #bjj1 :i* is express$ m]ely z #aj tw5ties4 ,any ev5 numb] ( hundr$s1 or any numb] ( ?\s&s1 is !n indicat$ z be+ s _m times #aj tw5ties2 & ! odd hundr$s are s _m times #aj tw5ties1 plus #e tw5ties m4 ,?is scale is an excell5t example ( ! cumb]some me?ods us$ by unciviliz$ races 9 ext5d+ _! numb] sy/ems beyond ! ord9>y ne$s ( daily life4 ,9 ,c5tral ,asia a s+le vigesimal scale comes to light 9 ! foll[+ fragm5t ( ! ,lepts*a scale1 ( ! ,himalaya region3#ced #aj4 kati4 #dj4 kafali #d #aj1 or kha nat #b #bj4 #ej4 kafano #e #aj1 or kha nat sa kati #b #bj #aj4 #ajj4 gjo1 or kat4 ,fur!r to ! s\?1 among ! ,dravidian races1 ! vigesimal elem5t is also f\nd4 ,! foll[+ w suffice to illu/rate ! numb] sy/ems ( ^! dialects1 :i*1 z f> z ! mat]ial at h& %[s1 are diff]5t f ea* o!r only 9 m9or p>ticul>s3 ,,mund>i4#cee #aj4 gelea4 #bj4 mi hisi4 #cj4 mi hisi gelea #bj #aj4 #dj4 b> hisi #b #bj4 #fj4 api hisi #c #bj4 #hj4 upun hisi #d #bj4 #ajj4 mone hisi #e #bj4 ,9 ! ,nicob> ,isl&s ( ! ,indian ,ocean a well-develop$ example ( vigesimal num]ation is f\nd4 ,! inhabitants ( ^! isl&s are s l[ 9 ! scale ( civilization t a def9ite num]al sy/em ( any k9d is a s\rce ( "s surprise4 ,_! neighb\rs1 ! ,&aman ,isl&]s1 x w be rememb]$1 h b two num]als at _! comm&2 _! intellig5ce does n seem 9 any way inf]ior to t ( ! ,nicob> tribes1 & "o is at a loss to acc\nt = ! sup]ior developm5t ( ! numb] s5se 9 ! case ( ! latt]4 ,! int]c\rse ( ! coa/ tribes ) trad]s might furni% an explanation ( ! difficulty 7 x n = ! fact t ! num]ation ( ! inl& tribes is q z well develop$ z t ( ! coa/ tribes2 & z ! =m] nev] come 9 contact ) trad]s & nev] engage 9 b>t] ( any k9d except 9 ! mo/ limit$ way1 ! conclusion seems inevitable t ?is is m]ely "o ( ! ph5om5a ( m5tal developm5t among savage races = :i* we h at pres5t no adequate explanation4 ,! pr9cipal num]als ( ! inl& & ( ! coa/ tribes are3#cef ,,inl& ,,tribes ,,coa/ ,,tribes #aj4 teya4 #aj4 %am4 #bj4 h5g-inai4 #bj4 heang-inai4 #cj4 h5g-inai-ta9 #cj4 heang-inai-tanai #bj #e 7c\ples74 #bj #e 7c\ples74 #dj4 au-inai #b #bj4 #dj4 an-inai #b #bj4 #ajj4 ta9-inai #e #bj4 #ajj4 tanai-inai #e #bj4 #bjj4 teya-inai #aj #bj4 #bjj4 %am-inai #aj #bj4 #cjj4 teya-ta9-inai #cjj4 heang-tanai-inai 7#aj #e7 #bj4 7#aj #e7 #bj4 #djj4 h5g-teo4 #djj4 heang-mom*iama4 ,9 no o!r "p ( ! _w is vigesimal c\nt+ f\nd s p]fectly develop$1 &1 among native races1 s g5]ally pref]r$1 z 9 ,nor? & ,s\? ,am]ica4 ,9 ! ea/]n portions ( ,nor? ,am]ica & 9 ! extreme we/]n portions ( ,s\? ,am]ica ! decimal or ! qu9>y decimal scale is 9 g5]al use4 ,b 9 ! nor!rn regions ( ,nor? ,am]ica1 9 we/]n ,canada & nor?we/]n ,unit$ ,/ates1 9 ,mexico & ,c5tral ,am]ica1 & 9 ! nor!rn & we/]n p>ts ( ,s\? ,am]ica1 ! unit ( c\nt+ among ! great majority ( ! native races 0 #bj4 ,! e?nological aff9ities ( ^! races are n yet def9itely asc]ta9$2 & x is no "p ( ! scope ( ?is "w to ent] into any discussion ( t involv$ "q4 ,b ei!r ?r\gh contact or aff9ity1 ?is =m ( num]ation spread 9 prehi/oric times ov] half or m ?an half ( ! we/]n hemisph]e4 ,x 0 ! me?od employ$ by ! rude ,eskimos ( ! nor? & _! equally rude k9sm5 ( ,p>aguay & ea/]n ,brazil2 by ! =e/ ,indians ( ,oregon & ,briti% ,columbia1 & by _! m s\!rn k9sm51 ! wild tribes ( ! ,rio ,gr&e & ( ! ,or9oco4 ,&1 mo/ /rik+ & int]e/+ ( all1 x 0 ! me?od ^u :i* 7 bas$ ! num]al sy/ems ( ! highly civiliz$ races ( ,mexico1 ,yucatan1 & ,new ,granada4 ,"s ( ! sy/ems obta9$ f ! languages ( ^! peoples are p]fect1 ext5d$ examples ( vigesimal c\nt+1 n to be duplicat$ 9 any o!r qu>t] ( ! globe4 ,! ord9>y unit 01 z w\ld be expect$1 "o man1 & 9 num]\s languages ! words = #bj & man are id5tical4 ,b 9 o!r cases ! orig9al mean+ ( t num]al ^w has be5 lo/2 & 9 o!rs /ill x has a signification q remote f t giv5 above4 ,^! mean+s w be notic$ 9 connection ) ! scales !mselves1 :i* are giv51 r\ghly speak+1 9 _! geographical ord]1 beg9n+ ) ! ,eskimo ( ! f> nor?4 ,! sy/ems ( "s ( ! tribes are z foll[s3 ,,alaskan ,,eskimos4#ceg #aj4 koleet4 #bj4 enu5ok4 #cj4 enu5ok kol9ik #bj #aj4 #dj4 malho kepe ak #b #bj4 #ej4 malho-kepe ak-kolmik *e pah ak to #b #bj #aj4 #fj4 p+i %u-kepe ak #c #bj4 #ajj4 tale ma-kepe ak #e #bj4 #djj4 enue nok ke pe ak #bj #bj4 ,,t*iglit4#ceh #aj4 krolit4 #bj4 kroleti1 or innun man4 #cj4 innok krol9ik-t*ikpalik man #b h&s4 #dj4 innum mall]ok #b m54 #ej4 adjigayn>mitoat z _m times #aj z ! f+]s ( ! h&4 #fj4 innumipit #c m54 #gj4 innunmallo]onik arv5elo]it #g m58 #hj4 innun p9atunik arv5elo]it #h m58 #ij4 innun tcitamanik arv5elo]it #i m58 #ajj4 it*angn]kr4 #ajjj4 it*angn]-p>k great #ajj4 ,! mean+s = #gj1 #hj1 #ij1 are n giv5 by ,fa!r ,petitot1 b are ( su* a =m t ! significations seem to be :at are giv5 above4 ,only a full acqua9tance ) ! ,t*iglit language w\ld ju/ify "o 9 giv+ def9ite mean+s to ^! words1 or 9 ass]t+ t an error _h be5 made 9 ! num]als4 ,b x is s rem>kable & anomal\s to f9d ! decimal & vigesimal scales m+l$ 9 ?is mann] t "o involunt>ily suspects ei!r incomplet5ess ( =m1 or an actual mi/ake4 ,,tl+it4#cei #aj4 dj9kat bo? h&s8 #bj4 tle ka #a man4 #cj4 natsk dj9kat #c #aj4 #dj4 dak'on dj9kat #d #aj4 #ej4 k$j9 dj9kat #e #aj4 #fj4 tle durcu dj9kat #f #aj4 #gj4 daqa durcu dj9kat #g #aj4 #hj4 natska durcu dj9kat #h #aj4 #ij4 gocuk durcu dj9kat #i #aj4 #ajj4 k$j9 ka #e m51 or #e #bj4 #bjj4 dj9kat ka #aj #bj4 #cjj4 natsk dj9kat ka #cj m54 #djj4 dak'on dj9kat ka #dj m54 ,?is scale conta9s a /range comm+l+ ( decimal & vigesimal c\nt+4 ,! words = #bj1 #ajj1 & #bjj are cle> evid5ce ( vigesimal1 :ile #cj to #ij1 & ! rema9+ hundr$s1 are equally unmi/akable pro( ( decimal1 num]ation4 ,! ^w ka1 man1 seems to mean ei!r #aj or #bj2 a mo/ unusual occurr5ce4 ,! fact t a numb] sy/em is p>tly decimal & p>tly vigesimal is f\nd to be ( su* frequ5t occurr5ce t ?is po9t 9 ! ,tl+it scale ne$ excite no special wond]4 ,b x is rem>kable t ! same ^w %\ld ent] into num]al composition "u su* diff]5t mean+s4 ,,nootka4#cfj #aj4 haiu4 #bj4 tsakeits4 #cj4 tsakeits ic haiu #bj #aj4 #dj4 atlek #b #bj4 #fj4 kat/sek #c #bj4 #hj4 moyek #d #bj4 #ajj4 sutc'ek #e #bj4 #abj4 nop'ok #f #bj4 #adj4 atlpok #g #bj4 #afj4 atlakutlek #h #bj4 #ahj4 ts'owakutlek #i #bj4 #bjj4 haiuk #aj #bj4 ,?is scale is qu9>y-vigesimal1 ) no app>5t decimal elem5t 9 its composition4 ,b ! d]ivation ( "s ( ! t]ms us$ is detect$ ) difficulty4 ,9 ! foll[+ scale ! vigesimal /ructure is /ill m obscure4 ,,tsim%ian4#cfa #aj4 gy'ap4 #bj4 ky$eel #a man4 #cj4 gulewulgy'ap4 #dj4 t'epqadalgyitk1 or tqalpqwulgyap4 #ej4 kctoncwulgyap4 #ajj4 kc5ecal4 #bjj4 k'pal4 #cjj4 k'pal te kc5ecal #bjj #ajj4 #djj4 ky$al4 #ejj4 ky$al te kc5ecal #djj #ajj4 #fjj4 gulalegyitk4 #gjj4 gulalegyitk te kc5ecal #fjj #ajj4 #hjj4 tqalpqtalegyitk4 #ijj4 tqalpqtalegyitk te kc5ecal #hjj #ajj4 #ajjj4 k'pal4 ,to ! unobs]vant eye ?is scale w\ld c]ta9ly appe> to conta9 no m ?an a trace ( ! vigesimal 9 its /ructure4 ,b ,dr4 ,boas1 :o is "o ( ! mo/ c>eful & accurate ( inve/igators1 says 9 8 comm5t on ?is sy/em3 ,x w be se5 at once t ?is sy/em is qu9>y-vigesimal4444 ,9 #bj we f9d ! ^w gyat1 man4 ,! hundr$s are id5tical ) ! num]als us$ 9 c\nt+ m5 7see p4 #hg71 & !n ! qu9>y-vigesimal sy/em is mo/ evid5t4 ,,rio ,,norte ,,indians4#cfb #bj4 taiguaco4 #cj4 taiguaco co juyopamauj ajte #bj #b #e4 #dj4 taiguaco ajte #bj #b4 #ej4 taiguaco ajte co juyopamauj ajte #bj #b #e #b4 ,,c>ibs ,,( ,,essiquibo1 ,,guiana #aj4 owe5-abatoro4 #bj4 owee-c>5a #a p]son4 #dj4 oko-c>5a #b p]sons4 #fj4 oro[a-c>5a #c p]sons4 ,,otomi #aj4 ra-tta4 #bj4 na-te4 #cj4 na-te-m'a-ratta #bj #aj4 #dj4 yo-te #b #cj4 #ej4 yote-m'a-ratta #b #bj #aj4 #fj4 hiu-te #c #bj4 #gj4 hiute-m'a-ratta #c #bj #aj4 #hj4 gooho-rate #d #bj4 #ij4 gooho-rate-m'a ratta #d #bj #aj4 #ajj4 cytta-te #e #bj1 or nan!be #a #ajj4 ,,maya1 ,,yucatan4#cfc #a4 hun4 #aj4 lahun x is f9i%$4 #bj4 hunkal a measure1 or m correctly1 a fa/5+ toge!r4 #cj4 lahucakal #dj - #aj8 #dj4 cakal #b #bj4 #ej4 lahuyoxkal #fj - #aj4 #fj4 oxkal #c #bj4 #gj4 lahucankal #hj - #aj4 #hj4 cankal #d #bj4 #ij4 lahuyokal #ajj - #aj4 #ajj4 hokal #e #bj4 #aaj4 lahu uackal #abj - #aj4 #abj4 uackal #f #bj4 #acj4 lahu uuckal #adj - #aj4 #adj4 uuckal #g #bj4 #bjj4 lahuncal #aj #bj4 #cjj4 holhukal #ae #bj4 #djj4 hunbak #a ty+ ar\nd4 #ejj4 hotubak4 #fjj4 lahutubak #hjj4 calbak #b #djj4 #ijj4 hotu yoxbak4 #ajjj4 lahuyoxbak4 #abjj4 oxbak #c #djj4 #bjjj4 capic 7mod]n74 #hjjj4 hunpic #a sack4 #af1jjj4 ca pic 7anci5t74 #afj1jjj4 calab a fill+ full #c1bjj1jjj4 k9*il4 #fd1jjj1jjj4 hunalau4 ,9 ! ,maya scale we h "o ( ! be/ & mo/ ext5d$ examples ( vigesimal num]ation ev] develop$ by any race4 ,to %[ 9 a m /rik+ & =cible mann] ! p]fect regul>ity ( ! sy/em1 ! foll[+ tabulation is made ( ! v>i\s ,maya units1 :i* w correspond to ! #aj units make "o t51 #aj t5s make "o hundr$1 #aj hundr$s make "o ?\s&1 etc41 :i* old-fa%ion$ ari?metic compell$ u to le>n 9 *ildhood4 ,! scale is j z regul> by tw5ties 9 ,maya z by t5s 9 ,engli%4 ,x is#cfd #bj hun #a kal #bj4 #bj kal #a bak #djj4 #bj bak #a pic #hjjj4 #bj pic #a calab #afj1jjj4 #bj calab #a k9*il #c1bjj1jjj4 tzotzceh #bj k9*il #a alau #fd1jjj1jjj4 ,! orig9al mean+ ( pic1 giv5 9 ! scale z a sack1 0 r a %ort petticoat1 somtimes us$ z a sack4 ,! ^w tzotzceh signifi$ de]sk94 ,no reason c be giv5 = ! *oice ( ?is ^w z a num]al1 ?\gh ! appropriat5ess ( ! o!rs is suffici5tly manife/4 ,no evid5ce ( digital num]ation appe>s 9 ! fir/ #aj units1 b1 judg+ f ! almo/ univ]sal practice ( ! ,indian tribes ( bo? ,nor? & ,s\? ,am]ica1 su* may readily h be5 ! orig9 ( ,maya c\nt+4 ,:atev] its orig91 x c]ta9ly exp&$ & grew into a sy/em ^: p]fection *all5ges our admiration4 ,x 0 wor?y ( ! spl5did civilization ( ?is un=tunate race1 &1 ?r\gh its simplicity & regul>ity1 be>s ample te/imony to ! intellectual capacity :i* orig9at$ x4 ,! only example ( vigesimal reckon+ :i* is comp>able ) t ( ! ,mayas is ! sy/em employ$ by _! nor!rn neighb\rs1 ! ,nahuatl1 or1 z !y are m commonly designat$1 ! ,aztecs ( ,mexico4 ,?is sy/em is q z pure & q z simple z ! ,maya1 b diff]s f x 9 "s important p>ticul>s4 ,9 its fir/ #bj num]als x is qu9>y 7see p4 #ada71 & z a sy/em mu/ be reg>d$ z qu9>y-vigesimal4 ,! ,maya scale is decimal ?r\gh its fir/ #bj num]als1 &1 if x is to be reg>d$ z a mix$ scale1 mu/ be *>act]iz$ z decimal-vigesimal4 ,b 9 bo? ^! in/ances ! vigesimal elem5t prepond]ates s /rongly t ^!1 9 common ) _! k9dr$ numb] sy/ems ( ,mexico1 ,yucatan1 & ,c5tral ,am]ica1 are always ?\ght ( & allud$ to z vigesimal scales4 ,on acc\nt ( its importance1 ! ,nahuatl sy/em#cfe is giv5 9 full] detail ?an mo/ ( ! o!r sy/ems ,i h made use (4 #aj4 matlactli #b h&s4 #bj4 cempoalli #a c\nt+4 #ba4 cempoalli once #bj-a4 #bb4 cempoalli omome #bj-b4 #cj4 cempoalli ommatlactli #bj-aj4 #ca4 cempoalli ommatlactli once #bj-aj-a4 #dj4 ompoalli #b #bj4 #ej4 ompoalli ommatlactli #dj-aj4 #fj4 eipoalli1 or epoalli1 #c #bj4 #gj4 epoalli ommatlactli #fj-aj4 #hj4 nauhpoalli #d #bj4 #ij4 nauhpoalli ommatlactli #ij-aj4 #ajj4 macuilpoalli #e #bj4 #abj4 *iquacempoalli #f #bj4 #adj4 *icompoalli #g #bj4 #afj4 *icuepoalli #h #bj4 #ahj4 *iconauhpoalli #i #bj4 #bjj4 matlacpoalli #aj #bj4 #bbj4 matlactli oncempoalli #aa #bj4 #bdj4 matlactli omompoalli #ab #bj4 #bfj4 matlactli omeipoalli #ac #bj4 #bhj4 matlactli onnauhpoalli #ad #bj4 #cjj4 caxtolpoalli #ae #bj4 #cbj4 caxtolli oncempoalli4 #cii4 caxtolli onnauhpoalli ipan caxtolli onnaui #ai #bj #ai4 #djj4 c5tzontli #a bun* ( grass1 or #a tuft ( hair4 #hjj4 ometzontli #b #djj4 #abjj4 eitzontli #c #djj4 #gfjj4 caxtolli onnauhtzontli #ai #djj4 #hjjj4 c5xiquipilli1 or cexiquipilli4 #afj1jjj4 cempoalxiquipilli #bj #hjjj4 #c1bjj1jjj4 c5tzonxiquipilli #djj #hjjj4 #fd1jjj1jjj4 cempoaltzonxiquipilli #bj #djj #hjjj4 ,up to #afj1jjj ! ,nahuatl sy/em is z simple & regul> 9 its con/ruction z ! ,engli%4 ,b at ?is po9t x fails 9 ! =mation ( a new unit1 or r 9 ! expression ( its new unit by a simple ^w2 & 9 ! expression ( all high] numb]s x is =c$ to resort 9 "s measure to comp\nd t]ms1 j z ! ,engli% might h done _h x n be5 able to borr[ f ! ,italian4 ,! high] num]al t]ms1 "u su* conditions1 rapidly become complex & cumb]some1 z ! foll[+ analysis ( ! numb] #a1bgi1iii1iii %[s4#cff ,! analysis w be readily und]/ood :5 x is rememb]$ t ipan signifies plus4 ,caxtolli onnauhpoaltzonxiquipilli ipan caxtolli onnauhtzonxiquipilli ipan caxtolli onnauhpoalxiquipilli ipan caxtolli onnauhxiquipilli ipan caxtolli onnauhtzontli ipan caxtolli onnauhpoalli ipan caxtolli onnaui2 i4e4 #a1baf1jjj1jjj #fj1hjj1jjj #c1jdj1jjj #aeb1jjj #gfjj #chj #ai4 ,to %[ ! comp\nd+ :i* takes place 9 ! high] num]als1 ! analysis may be made m lit]ally1 ?us3 7#ae #d7 #djj #hjj 7#ae #d7 #bj #hjjj 7#ae #d7 #hjjj 7#ae #d7 #djj 7#ae #d7 #bj #ae #d4 ,( c\rse ?is resolution suff]s f ! fact t x is giv5 9 digits arrang$ 9 accordance ) decimal notation1 :ile ! ,nahuatl num]als express values by a base twice z great4 ,?is gives ! effect ( a complexity & awkw>dness great] ?an really exi/$ 9 ! actual use ( ! scale4 ,except = ! pres5ce ( ! qu9>y elem5t ! numb] j giv5 is really express$ ) j z great simplicity z x c\ld be 9 ,engli% words if our words million & billion 7 replac$ by ?\s& ?\s& & ?\s& ?\s& ?\s&4 ,if ,mexico _h rema9$ undi/urb$ by ,europeans1 & sci5ce & comm]ce _h be5 left to _! natural gr[? & developm5t1 uncomp\nd$ words w\ld und\bt$ly h be5 f\nd = ! high] units1 #afj1jjj1 #c1bjj1jjj1 etc41 & ! sy/em ?us r5d]$ z simple z x is possible = a qu9>y-vigesimal sy/em to be4 ,o!r numb] scales ( ?is region are giv5 z foll[s3 ,,hua/eca4#cfg #aj4 laluh4 #bj4 hum-inic #a man4 #cj4 hum-inic-lahu #a man #aj4 #dj4 tzab-inic #b m54 #ej4 tzab-inic-lahu #b m5 #aj4 #fj4 ox-inic #c m54 #gj4 ox-inic-lahu #c m5 #aj4 #hj4 tze-tnic #d m54 #ij4 tze-ynic-kal-laluh #d m5 & #aj4 #ajj4 bo-inic #e m54 #bjj4 tzab-bo-inic #b #e m54 #cjj4 ox-bo-inic #c #e m54 #djj4 tsa-bo-inic #d #e m54 #fjj4 acac-bo-inic #f #e m54 #hjj4 huaxic-bo-inic #h #e m54 #ajjj4 xi4 #hjjj4 huaxic-xi #h-ajjj4 ,! ess5tially vigesimal "* ( ?is sy/em *anges 9 ! =mation ( "s ( ! high] num]als1 & a suspicion ( ! decimal ent]s4 ,"o hundr$ is bo9ic1 #e m52 b #bjj1 in/ead ( be+ simply lahuh-inic1 #aj m51 is tsa-bo-inic1 #b #ajj1 or m /rictly1 #b times #e m54 ,simil>ly1 #cjj is #c #ajj1 #djj is #d #ajj1 etc4 ,! ^w = #ajjj is simple in/ead ( comp\nd1 & ! ?\s&s appe> to be =m$ :olly on ! decimal base4 ,a comp>ison ( ?is scale ) t ( ! ,nahuatl %[s h[ mu* inf]ior x is to ! latt]1 bo? 9 simplicity & consi/5cy4 ,,totonaco4#cfh #aj4 cauh4 #bj4 puxam4 #cj4 puxamacauh #bj #aj4 #dj4 tipuxam #b #bj4 #ej4 tipuxamacauh #dj #aj4 #fj4 totonpuxam #c #bj4 #ajj4 quitziz puxum #e #bj4 #bjj4 copuxam #aj #bj4 #djj4 tontaman4 #ajjj4 titamanacopuxam #b #djj #bjj4 ,! ess5tial "* ( ! vigesimal elem5t is %[n by ! la/ two num]als4 ,tontam51 ! squ>e ( #bj1 is a simple ^w1 & #ajjj is1 z x %\ld be1 #b times #djj1 plus #bjj4 ,x is mo/ un=tunate t ! num]al = #hjjj1 ! cube ( #bj1 is n giv54 ,,cora4#cfi #aj4 tamoamata4 #bj4 cei-tevi4 #cj4 ceitevi apoan tamoamata #bj #aj4 #dj4 huapoa-tevi #b #bj4 #fj4 huaeica-tevi #c #bj4 #ajj4 anxu-tevi #e #bj4 #djj4 ceitevi-tevi #bj #bj4 ,closely alli$ ) ! ,maya num]als & me?od ( c\nt+ are ^? ( ! ,qui*es ( ,guatemala4 ,! resemblance is s obvi\s t no detail 9 ! ,qui*e scale calls = special m5tion4 ,,qui*e4#cgj #aj4 lahuh4 #bj4 hu-u9ac #a man4 #cj4 hu-u9ac-lahuh #bj #aj4 #dj4 ca-u9ac #b m54 #ej4 lahu-r-ox-kal -#aj #c #bj4 #fj4 ox-kal #c #bj4 #gj4 lahu-u-humu* -#aj #hj4 #hj4 humu*4 #ij4 lahu-r-ho-kal -#aj #ajj4 #ajj4 hokal4 #ajjj4 o-tuc-rox-o-kal4 ,among ,s\? ,am]ican vigesimal sy/ems1 ! be/ kn[n is t ( ! ,*ib*as or ,muyscas ( ! ,bogota region1 :i* 0 obta9$ at an e>ly date by ! mission>ies :o lab\r$ among !m4 ,?is sy/em is mu* less ext5sive ?an t ( "s ( ! m nor!rn races2 b x is z ext5sive z almo/ any o!r ,s\? ,am]ican sy/em ) ! exception ( ! ,p]uvian1 :i* 01 h[ev]1 a pure decimal sy/em4 ,z has already be5 /at$1 ! native races ( ,s\? ,am]ica 71 z a rule1 exce$+ly defici5t 9 reg>d to ! numb] s5se4 ,_! scales are rude1 & %[ great pov]ty1 bo? 9 =mation ( num]al words & 9 ! actual ext5t to :i* c\nt+ 0 c>ri$4 ,if ext5d$ z f> z #bj1 ^! scales are likely to become vigesimal1 b _m /op f> %ort ( t limit1 & no inconsid]able numb] ( !m fail to rea* ev5 #e4 ,9 ?is respect we are rem9d$ ( ! ,au/ralian scales1 :i* 7 s rudim5t>y z really to preclude any prop] use ( ! ^w sy/em 9 connection ) !m4 ,c\nt+ among ! ,s\? ,am]ican tribes 0 (t5 equally limit$1 & ev5 less regul>4 ,foll[+ are ! significant num]als ( ! scale 9 "q3 ,,*ib*a1 ,,or ,,muysca4#cga #aj4 hub*ibica4 #bj4 quihica ub*ihica ?us says ! foot1 #aj #aj-aj1 or gueta h\se4 #cj4 guetas asaqui ub*ihica #bj #aj4 #dj4 gue-bosa #bj #b4 #fj4 gue-mica #bj #c4 #hj4 gue-muyhica #bj #d4 #ajj4 gue-hisca #bj #e4 ,,nagr&a4#cgb #aj4 guha4 #bj4 d9o4 #cj4 'badioguhanu #bj #aj4 #dj4 apudio #b #bj4 #ej4 apudioguhanu #b #bj #aj4 #fj4 asudio #c #bj4 #gj4 asudioguhanu #c #bj #aj4 #hj4 acudio #d #bj4 #ij4 acudioguhanu #d #bj #aj4 #ajj4 huisudio #e #bj1 or guhamba great #aj4 #bjj4 guahadio #aj #bj4 #djj4 dioamba great #bj4 #ajjj4 guhaisudio #aj #e #bj4 #bjjj4 hisudioamba #e great #bj's4 #djjj4 guhadioamba #aj great #bj's4 ,9 consid]+ ! influ5ce on ! mann]s & cu/oms ( any p :i* c\ld prop]ly be ascrib$ to ! use among !m ( any o!r base ?an #aj1 x mu/ n be =gott5 t no races1 save ^? us+ t base1 h ev] atta9$ any great degree ( civilization1 ) ! exception ( ! anci5t ,aztecs & _! imm$iate neighb\rs1 nor? & s\?4 ,= reasons already po9t$ out1 no highly civiliz$ race has ev] us$ an exclusively qu9>y sy/em2 & all t c be said ( ! influ5ce ( ?is mode ( c\nt+ is t x gives rise to ! habit ( collect+ objects 9 gr\ps ( five1 r ?an ( t51 :5 any attempt is be+ made to asc]ta9 _! sum4 ,9 ! case ( ! subsidi>y base #ab1 = :i* ! ,teutonic races h always %[n su* a fondness1 ! doz5 & gross ( comm]ce1 ! divisions ( ,engli% money1 & ( our common weights & measures are probably an outgr[? ( ?is pref]5ce2 & ! ,babylonian base1 #fj1 has fa/5$ ^u ! _w =ev] a sexagesimal me?od ( divid+ "t1 & ( measur+ ! circumf]5ce ( ! circle4 ,! advanc$ civilization atta9$ by ! races ( ,mexico & ,c5tral ,am]ica r5d] x possible to see "s ( ! effects ( vigesimal c\nt+1 j z a s+le ?\ght w %[ h[ our entire lives are influ5c$ by our habit ( c\nt+ by t5s4 ,among ! ,aztecs ! univ]sal unit 0 #bj4 ,a load ( cloaks1 ( dresses1 or o!r articles ( conv5i5t size1 0 #bj4 ,"t 0 divid$ into p]iods ( #bj days ea*4 ,! armies 7 numb]$ by divisions ( #hjjj2cgc & 9 c\ntless o!r ways ! vigesimal elem5t ( numb]s ent]$ into _! lives1 j z ! decimal ent]s into ours2 & x is to be suppos$ t !y f\nd x z useful & z conv5i5t = all measur+ purposes z we f9d our own sy/em2 z ! tradesman ( to-day f9ds ! duodecimal sy/em ( comm]ce2 or z ! ,babylonians ( old f\nd t s+ul>ly curi\s sy/em1 ! sexagesimal4 ,habituation1 ! laws :i* ! habits & cu/oms ( e-day life impose ^u u1 are s p[]ful1 t our in/9ctive read9ess to make use ( any concept dep5ds1 n on ! intr9sic p]fection or imp]fection :i* p]ta9s to x1 b on ! famili>ity ) :i* previ\s use has inve/$ x4 ,h5ce1 :ile "o race may use a decimal1 ano!r a qu9>y-vigesimal1 & ano!r a sexagesimal scale1 & :ile "o sy/em may actually be inh]5tly sup]ior to ano!r1 no us] ( "o me?od ( reckon+ ne$ ev] ?9k ( any o!r me?od z possess+ practical inconv5i5ces1 ( :i* ^? employ+ x are ev] consci\s4 ,&1 to cite a s+le in/ance :i* illu/rates ! unconsci\s daily use ( two modes ( reckon+ 9 "o scale1 we h only to ?9k ( ! s+ul> vigesimal fragm5t :i* rema9s to ?is day imb$d$ 9 ! num]al scale ( ! ,fr5*4 ,9 c\nt+ f #gj to #ajj1 or 9 us+ any numb] :i* lies betwe5 ^? limits1 no ,fr5*man is consci\s ( employ+ a me?od ( num]ation less simple or less conv5i5t 9 any p>ticul>1 ?an :5 he is at "w ) ! /rictly decimal portions ( 8 scale4 ,he passes f ! "o /yle ( c\nt+ to ! o!r1 & f ! second back to ! fir/ aga91 entirely unconsci\s ( any break or *ange2 entirely unconsci\s1 9 fact1 t he is us+ any p>ticul> sy/em1 except t :i* ! daily habit ( ye>s has made a "p himself4 ,deep regret mu/ be felt by e /ud5t ( philology1 t ! primitive mean+s ( simple num]als h be5 s g5]ally lo/4 ,b1 j z ! pebble on ! bea* has be5 worn & r\nd$ by ! beat+ ( ! waves & by o!r pebbles1 until no trace ( its orig9al =m is left1 & until we c say ( x n[ only t x is qu>tz1 or t x is diorite1 s too ! num]als ( _m languages h suff]$ f ! attrition ( ! ages1 until all semblance ( _! orig9 has be5 lo/1 & we c say ( !m only t !y are num]als4 ,beyond a c]ta9 po9t we c c>ry ! /udy nei!r ( numb] nor ( numb] words4 ,at t po9t bo? ! ma!matician & ! philologi/ mu/ pause1 & leave ev]y?+ beyond to ! speculations ( ^? :o delight 9 no?+ else s mu* z 9 pure !ory4 ,,! ,,end4 ,,index ,,( ,,au?ors4 ,adam1 ,l41 #dd1 #aei1 #aff1 #age4 ,arm/rong1 ,r4,a41 #ahj4 ,aymoni]1 ,a41 #aef4 ,ba*(51 ,j4,j41 #aca4 ,balbi1 ,a41 #aea4 ,bancr(t1 ,h4,h41 #bi1 #dg1 #hi1 #ic1 #aac1 #aii4 ,b>l[1 ,h41 #ajh4 ,beaureg>d1 ,o41 #de1 #hc1 #aeb4 ,bellamy1 ,e4,w41 #i4 ,boas1 ,f41 #cj1 #de1 #df1 #fe1 #hg1 #hh1 #acf1 #afc1 #afd1 #aga1 #aig1 #aih4 ,bonwick1 ,j41 #bd1 #bg1 #ajg1 #ajh4 ,br9ton1 ,d4,g41 #b1 #bb1 #df1 #eb1 #eg1 #fa1 #aaa1 #aab1 #adj1 #aii1 #bjj4 ,burton1 ,r4,f41 #cg1 #ga4 ,*amb]la91 ,a4,f41 #de1 #fe1 #ic4 ,*ase1 ,p4,e41 #ii4 ,cl>ke1 ,h41 #aac4 ,codr+ton1 ,r4,h41 #af1 #ie1 #if1 #acf1 #ach1 #ade1 #aec1 #aed4 ,crawfurd1 ,j41 #hi1 #ic1 #acj4 ,curr1 ,e4,m41 #bd-bg1 #ajd1 #ajg-aaj1 #aab4 ,cu%+1 ,f4,h41 #ac1 #dh4 ,de ,flac\rt1 #h1 #i4 ,de ,qu9cey1 ,t41 #ce4 ,des*amps1 ,m41 #bh4 ,dobrizh(f]1 ,m41 #ga4 ,dorsey1 ,j4,o41 #ei4 ,du ,*aillu1 ,p4,b41 #ff1 #fg1 #aej1 #aea4 ,du ,graty1 ,a4,m41 #ach4 ,ellis1 ,a4,a41 #fd1 #ia4 ,ellis1 ,r41 #cg1 #adb4 ,ellis1 ,w41 #hc1 #aai4 ,ersk9e1 ,j4,e41 #aec1 #aed4 ,flegel1 ,r41 #acc4 ,gallat91 ,a41 #acf1 #aei1 #aff1 #aga1 #aii1 #bjd1 #bjf1 #bjh4 ,galton1 ,f41 #d4 ,gats*et1 ,a4,s41 #eh1 #ei1 #fh4 ,gilij1 ,f4,s41 #ed4 ,gill1 ,w4,w41 #ah1 #aah4 ,go$el1 ,m41 #hc1 #adg4 ,grimm1 ,j4,l4,c41 #dh4 ,grb]1 ,g41 #ahb4 ,guillome1 ,j41 #aha4 ,haddon1 ,a4,c41 #ah1 #aje4 ,hale1 ,h41 #fa1 #fe1 #ic1 #aad-aaf1 #abb1 #acj1 #aef1 #afc1 #afd1 #aga4 ,hankel1 ,h41 #acg4 ,haumont1 ,j4,d41 #dd4 ,h]vas1 ,l41 #agj4 ,humboldt1 ,a4 von1 #cb1 #bjg4 ,hyades1 ,m41 #bb4 ,kelly1 ,j4,w41 #aeg1 #aif4 ,kelly1 ,j41 #ahj4 ,kle9s*midt1 ,s41 #eb1 #hj4 ,lang1 ,j4,d41 #ajh4 ,lapp5b]g1 ,j4,m41 #abg4 ,la?am1 ,r4,g41 #bd1 #fg1 #ajg4 ,leibnitz1 ,g4,w4 von1 #ajb1 #ajc4 ,lloyd1 ,h4,e41 #g4 ,long1 ,c4,c41 #adh1 #ahf4 ,long1 ,s4,h41 #aba4 ,lubbock1 ,sir ,j41 #c1 #e4 ,lull1 ,e4,p41 #gi4 ,macdonald1 ,j41 #ae4 ,mack5zie1 ,a41 #bf4 ,man1 ,e4,h41 #bh1 #aid4 ,mann1 ,a41 #dg4 ,m>coy1 ,p4 7,sa9t ,cricq71 #bc1 #afh4 ,m>9]1 ,a41 #he4 ,m>tius1 ,c4,f4 von1 #bc1 #gi1 #aaa1 #abb1 #ach1 #adb1 #agd4 ,mason1 #aab4 ,mill1 ,j4,s41 #c4 ,moncelon1 ,m41 #adb4 ,morice1 ,a41 #ae1 #hf4 ,mll]1 ,fr41 #aj1 #bg1 #bh1 #de1 #dh1 #ee1 #ef1 #fj1 #fc1 #ff1 #fi1 #gh1 #hj1 #ij1 #ajh1 #aaa1 #aba1 #abb1 #acj1 #acf1 #aci1 #adf-aea1 #aef-aeh1 #afe-afg1 #ahe-ahg1 #aia1 #aic4 ,murdo*1 ,j41 #cj1 #di1acg4 ,ny/ron1 ,j4,w41 #acb4 ,o',donovan1 ,j41 #ahj4 ,oldfield1 ,a41 #bi1 #gg4 ,olmos1 ,a4 de1 #ada4 ,p>isot1 ,j41 #dd4 ,p>k1 ,m41 #ade-adg4 ,p>ry1 ,w4,e41 #cb4 ,peacock1 ,g41 #h1 #ef1 #hd1 #aaa1 #aah1 #aai1 #aed1 #ahf4 ,petitot1 ,e41 #ec1 #aeg1 #aif4 ,pott1 ,a4,f41 #ej1 #fh1 #ib1 #abj1 #ade1 #adh1 #adi1 #aeb1 #aeg1 #aff1 #ahb1 #ahd1 #ahi1 #aia1 #bje4 ,prun]-,bey1 #aj1 #ajd4 ,pughe1 ,w4,o41 #ada4 ,ralph1 ,j41 #abe4 ,ray1 ,s4,h41 #de1 #gh1 #hj4 ,ridley1 ,w41 #eg4 ,ro?1 ,h4,l41 #gi4 ,salt1 ,h41 #ahg4 ,sayce1 ,a4,h41 #ge4 ,s*oolcraft1 ,h4,r41 #ff1 #ha1 #hc1 #hd1 #aei1 #afj4 ,s*rd]1 ,p41 #ij4 ,s*we9fur?1 ,g41 #adc1 #adf1 #adi1 #ahf1 #ahg4 ,simeon1 ,r41 #bja4 ,spix1 ,j4,b4 von1 #g4 ,spurrell1 ,w41 #ahj4 ,squi]1 ,g4,e41 #hj1 #bjg4 ,/anley1 ,h4,m41 #ch1 #db1 #fd1 #fi1 #gh1 #aej1 #ahg4 ,tapl91 ,g41 #ajf4 ,?iel1 ,b4,a41 #agb4 ,toy1 ,c4,h41 #gj4 ,turn]1 ,g41 #aeb1 #aed4 ,tylor1 ,e4,b41 #b1 #c1 #ae1 #ah1 #bb1 #fc1 #fe1 #gh1 #gi1 #ha1 #hd1 #ig1 #abd4 ,van ,eys1 ,j4,w41 #ahb4 ,vignoli1 ,t41 #ie4 ,wallace1 ,a4,r41 #agd4 ,wells1 ,e4,r41 jr41 #aeg1 #aif4 ,:ewell1 ,w41 #c4 ,wick]%am1 ,j41 #if4 ,wi5]1 ,c41 #bb4 ,williams1 ,w4,l41 #abc4 ,,index ,,( ,,subjects4 ,abacus1 #ai4 ,abeokuta1 #cc4 ,abipone1 #ga1 #gb4 ,abkhasia1 #ahh4 ,abok]1 #adh4 ,actu>y1 ,life ins41 #ai4 ,adaize1 #afb4 ,addition1 #ai1 #dc1 #df1 #ib4 ,adelaide1 #ajh4 ,admiralty ,isl&s1 #de4 ,affadeh1 #ahd4 ,africa 7,african71 #i1 #af1 #bh1 #bi1 #cb1 #cc1 #ch1 #db1 #dg1 #fd1 #ff1 #fi1 #gh1 #hj1 #ia1 #aje1 #abj1 #ade1 #agj1 #agf1 #ahd1 #ahg4 ,a9o 7,a9u71 #de1 #aia4 ,akra1 #abj4 ,ak>i1 #aij4 ,alaska1 #aeg1 #aif4 ,albania1 #ahd4 ,alb]t ,riv]1 #bf4 ,aleut1 #aeg4 ,algonk9 7,algonqu971 #de1 #ib1 #afa4 ,amazon1 #bc4 ,ambrym1 #acf4 ,am]ican1 #aj1 #af1 #ai1 #ih1 #aje4 ,&aman1 #h1 #ae1 #bh1 #ca1 #gf1 #agd1 #aic4 ,aneitum1 #aed4 ,animal1 #c1 #f4 ,an?ropological1 #ba4 ,apho1 #acc4 ,api1 #hj1 #acf1 #aee4 ,ap9age1 #aaa4 ,arab1 #agj4 ,arawak1 #eb-ed1 #ace4 ,arctic1 #bi4 ,arik>a1 #df4 ,ari?metic1 #a1 #e1 #cj1 #cc1 #gc1 #ic4 ,aryan1 #gf1 #abh-acj4 ,a%antee1 #ade4 ,asia 7,asiatic71 #bh1 #aac1 #aca1 #ahg4 ,ass9ibo9e1 #ff1 #ib4 ,a?apaskan1#ib4 ,atlantic1 #abf4 ,aurora1 #aee4 ,au/ralia 7,au/ralian71 #b1 #f1 #ai1 #bb1 #bd-cj1 #eg1 #eh1 #ga1 #ge1 #gf1 #hd1 #ajc1 #aje1 #ajf1 #aaj1 #aab1 #aah1 #agc1 #bjf4 ,av>i1 #ahh4 ,aym>a1 #aff4 ,aztec1 #fc1 #gh1 #hc1 #hi1 #ic1 #bja1 #bjg1 #bjh4 ,babusess1 #ch4 ,babylonian1 #bjh4 ,bagrimma1 #adh4 ,bahn>s1 #ae4 ,bakairi1 #aaa4 ,balad1 #fg4 ,bal5que1 #aej4 ,bamb>ese1 #ie4 ,banks ,isl&s1 #af1 #if1 #aec4 ,b>ea1 #aea4 ,b>ga9+1 #ah1 #ai1 #cb4 ,b>i1 #acf4 ,b>re1 #agd4 ,basa1 #adf4 ,basque1 #dj1 #ahb4 ,bellacoola1 see ,bilqula4 ,bely&o ,riv]1 #aji4 ,b5gal1 ,bay (1 #bh4 ,b5u1 #acc4 ,betoya1 #eg1 #aab1 #ace1 #adj4 ,bilqula1 #df1 #afd4 ,b9>y1 *ap4 v4 ,b991 #adi4 ,bird-ne/+1 #e4 ,bisaye1 #ij4 ,bogota1 #bjf4 ,bolan1 #abj4 ,bolivia1 #b1 #ba4 ,bongo1 #adc1 #ahf4 ,bonz1 #aea4 ,bororo1 #bc4 ,botocudo1 #bb1 #ca1 #dh1 #ga4 ,b\rke1 #ajh4 ,boyne ,riv]1 #bd4 ,brazil1 #b1 #g1 #cj1 #agd1 #aie4 ,bretagne 7,breton71 #abj1 #abi1 #aha1 #ahb4 ,briti% ,columbia1 #de1 #df1 #fe1 #hf1 #hh1 #hi1 #aab1 #aac1 #aie4 ,bullom1 #adg4 ,bun*1 #fd4 ,burnett ,riv]1 #aab4 ,bu%man1 #bh1 #ca4 ,butong1 #ic4 ,caddoe1 #afb4 ,cahuillo1 #afe4 ,calculat+ ma*9e1 #ai4 ,campa1 #bb4 ,canada1 #bi1 #ec1 #ed1 #hf1 #aie4 ,canaque1 #adb1 #add4 ,c>aja1 #bc4 ,c>ib1 #aff1 #afg1 #aii4 ,c>n>von1 #ce1 #cf4 ,c>ri]1 #hf4 ,c>?ag9ian1 #agi4 ,caucasus1 #ahh4 ,cayriri 7see ,kiriri71 #gi4 ,cayubaba 7,cayubabi71 #hd1 #afg4 ,celtic1 #dj1 #afi1 #agi1 #aha1 #aij4 ,cely1 ,mom1 #i4 ,c5tral ,am]ica1 #bi1 #fi1 #gi1 #aba1 #aca1 #aie1 #bja1 #bjh4 ,ceylon1 #bh4 ,*aco1 #bb4 ,*ampion ,bay1 #aji4 ,*>les ,,xii41 #acb4 ,*ey5ne1 #fb4 ,*ib*a1 #bjf4 ,*9a 7,*9ese71 #dj1 #aca4 ,*ippeway1 #fb1 #aei1 #afb4 ,*iquito1 #b1 #f1 #ba1 #dj1 #ga1 #gf4 ,*octaw1 #fe1 #he1 #afb4 ,*unsag1 #ahi4 ,circassia1 #aij4 ,cobeu1 #agd4 ,co*9 ,*9a1 #ae4 ,columbian1 #aac4 ,coman*e1 #bi1 #hc4 ,conibo1 #bc4 ,coop]'s ,creek1 #ajh4 ,cora1 #aff4 ,cotoxo1 #aaa4 ,c[rie1 #fd1 #gj1 #ga4 ,cree1 #ia4 ,crock] ,isl&1 #ajg4 ,cr[1 #c1 #d1 #ib4 ,crusoe1 ,rob9son1 #g4 ,curetu1 #aaa4 ,dahomey1 #ga4 ,dakota1 #ha1 #ia1 #ib4 ,dani%1 #cj1 #df1 #abi1 #ahc4 ,d>nley ,isl&s1 #bd4 ,delaw>e1 #ia1 #afj4 ,dem>a1 #d1 #f4 ,dn1 #hf4 ,dido1 #ahi4 ,d9ka1 #acf1 #adg4 ,dippil1 #ajg4 ,division1 #ai4 ,dravidian1 #ajd1 #aic4 ,dual numb]1 #ge4 ,dulu?1 #cd4 ,duodecimal1 *ap4 v4 ,dut*1 #abi4 ,eaw1 #bd4 ,ebon1 #aeb4 ,efik1 #adh1 #ahe4 ,encabellada1 #bb4 ,enc\nt] ,bay1 #ajh4 ,ende1 #fh1 #aeb4 ,engli%1 #bh1 #ch-dd1 #fj1 #ha1 #he1 #hi1 #aah1 #abc1 #abd1 #abi1 #ahc1 #bjj1 #bjc1 #bjh4 ,eromanga1 #if1 #acf1 #aed4 ,eskimo1 #af1 #cj1 #ca1 #cb1 #cf1 #dh1 #ea1 #eb1 #ed1 #fa1 #fd1 #hc1 #acg1 #aeg1 #aei1 #aie1 #aif4 ,essequibo1 #aff4 ,europe 7,european71 #bg1 #ci1 #afh1 #afi1 #agi1 #ahb1 #ahc1 #ahe1 #bjd4 ,eye1 #ad1 #ig4 ,ey]'s ,s& ,pat*1 #bf4 ,ewe1 #fd1 #ia4 ,fall1 #afc4 ,fate1 #ach1 #aee4 ,fatuhiva1 #acj4 ,feloop1 #ade4 ,f]n&o ,po1 #aej4 ,fiji1 #if4 ,f+] pantomime1 #aj1 #bc1 #bi1 #fg1 #hb4 ,f+oe1 #cc4 ,fi/1 #af1 #ei1 #gb4 ,fl9d]'s ,riv]1 #bd4 ,flores1 #fh1 #aeb4 ,=ef+]1 #ab1 #ae1 #af1 #ed1 #fa1 #ia1 #aac4 ,f\lah1 #adg4 ,f\r? f+]1 #ah4 ,fraz]'s ,isl&1 #ajh4 ,fr5*1 #dj1 #da1 #abd1 #abi1 #aha1 #ahb1 #bji4 ,fuegan1 #bb4 ,gaelic1 #ahj4 ,galibi1 #ach4 ,gaul1 #afi1 #ahb4 ,georgia1 #ahi4 ,g]man1 #ch-dc1 #abi1 #ahc4 ,ge/ure1 #ah1 #ei4 ,gola1 #aea4 ,golo1 #adf4 ,gonn ,/ation1 #aaj4 ,go?1 #afi4 ,greek1 #hf1 #abi1 #afh1 #afi4 ,gre5 ,isl&1 #de4 ,gre5l&1 #bi1 #eb1 #hj1 #aeh4 ,gua*i1 #bc1 #ca4 ,gu>ani1 #ee1 #ach4 ,guatemala1 #bje4 ,guato1 #adb4 ,guaycuru1 #bb4 ,gudang1 #bd4 ,haida1 #aab4 ,hawaii1 #aac1 #aad1 #aaf1 #aag4 ,head1 #ga4 ,heap1 #h1 #i1 #be1 #gj1 #gg1 #ajj4 ,hebrew1 #hf1 #hi1 #ie4 ,heiltsuk1 #fe1 #hh1 #afc4 ,h]]o1 #aej4 ,h]vey ,isl&s1 #aah4 ,hidatsa1 #hj1 #ia4 ,hill ,end1 #aji4 ,himalaya1 #aic4 ,hott5tot1 #hj1 #ib4 ,hua/eca1 #bjd4 ,hudson's ,bay1 #dh1 #fa4 ,hun1 #afi4 ,hunt1 ,leigh1 #cc4 ,ibo1 #ahe4 ,icel&ic1 #abi1 #ahc4 ,ill9ois1 #ia4 ,index f+]1 #aa1 #ad4 ,india1 #if1 #aab1 #aca4 ,indian1 #h1 #aj1 #ac1 #af1 #ag1 #ai1 #cb1 #cf1 #ed1 #ee1 #ei1 #fb1 #fe1 #ff1 #gi1 #hj1 #hb1 #hc1 #hi1 #ij1 #ih1 #aje1 #aab1 #aga1 #bja4 ,indian ,ocean1 #fc1 #aic4 ,indo-,european1 #gf4 ,iri%1 #abi1 #ahj4 ,italian1 #ci1 #hj1 #abd1 #abi1 #bjc4 ,jaj[]ong1 #aef4 ,jallonkas1 #adf4 ,jal(f1 #adf4 ,japanese1 #dj1 #hf1 #hi1 #ic-ie4 ,java1 #ic1 #abj4 ,jiviro1 #fa1 #acf4 ,jo9ts ( f+]s1 #g1 #ah1 #agc4 ,juri1 #gi4 ,kamass91 #acj4 ,kamil>oi1 #bg1 #ajg1 #aab4 ,kamts*atka1 #ge1 #aeg4 ,kanuri1 #acf1 #adi4 ,k>ankawa1 #fh4 ,k>51 #aab4 ,keppel ,bay1 #bd4 ,ki-,nyassa1 #aej4 ,kiriri1 #ee1 #ach1 #aci1 #afg4 ,kissi1 #ade4 ,ki-,swahili1 #db4 ,ki-,yau1 #aej4 ,klama?1 #eh1 #ei4 ,knot1 #g1 #i1 #ai1 #dj1 #ic1 #aae4 ,kolyma1 #ge4 ,koot5ay1 #fe4 ,koriak1 #ge4 ,kr$y1 #adi4 ,kru1 #adf4 ,ku-,mbutti1 #gh4 ,kunama1 #aea4 ,kuri1 #ahh4 ,kusaie1 #gh1 #hj4 ,kwakiutl1 #de4 ,labill>dire1 #he4 ,labrador1 #bi4 ,lake ,kopp]amana1 #ajg4 ,lat91 #dj1 #dd1 #gf1 #ha1 #hf1 #abd1 #abh1 #afh1 #afi1 #aha1 #ahb4 ,lazi1 #ahi4 ,left h&1 #aj-ag1 #ed4 ,lep]'s ,isl&1 #af4 ,lepts*a1 #aic4 ,lifu1 #adc4 ,little f+]1 #aj-ah1 #dh1 #ed1 #fa1 #ia4 ,logone1 #ahf4 ,london1 #abd4 ,l[] ,cali=nia1 #bi4 ,luli1 #aah4 ,lutuami1 #afd4 ,maba1 #hj4 ,macass>1 #ic4 ,ma*9e1 ,calculat+1 #ai1 #bj4 ,mack5zie ,riv]1 #aeg4 ,macuni1 #agd4 ,madagasc>1 #h1 #i4 ,maipures1 #ae1 #ef4 ,mairassis1 #aj4 ,malagasy1 #hc1 #ie4 ,malanta1 #if4 ,malay1 #h1 #de1 #ij1 #ic1 #agj4 ,mallicolo1 #aeb4 ,manadu1 #ic4 ,m&+o1 #ahf4 ,mang>eva1 #aad4 ,manx1 #ahj4 ,_m1 #b1 #ba-bc1 #be1 #bh1 #ajj4 ,maori1 #fd1 #ic1 #abb4 ,m>a*[ie1 #bf4 ,m>1 #hd4 ,m>\ra1 #ajf4 ,m>quesas1 #ic1 #aad1 #aae4 ,m>%all ,isl&s1 #abb1 #aeb4 ,massa*usetts1 #ia1 #aei4 ,ma!matician1 #b1 #c1 #ce1 #ajb1 #abg1 #baj4 ,matibani1 #aea4 ,matlaltz9ca1 #aff4 ,maya1 #de1 #df1 #aii1 #bje4 ,mbayi1 #aaa4 ,mbocobi1 #bb4 ,mb\%a1 #ff4 ,melanesia1 #af1 #bb1 #bh1 #hd1 #ie4 ,m5de1 #ahf4 ,mexico1 #bi1 #aie1 #bja1 #bjd1 #bjh4 ,miami1 #ia4 ,micmac1 #ij1 #afj4 ,middle f+]1 #ab1 #ae1 #fb4 ,mille1 #abb4 ,m9nal ,yung>1 #bf4 ,m9si1 #afb4 ,mississaga1 #dd1 #ib4 ,mississippi1 #abe4 ,mocobi1 #aai4 ,mohegan1 #ia4 ,mohican1 #agb4 ,mokko1 #adi4 ,molele1 #afd4 ,mon]oo1 #aji4 ,mongolian1 #h4 ,montagnais1 #ec1 #ed1 #age4 ,moree1 #bd4 ,moreton ,bay1 #ajh4 ,mort ,n\l>1 #ajg4 ,mosquito1 #fi1 #gj1 #aba4 ,mota1 #ie1 #aec4 ,mpovi1 #aeb4 ,multiplication1 #ai1 #cc1 #dj1 #dc1 #ei4 ,mund>i1 #aic4 ,mundo1 #ahf4 ,muralug1 #ag4 ,murray ,riv]1 #ajf1 #aji4 ,muysca1 #bjf4 ,nagr&a1 #bjg4 ,nahuatl1 #ada1 #add1 #agg1 #bja1 #bje4 ,nakuhiva1 #aaf1 #acj4 ,negro1 #h1 #i1 #ae1 #bi1 #ahd4 ,n5gone1 #fc1 #acf4 ,new1 #abh-acj4 ,new ,cal$onia1 #aed4 ,new ,granada1 #aie4 ,new ,gu9ea1 #aj1 #aeb4 ,new ,hebrides1 #aee4 ,new ,irel&1 #de4 ,new ,zeal&1 #abc4 ,nez ,p]ces1 #fe1 #aeh4 ,ng>rim[ro1 #aaj4 ,niam ,niam1 #fd1 #acf4 ,nic>agua1 #hj4 ,nicob>1 #gh1 #aic4 ,night+ale1 #d4 ,nootka1 #afc1 #aih4 ,norman ,riv]1 #bd4 ,nor? ,am]ica1 #bh1 #hb1 #aga1 #agc1 #agf1 #aid1 #bja4 ,not*1 #g1 #i1 #ic4 ,num]al frame1 #ai4 ,nupe1 #adi1 #ahf4 ,nusqually1 #if4 ,oceania1 #aae1 #agf4 ,octon>y1 *ap4 v4 ,odessa1 #cd4 ,ojibwa1 #hd1 #aei4 ,okanak51 #hh4 ,omaha1 #afa4 ,omeo1 #aaj4 ,oregon1 #eh1 #aie4 ,orejone1 #bc4 ,or9oco1 #ed1 #ef1 #aie4 ,o/ri*1 #ga1 #gb4 ,otomac1 #ae4 ,otomi1 #afe1 #aii4 ,ottawa1 #aei4 ,oy/] ,bay1 #gi4 ,pacific1 #bi1 #aac1 #aaf1 #aag1 #aca4 ,palm 7( ! h&71 #ab1 #ad1 #ae4 ,palm ,isl&1 #aef4 ,pama1 #acf1 #aee4 ,pampanaga1 #ff4 ,papaa1 #adh4 ,p>aguay1 #ee1 #ga1 #aah1 #aie4 ,p>ana1 #aai4 ,p>is1 #ahb4 ,pawnee1 #ia1 #aba1 #afb4 ,pebble1 #g-i1 #ai1 #dj1 #ic1 #agi4 ,p5o1 #b4 ,p]u 7,p]uvian71 #b1 #bb1 #fa1 #bjf4 ,philipp9e1 #ff4 ,philology 7,philologi/71 #abh1 #bji1 #baj4 ,pho5ician1 #ij1 #agi4 ,pigmy1 #fi1 #gj1 #gh4 ,pikumbul1 #eg1 #ach4 ,p9es1 ,isle (1 #aec4 ,p9j>ra1 #bf4 ,pl5ty1 #be1 #gg4 ,po9t ,b>r[1 #cj1 #ea1 #fd1 #hc1 #acg1 #aei4 ,polynesia1 #bb1 #bh1 #aah1 #acj1 #agj4 ,pondo1 #cc4 ,popham ,bay1 #ajg4 ,port ,d>w91 #aji4 ,port ,ess+ton1 #bd1 #ajg4 ,port ,mackay1 #bf4 ,port ,macqu>ie1 #aji4 ,puget ,s\nd1 #if4 ,puri1 #bb1 #ib4 ,quappa1 #aga1 #agb4 ,quat]n>y1 *ap4 v4 ,queanbeyan1 #bd4 ,qui*e1 #bje4 ,qui*ua1 #fa4 ,rapid1 #afc4 ,r>otonga1 #aad4 ,ri*mond ,riv]1 #aji4 ,"r h&1 #aj-ah1 #ed4 ,"r-h&$ness1 #ac1 #ad4 ,r+ f+]1 #ae4 ,rio ,gr&e1 #aie4 ,rio ,napo1 #bb4 ,rio ,norte1 #acf1 #aii4 ,russia 7,russian71 #cj1 #ce4 ,sahapt91 #aeh4 ,san ,antonio1 #acf4 ,san ,blas1 #gi1 #hj4 ,sanskrit1 #dj1 #ib1 #ig1 #abh4 ,sapibocone1 #hd1 #afg4 ,sa/e 7,%a/a71 #afe4 ,scrat*1 #g4 ,scy?ian1 #afi4 ,se$1 #ic4 ,semitic1 #hi4 ,s5>y1 *ap4 v4 ,sesake1 #acf1 #aee4 ,sev]al1 #bb4 ,sexagesimal1 #abd1 #bjh4 ,%awnoe1 #afj4 ,%ell1 #g1 #ai1 #gj1 #ic4 ,%u%wap1 #hh4 ,sib]ia1 #bi1 #cj1 #ahg1 #aij4 ,si]ra ,leone1 #hc4 ,sign language1 #f4 ,si\x1 #hc4 ,slang1 #abd4 ,slavonic1 #dj4 ,sn[y ,riv]1 #aaj4 ,s\ss\1 #hc1 #adg4 ,s\? ,africa1 #d1 #ae1 #bh4 ,s\? ,am]ica1 #b1 #ae1 #bb1 #bc1 #bg-bi1 #ed1 #eg1 #gb1 #gf1 #gh1 #gi1 #ajd1 #aaj1 #agc1 #agd1 #aid1 #bja1 #bjf4 ,spani%1 #b1 #bc1 #db4 ,spl9t1 #g4 ,/ick1 #g1 #agi4 ,/latlumh1 #hh4 ,/reaky ,bay1 #bf4 ,/r+1 #g1 #i1 #fd1 #ga4 ,/rong's ,isl&1 #gh4 ,subtraction1 #ai1 #dd-dg4 ,sunda1 #abj4 ,sw$5 7,sw$i%71 #abi1 #acb1 #ahc4 ,tacona1 #b4 ,ta5sa1 #dd4 ,tagala1 #ff4 ,tahiti1 #aad4 ,tahuata1 #aae4 ,tama1 #aaa4 ,tamanac1 #ed1 #ace4 ,tambi1 #abj4 ,tanna1 #aed4 ,t>ascan1 #afe4 ,t>iana1 #agd4 ,tasmania1 #bd1 #bg1 #gi1 #ajd1 #ajf4 ,tawgy1 #acj4 ,t*et*nia1 #ahh4 ,t*iglit1 #aeg1 #aif4 ,tembu1 #cc4 ,temne1 #adh4 ,t]n>y1 *ap4 v4 ,t]raba1 #agb4 ,teutonic1 #dj1 #da1 #dc1 #agi1 #aha1 #bjh4 ,texas1 #fi4 ,?ibet1 #if4 ,?umb1 #aj-ah1 #ed1 #ei1 #fa1 #fb1 #aac1 #agc4 ,?us*1 #ahi4 ,ticuna1 #afh4 ,timukua1 #afe4 ,tl+it1 #acf1 #afc1 #aig4 ,tobi1 #aef4 ,tonga1 #cc1 #he4 ,torres1 #ag1 #if1 #ajd1 #aje4 ,totonaco1 #bje4 ,t[ka1 #gh4 ,triton's ,bay1 #aeb4 ,ts*uk%i1 #aef1 #aia4 ,tsim%ian1 #hf1 #afd1 #aih4 ,twe$ ,riv]1 #bf4 ,ua9uma1 #abb4 ,udi1 #ahh4 ,uea1 #fg1 #aec4 ,unit$ ,/ates1 #bi1 #hc1 #aie4 ,upp] ,y>ra1 #aaj4 ,urep>ap>a1 #aec4 ,vaturana1 #if4 ,v$da1 #bh1 #ca1 #gf1 #agd4 ,vei1 #af1 #adg1 #ahe4 ,victoria1 #aef4 ,vilelo1 #fj4 ,waiclatpu1 #afd4 ,wales 7,wel%71 #ce1 #df1 #ada1 #add1 #agg1 #ahj4 ,walla*ia1 #aba4 ,w>rego1 #ajg1 #aji4 ,w>rior ,isl&1 #ajg4 ,wasp1 #e4 ,wat*&ie1 #bi1 #gg4 ,watji1 #abj4 ,we$ook>ry1 #bd4 ,wimm]a1 #ajg4 ,w9nebago1 #he4 ,wiraduroi1 #bg1 #ajh4 ,wirri-,wirri1 #ajh4 ,wokke1 #aab4 ,worce/]1 ,mass41 ,s*ools (1 #aa4 ,yahua1 #afh4 ,y>uro1 #aci4 ,y5g51 #aed4 ,yit-?a1 #aji4 ,yoruba1 #cc1 #dg1 #fd1 #gj1 #ahe4 ,yucatan1 #aie1 #bja4 ,yuckaburra1 #bf4 ,zamuco1 #ee1 #fj1 #ach1 #aci4 ,zap>a1 #aaa4 ,zulu1 #af1 #fb4 ,zui1 #ac1 #ad1 #dh1 #di1 #ec1 #ed1 #fj1 #hc1 #acg4 ,,footnotes3 #a ,br9ton1 ,d4,g41 ,essays ( an ,am]icani/1 p4 #djf2 & ,am]ican ,race1 p4 #cei4 #b ,?is in=mation ,i receiv$ f ,dr4 ,br9ton by lett]4 #c ,tylor1 ,primitive ,culture1 ,vol4 ,i4 p4 #bdj4 #d ,nature1 ,vol4 ,,xxxiii4 p4 #de4 #e ,spix & ,m>tius1 ,travels 9 ,brazil1 ,tr4 f ,g]man by ,h4,e4 ,lloyd1 ,vol4 ,,ii4 p4 #bee4 #f ,de ,flac\rt1 ,hi/oire de le gr&e ,isle de ,madagasc>1 *4 xxviii4 ,quot$ by ,peacock1 ,encyc4 ,met41 ,vol4 ,i4 p4 #cic4 #g ,bellamy1 ,elizabe? ,w41 ,atlantic ,mon?ly1 ,m>*1 #ahic1 p4 #cag4 #h ,grundriss d] ,spra*wiss5s*aft1 ,bd4 ,,iii4 ,abt4 i41 p4 #id4 #i ,prun]-,bey1 ,bullet9 de la ,socit d',an?r4 de ,p>is1 #ahfa1 p4 #dfb4 #aj ,manual ,concepts1 ,am4 ,an?ropologi/1 #ahib1 p4 #bib4 #aa ,tylor1 ,primitive ,culture1 ,vol4 ,i4 p4 #bde4 #ab ,op4 cit41 loc4 cit4 #ac ,aborig9al ,inhabitants ( ,&aman ,isl&s1 ,j\rn4 ,an?4 ,in/41 #ahhb1 p4 #ajj4 #ad ,morice1 ,a41 ,revue d',an?ropologie1 #ahgh1 p4 #fcd4 #ae ,macdonald1 ,j41 ,mann]s1 ,cu/oms1 etc41 ( ,s\? ,african ,tribes1 ,j\rn4 ,an?r4 ,in/41 #ahhi1 p4 #bij4 ,ab\t a doz5 tribes are enum]at$ by ,mr4 ,macdonald3 ,pondos1 ,tembucs1 ,bacas1 ,tolas1 etc4 #af ,codr+ton1 ,r4,h41 ,melanesians1 _! ,an?ropology & ,folk-,lore1 p4 #cec4 #ag ,e4g4 ! ,zuis4 ,see ,cu%+'s pap] quot$ above4 #ah ,haddon1 ,a4,c41 ,e?nography ,we/]n ,tribes ,torres ,/rait1 ,j\rn4 ,an?4 ,in/41 #ahhi1 p4 #cje4 ,= a simil> me?od1 see ,life 9 ! ,s\!rn ,isles1 by ,w4,w4 ,gill4 #ai ,tylor1 ,primitive ,culture1 ,vol4 ,i4 p4 #bdf4 #bj ,br9ton1 ,d4,g41 ,lett] ( ,sept4 #bc1 #ahic4 #ba ,ibid4 ,! ref]5ce = ! ,mbocobi1 infra1 is ! same4 ,see also ,br9ton's ,am]ican ,race1 p4 #cfa4 #bb ,tylor1 ,primitive ,culture1 ,vol4 ,i4 p4 #bdc4 #bc ,op4 cit41 loc4 cit4 #bd ,hyades1 ,bullet9 de la ,socit d',an?r4 de ,p>is1 #ahhg1 p4 #cdj4 #be ,wi5]1 ,c41 ,pr\ et ,bolivie1 p4 #cfj4 #bf ,m>coy1 ,p41 ,travels 9 ,s\? ,am]ica1 ,vol4 ,,ii p4 #dg4 ,accord+ to ! same au?ority1 mo/ ( ! tribes ( ! ,upp] ,amazon _c c\nt above #b or #c except by r$uplication4 #bg ,op4 cit41 ,vol4 ,,ii4 p4 #bha4 #bh ,gloss>ia ,l+u>um ,brasili5sium4 ,bororos1 p4 #ae2 ,gua*i1 p4 #acc2 ,c>ajas1 p4 #bfe4 #bi ,curr1 ,e4,m41 ,! ,au/ralian ,race1 ,vol4 ,i4 p4 #bhb4 ,! next eight li/s are1 9 ord]1 f ,i4 p4 #bid1 ,,iii4 p4 #dbd1 ,,iii4 p4 #aad1 ,,iii4 p4 #abd1 ,,ii4 p4 #cdd1 ,,ii4 p4 #cjh1 ,i4 p4 #cad1 ,,iii4 p4 #cad1 respectively4 #cj ,bonwick1 ,j41 ,! ,daily ,life & ,orig9 ( ! ,tasmanians1 p4 #add4 #ca ,la?am1 ,comp>ative ,philology1 p4 #ccf4 #cb ,! ,au/ralian ,race1 ,vol4 ,i4 p4 #bje4 #cc ,mack5zie1 ,a41 ,native ,au/ralian ,langs41 ,j\rn4 ,an?r4 ,in/41 #ahgd1 p4 #bfc4 #cd ,curr1 ,! ,au/ralian ,race1 ,vol4 ,,ii4 p4 #acd4 ,! next f\r li/s are f ,,ii4 p4 #d1 ,i4 p4 #cbb1 ,i4 p4 #cdf1 & ,i4 p4 #cih1 respectively4 #ce ,curr1 op4 cit41 ,vol4 ,,iii4 p4 #ej4 #cf ,op4 cit41 ,vol4 ,,iii4 p4 #bcf4 #cg ,mll]1 ,spra*wiss5s*aft4 ,,ii4 i4 p4 #bc4 #ch ,op4 cit41 ,,ii4 i4 p4 #ca4 #ci ,bonwick1 op4 cit41 p4 #adc4 #dj ,curr1 op4 cit41 ,vol4 ,i4 p4 #ca4 #da ,des*amps1 ,l',an?ropologie1 #ahia1 p4 #cah4 #db ,man1 ,e4,h4 ,aborig9al ,inhabitants ( ! ,&aman ,isl&s1 p4 #cb4 #dc ,mll]1 ,spra*wiss5s*aft1 ,i4 ii4 p4 #bi4 #dd ,oldfield1 ,a41 ,tr4 ,e?4 ,soc4 ,vol4 ,,iii4 p4 #bia4 #de ,bancr(t1 ,h4,h41 ,native ,races1 ,vol4 ,i4 p4 #efd4 #df ,notes on ,c\nt+1 etc41 among ! ,eskimos ( ,po9t ,b>r[4 ,am4 ,an?rop41 #ahij1 p4 #ch4 #dg ,second ,voyage1 p4 #eef4 #dh ,p]sonal ,n>rative1 ,vol4 ,i4 p4 #caa4 #di ,burton1 ,b4,f41 ,mem4 ,an?r4 ,soc4 ( ,london1 ,vol4 ,i4 p4 #cad4 #ej ,confessions4 ,9 collect$ works1 ,ed9burgh1 #ahij1 ,vol4 ,,iii4 p4 #ccg4 #ea ,ellis1 ,rob]t1 ,on ,num]als z ,signs ( ,primeval ,unity4 ,see also ,p]uvia ,scy?ia1 by ! same au?or4 #eb ,/anley1 ,h4,m41 ,9 ,d>ke/ ,africa1 ,vol4 ,,ii4 p4 #dic4 #ec ,/anley1 ,h4,m41 ,?r\gh ! ,d>k ,cont95t1 ,vol4 ,,ii4 p4 #dhf4 #ed ,haumont1 ,p>isot1 ,adam1 ,grammaire et ,vocabulaire de la ,langue ,ta5sa1 p4 #bj4 #ee ,*amb]la91 ,a4,f41 ,lang4 ( ! ,mississaga ,indians ( ,skugog4 ,vocab4 #ef ,boas1 ,fr41 ,six? ,report on ! ,indians ( ! ,nor?we/1 p4 #aje4 #eg ,beaureg>d1 ,o41 ,bullet9 de la ,soc4 d',an?r4 de ,p>is1 #ahhf1 p4 #ebf4 #eh ,ray1 ,s4,h41 ,j\rn4 ,an?r4 ,in/41 #ahia1 p4 #h4 #ei ,op4 cit41 p4 #ab4 #fj ,mll]1 ,spra*wiss5s*aft1 ,,iv4 i4 p4 #acf4 #fa ,br9ton1 ,! ,maya ,*ronicles1 p4 #ej4 #fb ,trumbull1 ,on ,num]als 9 ,am4 ,ind4 ,lang41 p4 #ce4 #fc ,boas1 ,fr4 ,?is in=mation 0 receiv$ directly f ,dr4 ,boas4 ,x has nev] be=e be5 publi%$4 #fd ,bancr(t1 ,h4,h41 ,native ,races1 ,vol4 ,,ii4 p4 #gec4 ,see also p4 #aii1 infra4 #fe ,mann1 ,a41 ,notes on ! ,num]al ,sy/4 ( ! ,yoruba ,nation1 ,j\rn4 ,an?4 ,in/41 #ahhf1 p4 #ei1 et seq4 #ff ,mll]1 ,spra*wiss5s*aft1 ,,iv4 i4 p4 #bjb4 #fg ,trumbull1 ,j4,h41 ,on ,num]als 9 ,am4 ,ind4 ,langs41 p4 #aa4 #fh ,cu%+1 ,f4,h41 ,manual ,concepts1 ,am4 ,an?r41 #ahib1 p4 #bhi4 #fi ,grimm1 ,ges*i*te d] deuts*5 ,spra*e1 ,vol4 ,i4 p4 #bci4 #gj ,murdo*1 ,j41 ,am]ican ,an?ropologi/1 #ahij1 p4 #ci4 #ga ,kle9s*midt1 ,s41 ,grammatik d] ,grnl&is*5 ,spra*e1 p4 #cg4 #gb ,br9ton1 ,! ,arawak ,lang4 ( ,guiana1 p4 #d4 #gc ,petitot1 ,e41 ,dictionnaire de la langue ,dn-,d9djie1 p4 lv4 #gd ,gilij1 ,f4,s41 ,saggio di ,/oria ,am41 ,vol4 ,,ii4 p4 #ccc4 #ge ,mll]1 ,spra*wiss5s*aft1 ,,ii4 i4 p4 #chi4 #gf ,op4 cit41 p4 #cie4 #gg ,mll]1 ,spra*wiss5s*aft1 ,,ii4 i4 p4 #dch4 #gh ,peacock1 ,ari?metic1 9 ,encyc4 ,metropolitana1 #a1 p4 #dhj4 #gi ,br9ton1 ,d4,g41 ,! ,betoya ,dialects1 ,proc4 ,am4 ,philos4 ,soc41 #ahib1 p4 #bgc4 #hj ,ridley1 ,w41 ,report on ,au/ralian ,languages & ,traditions4 ,j\rn4 ,an?4 ,in/41 #ahgc1 p4 #bfb4 #ha ,gats*et1 ,gram4 ,klama? ,lang4 ,u4,s4 ,geog4 & ,geol4 ,survey1 ,vol4 ,,ii4 "p #a1 pp4 #ebd & #ecf4 #hb ,lett] ( ,nov4 #ag1 #ahic4 #hc ,mll]1 ,spra*wiss5s*aft1 ,,ii4 i4 p4 #dci4 #hd ,hale1 ,indians ( ,no4 ,we/4 ,am41 ,tr4 ,am4 ,e?4 ,soc41 ,vol4 ,,ii4 p4 #hb4 #he ,br9ton1 ,d4,g41 ,/udies 9 ,s4 ,am4 ,native ,languages1 p4 #be4 #hf ,tr4 ,am4 ,philological ,association1 #ahgd1 p4 #da4 #hg ,tylor1 ,primitive ,culture1 ,vol4 ,i4 p4 #bea4 #hh ,mll]1 ,spra*wiss5s*aft1 ,,iv4 i4 p4 #bg4 #hi ,see infra1 ,*apt] ,,vii4 #ij ,ellis1 ,a4,b41 ,ewe ,speak+ ,peoples1 etc41 p4 #bec4 #ia ,tylor1 ,primitive ,culture1 ,vol4 ,i4 p4 #bef4 #ib ,/anley1 ,9 ,d>ke/ ,africa1 ,vol4 ,,ii4 p4 #dic4 #ic ,*amb]la91 ,a4,f41 ,proc4 ,brit4 ,ass4 ,adv4 ( ,sci41 #ahib1 p4 #eii4 #id ,boas1 ,fr41 ,six? ,report on ,nor?we/]n ,tribes ( ,canada1 ,proc4 ,brit4 ,ass4 ,adv4 ,sci41 #ahij1 p4 #feg4 #ie ,hale1 ,h41 ,indians ( ,nor?we/]n ,am41 ,tr4 ,am4 ,e?4 ,soc41 ,vol4 ,,ii4 p4 #hh4 #if ,op4 cit41 p4 #ie4 #ig ,mll]1 ,spra*wiss5s*aft1 ,,ii4 ii4 p4 #adg4 #ih ,s*oolcraft1 ,ar*ives ( ,aborig9al ,k1 ,vol4 ,,iv4 p4 #dbi4 #ii ,du ,*aillu1 ,p4,b41 ,tr4 ,e?4 ,soc41 ,london1 ,vol4 ,i4 p4 #cae4 #ajj ,la?am1 ,r4,g41 ,essays1 *iefly ,philological & ,e?nographical1 p4 #bdg4 ,! above are s unlike any?+ else 9 ! _w1 t !y are n to be accept$ )\t c>eful v]ification4 #aja ,pott1 ,zhlme?ode1 p4 #de4 #ajb ,gats*et1 ,a4,s41 ,! ,k>ankawa ,indians1 ! ,coa/ ,p ( ,texas4 ,! mean+s ( #f1 #g1 #h1 & #i are conjectural ) me4 #ajc ,/anley1 ,h4,m41 ,9 ,d>ke/ ,africa1 ,vol4 ,,ii4 p4 #dib4 #ajd ,mll]1 ,spra*wiss5s*aft1 ,,ii4 i4 p4 #cag4 #aje ,toy1 ,c4,h41 ,trans4 ,am4 ,phil4 ,assn41 #ahgh1 p4 #bi4 #ajf ,burton1 ,r4,f41 ,mem4 ,an?rop4 ,soc4 ( ,london4 #a1 p4 #cad4 ,9 ! illu/ration :i* foll[s1 ,burton gives #fhbj1 in/ead ( #dhbj2 :i* is obvi\sly a mispr9t4 #ajg ,dobrizh(f]1 ,hi/ory ( ! ,abipones1 ,vol4 ,,ii4 p4 #afi4 #ajh ,sayce1 ,a4,h41 ,comp>ative ,philology1 p4 #bed4 #aji ,tr4 ,e?4 ,society ( ,london 1 ,vol4 ,,iii4 p4 #bia4 #aaj ,ray1 ,s4,h41 ,j\rn4 ,an?r4 ,in/41 #ahhi1 p4 #eja4 #aaa ,/anley1 ,9 ,d>ke/ ,africa1 ,vol4 ,,ii4 p4 #dib4 #aab ,op4 cit41 loc4 cit4 #aac ,tylor1 ,primitive ,culture1 ,vol4 ,i4 p4 #bdi4 #aad ,mll]1 ,spra*wiss5s*aft1 ,,iv4 i4 p4 #cf4 #aae ,m>tius1 ,glos4 ,l+4 ,brasil41 p4 #bga4 #aaf ,tylor1 ,primitive ,culture1 ,vol4 ,i4 p4 #bdh4 #aag ,ro?1 ,h4 ,l+1 ,aborig9es ( ,tasmania1 p4 #adf4 #aah ,lull1 ,e4,p41 ,tr4 ,am4 ,phil1 ,soc41 #ahgc1 p4 #ajh4 #aai ,ray1 ,s4,h4 ,sket* ( ,api ,gram41 ,j\rn4 ,an?r4 ,in/41 #ahhh1 p4 #cjj4 #abj ,kle9s*midt1 ,s41 ,grammatik d] ,grnl&is*5 ,spr41 p4 #ci4 #aba ,mll]1 ,spra*wiss5s*aft1 ,i4 ii4 p4 #ahd4 #abb ,op4 cit41 ,i4 ii4 p4 #ah1 & ,,ii4 i4 p4 #bbb4 #abc ,squi]1 ,g4,e41 ,nic>agua1 ,vol4 ,,ii4 p4 #cbf4 #abd ,s*oolcraft1 ,h4,r41 ,ar*ives ( ,aborig9al ,k1 ,vol4 ,,ii4 p4 #bjh4 #abe ,tylor1 ,primitive ,culture1 ,vol4 ,i4 p4 #bfd4 #abf ,go$el1 ,e?nol4 des ,s\ss\s1 ,bull4 de la ,soc4 d',an?r4 de ,p>is1 #ahib1 p4 #ahe4 #abg ,ellis1 ,w41 ,hi/ory ( ,madagasc>1 ,vol4 ,i4 p4 #ejg4 #abh ,beaureg>d1 ,o41 ,bull4 de la ,soc4 d',an?r4 de ,p>is1 #ahhf1 p4 #bcf4 #abi ,s*oolcraft1 ,h4,r41 ,ar*ives ( ,aborig9al ,k1 ,vol4 ,,ii4 p4 #bjg4 #acj ,tylor1 ,primitive ,culture1 ,vol4 ,i4 p4 #bdi4 #aca ,op4 cit4 ,vol4 ,i4 p4 #bej4 #acb ,peacock1 ,encyc4 ,metropolitana1 #a1 p4 #dgh4 #acc ,op4 cit41 loc4 cit4 #acd ,s*oolcraft1 ,h4,r41 ,ar*ives ( ,aborig9al ,k1 ,vol4 ,,ii4 p4 #bac4 #ace ,op4 cit41 p4 #baf4 #acf ,op4 cit41 p4 #bjf4 #acg ,m>9]1 ,gram4 ,tonga ,lang41 la/ "p ( book4 ,n pag$4 #ach ,morice1 ,a4,g41 ,! ,dn ,langs1 ,trans4 ,c4 ,in/41 ,m>* #ahij1 p4 #ahf4 #aci ,boas1 ,fr41 ,fif? ,report on ! ,nor?we/]n ,tribes ( ,canada1 ,proc4 ,brit4 ,ass4 ,adv4 ( ,sci5ce1 #ahhi1 p4 #hha4 #adj ,d4 ,six? ,rep41 #ahij1 pp4 #fhd1 #fhf1 #fhg4 #ada ,op4 cit41 p4 #feh4 #adb ,bancr(t1 ,h4,h41 ,native ,races1 ,vol4 ,,ii4 p4 #dii4 #adc ,tr4 ,e?nological ,soc4 ( ,london1 ,vol4 ,,iv4 p4 #ib4 #add ,any ,hebrew lexicon4 #ade ,s*rd]1 ,p41 ,die ,phnizis*e ,spra*e1 p4 #ahd et seq4 #adf ,mll]1 ,spra*wiss5s*aft1 ,,ii4 ii4 p4 #adg4 #adg ,on ,num]als 9 ,am4 ,indian ,languages4 #adh ,ellis1 ,a4,b41 ,ewe ,speak+ ,peoples1 etc41 p4 #bec4 ,! mean+s "h giv5 are p>tly conjectural4 #adi ,pott1 ,zhlme?ode1 p4 #bi4 #aej ,s*oolcraft1 op4 cit41 ,vol4 ,,iv4 p4 #dbi4 #aea ,trumbull1 op4 cit4 #aeb ,*amb]la91 ,a4,f41 ,lang1 ( ! ,mississaga ,indians1 ,vocab4 #aec ,crawfurd1 ,hi/4 ,ind4 ,ar*ipelago1 #a1 p4 #beh4 #aed ,hale1 ,h41 ,e?4 & ,philol41 ,vol4 ,,vii42 ,wilkes1 ,expl4 ,exp$ition1 ,phil4 #ahdf1 p4 #agb4 #aee ,crawfurd1 op4 cit41 #a1 p4 #beh4 #aef ,op4 cit41 loc4 cit4 #aeg ,bancr(t1 ,h4,h41 ,native ,races1 ,vol4 ,,ii4 p4 #dih4 #aeh ,vignoli1 ,t41 ,my? & ,sci5ce1 p4 #bjc4 #aei ,codr+ton1 ,r4,h41 ,! ,melanesian ,languages1 p4 #bdi4 #afj ,op4 cit41 loc4 cit4 #afa ,codr+ton1 ,r4,h41 ,! ,melanesian ,languages1 p4 #bdi4 #afb ,wick]%am1 ,j41 ,japanese ,art on ,puget ,s\nd1 ,am4 ,antiq41 #ahid1 p4 #gi4 #afc ,codr+ton1 ,r4,h41 op4 cit41 p4 #bej4 #afd ,tylor1 ,primitive ,culture1 ,vol4 ,i4 p4 #beb4 #afe ,comp>e a simil> table by ,*ase1 ,proc4 ,am]4 ,philos4 ,soc41 #ahfe1 p4 #bc4 #aff ,leibnitzii ,op]a1 ,,iii4 p4 #cdf4 #afg ,prun]-,bey1 ,bullet9 de la ,soc4 d',an?r4 de ,p>is1 #ahfj1 p4 #dhf4 #afh ,curr1 ,e4,m41 ,! ,au/ralian ,race1 ,vol4 ,i4 p4 #cb4 #afi ,haddon1 ,a4,c41 ,we/]n ,tribes ( ! ,torres ,/raits1 ,j\rn4 ,an?r4 ,in/41 #ahhi1 p4 #cjc4 #agj ,tapl91 ,rev4 ,g41 ,notes on a ,table ( ,au/ralian ,languages1 ,j\rn4 ,an?r4 ,in/41 #ahgb1 p4 #hh4 ,! fir/ n9e scales are tak5 f ?is s\rce4 #aga ,la?am1 ,r4,g41 ,comp>ative ,philology1 p4 #ceb4 #agb ,x w be obs]v$ t ?is li/ diff]s slightly f t giv5 9 ,*apt] ,,ii4 #agc ,curr1 ,e4,m41 ,! ,au/ralian ,race1 ,vol4 ,,iii4 p4 #fhd4 #agd ,bonwick1 ,tasmania1 p4 #adc4 #age ,lang1 ,j4,d41 ,que5sl&1 p4 #dce4 #agf ,bonwick1 ,tasmania1 p4 #adc4 #agg ,mll]1 ,spra*wiss5s*aft1 ,,ii4 i4 p4 #eh4 #agh ,op4 cit41 ,,ii4 i4 p4 #gj4 #agi ,op4 cit41 ,,ii4 i4 p4 #bc4 #ahj ,b>l[1 ,h41 ,aborig9al ,dialects ( ,que5sl&1 ,j\rn4 ,an?4 ,in/41 #ahgc1 p4 #aga4 #aha ,curr1 ,e4,m41 ,! ,au/ralian ,race1 ,vol4 ,,ii4 p4 #bf4 #ahb ,op4 cit41 ,vol4 ,,ii4 p4 #bjh4 #ahc ,op4 cit41 ,vol4 ,,ii4 p4 #bgh4 #ahd ,op4 cit41 ,vol4 ,,ii4 p4 #bhh4 #ahe ,op4 cit41 ,vol4 ,i4 p4 #beh4 #ahf ,op4 cit41 ,vol4 ,i4 p4 #caf4 #ahg ,op4 cit41 ,vol4 ,,iii4 p4 #cb4 ,! next t5 li/s are tak5 f ! same volume1 pp4 #bhb1 #bhh1 #cdj1 #cgf1 #dcb1 #ejf1 #ecj1 #eeh1 #efj1 #ehh1 respectively4 #ahh ,br9ton1 ,! ,am]ican ,race1 p4 #cea4 #ahi ,m>tius1 ,gloss>ia ,l+4 ,brazil41 p4 #cjg4 #aij ,op4 cit41 p4 #adh4 #aia ,mll]1 ,spra*wiss5s*aft1 ,,ii4 i4 p4 #dch4 #aib ,peacock1 ,ari?metic1 ,encyc4 ,metropolitana1 #a1 p4 #dhj4 #aic ,br9ton1 ,/udies 9 ,s4 ,am4 ,native ,langs41 p4 #fg4 #aid ,op4 cit41 loc4 cit4 #aie ,br9ton1 ,/udies 9 ,s4 ,am4 ,native ,langs41 p4 #fg4 ,! mean+s ( ! num]als are f ,peacock1 ,encyc4 ,metropolitana1 #a1 p4 #dhj4 #aif ,mason1 ,j\rn4 ,z4 ,soc4 ( ,b5gal1 ,vol4 ,,xxvi4 p4 #adf4 #aig ,curr1 ,e4,m41 ,! ,au/ralian ,race1 ,vol4 ,,iii4 p4 #ajh4 #aih ,bancr(t1 ,h4,h41 ,native ,races1 ,vol4 ,i4 p4 #bgd4 #aii ,cl>ke1 ,hyde1 ,j\rn4 ,an?r4 ,in/41 #ahgb1 p4 clvii4 ,9 ! article f :i* ?is is quot$1 no evid5ce is giv5 to sub/antiate ! ass]tion made4 ,x is to be receiv$ ) great caution4 #bjj ,hale1 ,h41 ,wilkes ,explor+ ,exp$ition1 ,vol4 ,,vii4 p4 #agb4 #bja ,op4 cit41 p4 #bdh4 #bjb ,hale1 ,e?nography & ,philology1 p4 #bdg4 #bjc ,loc4 cit4 #bjd ,ellis1 ,polynesian ,rese>*es1 ,vol4 ,,iv4 p4 #cda4 #bje ,gill1 ,w4,w41 ,my?s & ,songs ( ! ,s\? ,pacific1 p4 #cbe4 #bjf ,peacock1 ,ari?metic1 ,encyc4 ,metropolitana1 #a1 p4 #dgi4 #bjg ,peacock1 ,encyc4 ,metropolitana1 #a1 p4 #dhj4 #bjh ,spra*v]s*i$5heit1 p4 #cj4 #bji ,crawfurd1 ,hi/ory ( ! ,indian ,ar*ipelago1 ,vol4 ,i4 p4 #bef4 #baj ,pott1 ,zhlme?ode1 p4 #ci4 #baa ,op4 cit41 p4 #da4 #bab ,mll]1 ,spra*wiss5s*aft1 ,,ii4 i4 p4 #cag4 ,see also ,*ap4 ,,iii41 supra4 #bac ,long1 ,s4,h41 ,exp$ition1 ,vol4 ,,ii4 p4 lxxviii4 #bad ,m>tius1 ,gloss>ia ,l+4 ,brasil41 p4 #bdf4 #bae ,hale1 ,e?nography & ,philology1 p4 #dcd4 #baf ,mll]1 ,spra*wiss5s*aft1 ,,ii4 ii4 p4 #hb4 #bag ,! in=mation ^u :i* ! above /atem5ts are bas$ 0 obta9$ f ,mr4 ,w4,l4 ,williams1 ( ,gisborne1 ,n4,z4 #bah ,primitive ,culture1 ,vol4 ,i4 p4 #bfh4 #bai ,ralph1 ,julian1 ,h>p]'s ,mon?ly1 ,vol4 #hf1 p4 #ahd4 #bbj ,lapp5b]g1 ,j4,m41 ,hi/ory ( ,eng4 "u ! ,anglo-,saxon ,k+s1 ,vol4 ,i4 p4 #hb4 #bba ,! compilation ( ?is table 0 sugge/$ by a comp>ison f\nd 9 ! ,bullet9 ,soc4 ,an?4 de ,p>is1 #ahhf1 p4 #ij4 #bbb ,hale1 ,e?nography & ,philology1 p4 #abf4 #bbc ,mll]1 ,spra*wiss5s*aft1 ,,ii4 ii4 p4 #ahc4 #bbd ,ba*(51 ,j4,j41 ,antiqu>is*e ,briefe1 ,vol4 ,i4 pp4 #aja-aae1 & ,vol4 ,,ii4 pp4 #a-ij4 #bbe ,an ext5d$ table ( ?is k9d may be f\nd 9 ! la/ "p ( ,ny/rom's ,me*anics4 #bbf ,s*ub]t1 ,h41 quot+ ,rob]t ,flegel1 9 ,neumay]'s ,anleitung zu ,wiss5s*aftli*5 ,beoba*tung auf ,reis51 ,vol4 ,,ii4 p4 #bij4 #bbg ,^! num]als1 & ^? 9 all ! sets imm$iately foll[+1 except ^? = :i* ! au?ority is giv51 are to be f\nd 9 ,*apt] ,,iii4 #bbh ,codr+ton1 ,! ,melanesian ,languages1 p4 #bbb4 #bbi ,mll]1 ,spra*wiss5s*aft1 ,,ii4 ii4 p4 #hc4 #bcj ,op4 cit41 ,i4 ii4 p4 #ee4 ,! next two are ! same1 p4 #hc & p4 #baj4 ,! mean+ giv5 = ! ,b>i puk is :olly conjectural4 #bca ,gallat91 ,semi-civiliz$ ,nations1 ,tr4 ,am4 ,e?4 ,soc41 ,vol4 ,i4 p4 #aad4 #bcb ,mll]1 ,spra*wiss5s*aft1 ,,ii4 ii4 p4 #hj4 ,erromango1 ! same4 #bcc ,boas1 ,fr41 ,proc4 ,brit4 ,ass'n4 ,adv4 ,sci5ce1 #ahhi1 p4 #heg4 #bcd ,hankel1 ,h41 ,ges*i*te d] ,ma!matik1 p4 #bj4 #bce ,murdo*1 ,j41 ,eskimos ( ,po9t ,b>r[1 ,am4 ,an?r41 #ahij1 p4 #dj4 #bcf ,m>tius1 ,glos4 ,l+4 ,brasil41 p4 #cfj4 #bcg ,du ,graty1 ,a4,m41 ,la ,rpublique du ,p>aguay1 p4 #bag4 #bch ,codr+ton1 ,! ,melanesian ,languages1 p4 #bba4 #bci ,mll]1 ,spra*wiss5s*aft1 ,,ii4 i4 p4 #cfc4 #bdj ,spurrell1 ,w41 ,wel% ,gramm>1 p4 #ei4 #bda ,olmos1 ,&r de1 ,grammaire ,nahuatl ou ,mexica9e1 p4 #aia4 #bdb ,moncelon1 ,bull4 ,soc4 d',an?r4 de ,p>is1 #ahhe1 p4 #ced4 ,?is is a purely digital scale1 b un=tunately ,m4 ,moncelon does n give ! mean+s ( any ( ! num]als except ! la/4 #bdc ,ellis1 ,p]uvia ,scy?ia1 p4 #cg4 ,"p ( ^! num]als are f ,m>tius1 ,glos4 ,brasil41 p4 #baj4 #bdd ,codr+ton1 ,! ,melanesian ,languages1 p4 #bcf4 #bde ,s*we9fur?1 ,g41 ,l+ui/is*e ,ergebnisse e9] ,reise na* ,c5tralafrika1 p4 #be4 #bdf ,p>k1 ,m41 ,travels 9 ! ,int]ior ,di/ricts ( ,africa1 p4 #h4 #bdg ,pott1 ,zhlme?ode1 p4 #cg4 #bdh ,op4 cit41 p4 #ci4 #bdi ,mll]1 ,spra*wiss5s*aft1 ,,iv4 i4 p4 #aja4 ,! ,kru scale1 k9dr$ ) ! ,basa1 is f ! same page4 #bej ,p>k1 9 ,p9k]ton's ,voyages & ,travels1 ,vol4 ,,xvi4 p4 #ijb4 #bea ,p>k1 ,travels1 ,vol4 ,i4 p4 #af4 #beb ,s*we9fur?1 ,g41 ,l+ui/is*e ,ergebnisse e9] ,reise na* ,c5tralafrika1 p4 #gh4 #bec ,p>k1 ,travels1 ,vol4 ,i4 p4 #eh4 #bed ,go$el1 ,e?nol4 des ,s\ss\s1 ,bull4 ,soc4 ,an?4 ,p>is1 #ahib1 p4 #ahe4 #bee ,mll]1 ,spra*wiss5s*aft1 ,i4 ii4 p4 #aad4 ,! ,temne scale is f ! same page4 ,^! two languages are closely relat$4 #bef ,op4 cit41 ,i4 ii4 p4 #aee4 #beg ,op4 cit41 ,i4 ii4 p4 #ee4 #beh ,long1 ,c4,c41 ,c5tral ,africa1 p4 #ccj4 #bei ,mll]1 ,spra*wiss5s*aft1 ,,iv4 i4 p4 #aje4 #bfj ,pott1 ,zhlme?ode1 p4 #da4 #bfa ,mll]1 op4 cit41 ,i4 ii4 p4 #adj4 #bfb ,mll]1 ,spra*wiss5s*aft1 ,,iv4 i4 p4 #ha4 #bfc ,pott1 ,zhlme?ode1 p4 #da4 #bfd ,mll]1 op4 cit41 ,i4 ii41 p4 #baj4 #bfe ,pott1 ,zhlme?ode1 p4 #db4 #bff ,s*we9fur?1 ,l+ui/is*e ,ergebnisse1 p4 #ei4 #bfg ,mll]1 ,spra*wiss5s*aft1 ,i4 ii4 p4 #bfa4 ,! t5 is n giv54 #bfh ,/anley1 ,?r\gh ! ,d>k ,cont95t1 ,vol4 ,,ii4 p4 #dij4 ,ki-,nyassa1 ! same page4 #bfi ,mll]1 op4 cit41 ,i4 ii4 p4 #bfa4 #bgj ,du ,*aillu1 ,adv5tures 9 ,equatorial ,africa1 p4 #ecd4 #bga ,mll]1 ,spra*wiss5s*aft1 ,,iii4 i4 p4 #fe4 #bgb ,du ,*aillu1 ,adv5tures 9 ,equatorial ,africa1 p4 #ecc4 #bgc ,mll]1 op4 cit41 ,,iii4 ii4 p4 #gg4 #bgd ,balbi1 ,a41 ,l',atlas ,e?41 ,vol4 ,i4 p4 #bbf4 ,9 ,balbi's text #g & #h are anspos$4 ,t>u = #e is probably a mispr9t = tana4 #bge ,du ,*aillu1 op4 cit41 p4 #ecc4 ,! next scale is op4 cit41 p4 #ecd4 #bgf ,beaureg>d1 ,o41 ,bull4 ,soc4 ,an?4 de ,p>is1 #ahhf1 p4 #ebf4 #bgg ,pott1 ,zhlme?ode1 p4 #df4 #bgh ,op4 cit41 p4 #dh4 #bgi ,turn]1 ,n9ete5 ,ye>s 9 ,polynesia1 p4 #ecf4 #bhj ,ersk9e1 ,j4,e41 ,isl&s ( ! ,we/]n ,pacific1 p4 #cda4 #bha ,op4 cit41 p4 #djj4 #bhb ,codr+ton1 ,melanesian ,languages1 pp4 #bce1 #bcf4 #bhc ,peacock1 ,encyc4 ,met41 ,vol4 #a4 p4 #che4 ,peacock does n specify ! dialect4 #bhd ,ersk9e1 ,isl&s ( ! ,we/]n ,pacific1 p4 #cfj4 #bhe ,turn]1 ,g41 ,samoa a ,hundr$ ,ye>s ,ago1 p4 #cgc4 ,! next ?ree scales are f ! same page ( ?is "w4 #bhf ,codr+ton1 ,melanesian ,languages1 p4 #bce4 ,! next f\r scales are f ! same page4 ,p]haps ! mean+s ( ! words = #f to #i are m prop]ly m #a1 m #b1 etc4 ,codr+ton m]ely indicates _! significations 9 a g5]al way4 #bhg ,hale1 ,e?nography & ,philology1 p4 #dbi4 ,! mean+s ( #f to #i 9 ?is & ! prec$+ are my conjectures4 #bhh ,mll]1 ,spra*wiss5s*aft1 ,,iv4 i4 p4 #abd4 #bhi ,aymoni]1 ,e41 ,dictionnaire ,francaise-,cambodgi54 #bij ,mll]1 ,op4 cit41 ,,ii4 i4 p4 #aci4 #bia ,mll]1 ,spra*wiss5s*aft1 ,,ii4 i4 p4 #abc4 #bib ,wells1 ,e4,r41 ,jr41 & ,john ,w4 ,kelly1 ,bureau ( ,ed41 ,circ4 ( ,inf41 ,no4 #b1 #ahij4 #bic ,pott1 ,zhlme?ode1 p4 #eg4 #bid ,mll]1 ,op4 cit41 ,,ii4 i4 p4 #afa4 #bie ,petitot1 ,vocabulaire ,franaise ,esquimau1 p4 lv4 #bif ,mll]1 ,spra*wiss5s*aft1 ,,ii4 i4 p4 #bec4 #big ,mll]1 ,op4 cit41 ,,ii4 ,i4 p4 #agi1 & ,kle9s*midt1 ,grnl&is*es ,grammatik4 #bih ,adam1 ,l41 ,congres ,int4 des ,am41 #ahgg1 p4 #bdd 7see p4 #afb infra74 #bii ,gallat91 ,synopsis ( ,indian ,tribes1 ,trans4 ,am4 ,antq4 ,soc41 #ahcf1 p4 #ceh4 ,! next f\rte5 li/s are1 ) ! exception ( ! ,micmac1 f ! same collection4 ,! mean+s are l>gely f ,trumbull1 op4 cit4 #cjj ,s*oolcraft1 ,ar*ives ( ,aborig9al ,k1 ,vol4 ,,ii4 p4 #baa4 #cja ,s*oolcraft1 ,ar*ives ( ,aborig9al ,k1 ,vol4 ,v4 p4 #ehg4 #cjb ,9 ! ,dakota dialects #aj is express$1 z "h1 by a ^w signify+ t ! f+]s1 :i* h be5 b5t d[n 9 c\nt+1 are n[ /raight5$ out4 #cjc ,boas1 ,fif? ,report ,b4,a4,a4,s41 #ahhi4 ,repr9t1 p4 #fa4 #cjd ,boas1 ,six? ,report ,b4,a4,a4,s41 #ahij4 ,repr9t1 p4 #aag4 ,dr4 ,boas does n give ! mean+s assign$ to #g & #h1 b m]ely /ates t !y are d]iv$ f #b & #c4 #cje ,op4 cit41 p4 #aag4 ,! d]ivations = #f & #g are obvi\s1 b ! mean+s are conjectural4 #cjf ,boas1 ,six? ,report ,b4,a4,a4,s41 #ahhi4 ,repr9t1 pp4 #aeh1 #afj4 ,! mean+s assign$ to ! ,tsim%ian #h & to ,bilqula #f to #h are conjectural4 #cjg ,hale1 ,e?nography & ,philology1 p4 #fai4 #cjh ,op4 cit41 loc4 cit4 #cji ,hale1 ,e?nography & ,philology1 p4 #fai4 #caj ,mll]1 ,spra*wiss5s*aft1 ,,ii4 i4 p4 #dcf4 #caa ,op4 cit41 ,,iv4 i4 p4 #afg4 #cab ,op4 cit41 ,,ii4 i4 p4 #bhb4 #cac ,op4 cit41 ,,ii4 i4 p4 #bhg4 ,! mean+s giv5 = ! words = #g1 #h1 #i are conjectures ( my own4 #cad ,mll]1 ,spra*wiss5s*aft1 ,,ii4 i4 p4 #big4 #cae ,pott1 ,zhlme?ode1 p4 #ij4 #caf ,mll]1 op4 cit41 ,,ii4 i4 p4 #cgi4 #cag ,gallat91 ,semi-,civiliz$ ,nations ( ,mexico & ,c5tral ,am]ica1 ,tr4 ,am4 ,e?n4 ,soc41 ,vol4 ,i4 p4 #aad4 #cah ,adam1 ,luci51 ,congres ,int]nationale des ,am]icani/es1 #ahgg1 ,vol4 ,,ii4 p4 #bdd4 #cai ,mll]1 ,spra*wiss5s*aft1 ,,ii4 i4 p4 #cie4 ,i c only guess at ! mean+s ( #f to #i4 ,!y are obvi\sly circumlocutions = #e-a1 #e-b1 etc4 #cbj ,op4 cit41 p4 #dch4 ,mll] has transpos$ ^! two scales4 ,see ,br9ton's ,am4 ,race1 p4 #ceh4 #cba ,m>coy1 ,p41 ,t\r du ,monde1 #ahff1 #bme sem4 p4 #adh4 #cbb ,op4 cit41 p4 #acb4 ,! mean+s are my own conjectures4 #cbc ,an elaborate argum5t 9 support ( ?is !ory is to be f\nd 9 ,h]vas' celebrat$ "w1 ,ari?metica di quasi tutte le nazioni conosciute4 #cbd ,see especially ! li/s ( ,hale1 ,gallat91 ,trumbull1 & ,boas1 to :i* ref]5ces h be5 giv5 above4 #cbe ,?iel1 ,b4,a41 ,vocab4 d] ,indiani] 9 ,co/a ,rica1 ,ar*iv fr ,an?41 xvi4 p4 #fbj4 #cbf ,^! ?ree examples are f ,a4,r4 ,wallace's ,n>rative ( ,travels on ! ,amazon & ,rio ,negro1 vocab4 ,simil> illu/rations may be f\nd 9 ,m>tius' ,glos4 ,brasil4 #cbg ,m>tius1 ,glos4 ,brasil41 p4 #agf4 #cbh ,adam1 ,l41 ,congres ,int]national des ,am]icani/es1 #ahgg1 ,vol4 ,,ii4 p4 #bdd4 ,giv5 also supra1 p4 #ec4 #cbi ,o',donovan1 ,iri% ,gramm>1 p4 #abc4 #ccj ,arm/rong1 ,r4,a41 ,gaelic ,dict41 p4 xxi4 #cca ,spurrell1 ,wel% ,diction>y4 #ccb ,kelly1 ,triglot ,dict41 pub4 by ! ,manx ,society4 #ccc ,guillome1 ,j41 ,grammaire ,franaise-,bretonne1 p4 #bg4 #ccd ,grb]1 ,g41 ,grundriss d] ,romanis*5 ,philologie1 ,bd4 ,i4 p4 #cji4 #cce ,pott1 ,zhlme?ode1 p4 #hh4 #ccf ,van ,eys1 ,basque ,gramm>1 p4 #bg4 #ccg ,pott1 ,zhlme?ode1 p4 #aja4 #cch ,op4 cit41 p4 #gh4 #cci ,mll]1 ,spra*wiss5s*aft1 ,i4 ii4 p4 #abd4 #cdj ,op4 cit41 p4 #aee4 #cda ,op4 cit41 p4 #adj4 #cdb ,op4 cit41 loc4 cit4 #cdc ,s*we9fur?1 ,reise na* ,c5tralafrika1 p4 #be4 #cdd ,mll]1 ,spra*wiss5s*aft1 ,,iv4 i4 p4 #hc4 #cde ,op4 cit41 ,,iv4 i4 p4 #ha4 #cdf ,op4 cit41 ,i4 ii4 p4 #aff4 #cdg ,long1 ,c4,c41 ,c5tral ,africa1 p4 #ccj4 #cdh ,peacock1 ,encyc4 ,met41 ,vol4 ,i4 p4 #chh4 #cdi ,mll]1 ,spra*wiss5s*aft1 ,,iii4 ii4 p4 #fd4 ,! next sev5 scales are f op4 cit41 pp4 #hj1 #acg1 #aee1 #ahb1 #bac4 #cej ,pott1 ,zhlme?ode1 p4 #hc4 #cea ,op4 cit41 p4 #hc1--;,ak>i1 p4 #hd2 ,circassia1 p4 #he4 #ceb ,mll]1 ,spra*wiss5s*aft1 ,,ii4 i4 p4 #adj4 #cec ,pott1 ,zhlme?ode1 p4 #hg4 #ced ,mll]1 ,spra*wiss5s*aft1 ,,ii4 ii4 p4 #cdf4 #cee ,op4 cit41 ,,iii4 i4 p4 #acj4 #cef ,man1 ,e4,h41 ,brief ,acc\nt ( ! ,nicob> ,isl&s1 ,j\rn4 ,an?r4 ,in/41 #ahhe1 p4 #dce4 #ceg ,wells1 ,e4,r41 ,jr41 & ,kelly1 ,j4,w41 ,eng4 ,esk4 & ,esk4 ,eng4 ,vocab41 ,bureau ( ,education ,circul> ( ,in=mation1 ,no4 #b1 #ahij1 p4 #fe4 #ceh ,petitot1 ,e41 ,vocabulaire ,franaise ,esquimau1 p4 lv4 #cei ,boas1 ,fr41 ,proc4 ,brit4 ,ass4 ,adv4 ,sci41 #ahhi1 p4 #heg4 #cfj ,boas1 ,six? ,report on ! ,nor?we/]n ,tribes ( ,canada1 p4 #aag4 #cfa ,boas1 ,fr41 ,fif? ,report on ! ,nor?we/]n ,tribes ( ,canada1 p4 #he4 #cfb ,gallat91 ,semi-,civiliz$ ,nations1 p4 #aad4 ,ref]5ces = ! next two are ! same4 #cfc ,bancr(t1 ,h4,h41 ,native ,races ( ! ,pacific ,/ates1 ,vol4 ,,ii4 p4 #gfc4 ,! mean+s are f ,br9ton's ,maya ,*ronicles1 p4 #ch et seq4 #cfd ,br9ton1 ,maya ,*ronicles1 p4 #dd4 #cfe ,simon ,rmi1 ,dictionnaire de la langue nahuatl1 p4 xxxii4 #cff ,an error occurs on p4 xxxiv ( ! "w f :i* ^! num]als are tak51 :i* makes ! numb] 9 "q appe> z #bgi1iii1iii in/ead ( #a1bgi1iii1iii4 #cfg ,gallat91 ,semi-,civiliz$ ,nations ( ,mexico & ,c5tral ,am]ica1 ,tr4 ,am4 ,e?n4 ,soc4 ,vol4 ,i4 p4 #aad4 #cfh ,pott1 ,zhlme?ode1 p4 #hi4 ,! ,totonacos 7 ! fir/ race ,cortez enc\nt]$ aft] l&+ 9 ,mexico4 #cfi ,op4 cit41 p4 #ij4 ,! ,coras are ( ! ,mexican /ate ( ,sonora4 #cgj ,gallat91 ,semi-,civiliz$ ,nations1 p4 #aad4 #cga ,humboldt1 ,re*]*es1 ,vol4 ,,ii4 p4 #aab4 #cgb ,squi]1 ,nic>agua1 ,vol4 ,,ii4 p4 #cbf4 #cgc ,gallat91 ,semi-,civiliz$ ,nations1 p4 #eg4