99,transcriber's ,note3 ,the following errors found in the original have been left as is4 ,chapter ,i1 #adth paragraph3 drop double quote before ',it is said'2 ,chapter ,,iv1 #ast paragraph3 'so similar than' read 'so similar that'2 ,chapter ,,iv1 table of ,hebrew numerals 7near footnote #add73 insert comma after 'shemoneh'2 ,chapter ,v1 table of ,tahuatan numerals 7near footnote #bja73 'tahi1' read 'tahi4'2 ,same table3 ' #bj1jjj4 tufa' read '#bjj1jjj4 tufa'2 ,chapter ,,vi1 table of ,bagrimma numerals 7near footnote #bei73 'marta #e #b' read 'marta #e #c'2 ,same table3 'do-so #e #c' read 'do-so #e #d'2 ,chapter ,,vii1 table of ,nahuatl numerals 7near footnote #cfe73 '#ij-aj' read '#hj-aj'2 ,in paragraph following that table3 ' 7#ae #d7 #djj #hjj' read '7#ae #d7 #bj #djj #hjjj 7#ae #d7 #djj #hjjj'2 ,in text of footnote #big3 ',,ii4 ,i4 p4 #agi' read ',,ii4 i4 p4 #agi'2 99 ,,the ,,macmillan ,,company ,,new ,,york ,,boston ,,chicago ,,dallas ,,atlanta ,,san ,,francisco ,,macmillan ,,co41 ,,limited ,,london ,,bombay ,,calcutta ,,melbourne ,,the ,,macmillan ,,company ,,of ,,canada1 ,,limited ,,toronto ,,the ,,number ,,concept ,,its ,,origin ,,and ,,development ,,by ,,levi ,,leonard ,,conant1 ,,ph4,d4 ,,associate ,,professor ,,of ,,mathematics ,,in ,,the ,,worcester ,,polytechnic ,,institute ,new ,york ,,macmillan ,,and ,,co4 ,,and ,,london #aica ,,copyright1 #ahif1 ,,by ,,the ,,macmillan ,,company4 ,,copyright1 #aibd1 ,,by ,,emma ,b4 ,,conant4 ,all rights reserved--no part of this book may be reproduced in any form without permission in writing from the publisher4 ,set up and electrotyped4 ,published ,july1 #ahif4 ,norwood ,press ,j4,s4 ,cushing ,co4--,berwick ,smith ,co4 ,norwood1 ,mass41 ,u4,s4,a4 ,,preface4 ,in the selection of authorities which have been consulted in the preparation of this work1 and to which reference is made in the following pages1 great care has been taken4 ,original sources have been drawn upon in the majority of cases1 and nearly all of these are the most recent attainable4 ,whenever it has not been possible to cite original and recent works1 the author has quoted only such as are most standard and trustworthy4 ,in the choice of orthography of proper names and numeral words1 the forms have1 in almost all cases1 been written as they were found1 with no attempt to reduce them to a systematic ,english basis4 ,in many instances this would have been quite impossible2 and1 even if possible1 it would have been altogether unimportant4 ,hence the forms1 whether ,german1 ,french1 ,italian1 ,spanish1 or ,danish in their transcription1 are left unchanged4 ,diacritical marks are omitted1 however1 since the proper key could hardly be furnished in a work of this kind4 ,with the above exceptions1 this study will1 it is hoped1 be found to be quite complete2 and as the subject here investigated has never before been treated in any thorough and comprehensive manner1 it is hoped that this book may be found helpful4 ,the collections of numeral systems illustrating the use of the binary1 the quinary1 and other number systems1 are1 taken together1 believed to be the most extensive now existing in any language4 ,only the cardinal numerals have been considered4 ,the ordinals present no marked peculiarities which would1 in a work of this kind1 render a separate discussion necessary4 ,accordingly they have1 though with some reluctance1 been omitted entirely4 ,sincere thanks are due to those who have assisted the author in the preparation of his materials4 ,especial acknowledgment should be made to ,horatio ,hale1 ,dr4 ,d4,g4 ,brinton1 ,frank ,hamilton ,cushing1 and ,dr4 ,a4,f4 ,chamberlain4 ,,worcester1 ,,mass41 ,nov4 #ab1 #ahie4 ,,contents4 ,chapter ,i4 ,counting #a ,chapter ,,ii4 ,number ,system ,limits #ba ,chapter ,,iii4 ,origin of ,number ,words #cg ,chapter ,,iv4 ,origin of ,number ,words 7continued7 #gd ,chapter ,v4 ,miscellaneous ,number ,bases #ajj ,chapter ,,vi4 ,the ,quinary ,system #acd ,chapter ,,vii4 ,the ,vigesimal ,system #agf 99 99 99 99 99 ,index #baa ,,the ,,number ,,concept3 ,,its ,,origin ,,and ,,development4 ,,chapter ,i4 ,,counting4 ,among the speculative questions which arise in connection with the study of arithmetic from a historical standpoint1 the origin of number is one that has provoked much lively discussion1 and has led to a great amount of learned research among the primitive and savage languages of the human race4 ,a few simple considerations will1 however1 show that such research must necessarily leave this question entirely unsettled1 and will indicate clearly that it is1 from the very nature of things1 a question to which no definite and final answer can be given4 ,among the barbarous tribes whose languages have been studied1 even in a most cursory manner1 none have ever been discovered which did not show some familiarity with the number concept4 ,the knowledge thus indicated has often proved to be most limited2 not extending beyond the numbers #a and #b1 or #a1 #b1 and #c4 ,examples of this poverty of number knowledge are found among the forest tribes of ,brazil1 the native races of ,australia and elsewhere1 and they are considered in some detail in the next chapter4 ,at first thought it seems quite inconceivable that any human being should be destitute of the power of counting beyond #b4 ,but such is the case2 and in a few instances languages have been found to be absolutely destitute of pure numeral words4 ,the ,chiquitos of ,bolivia had no real numerals whatever1#a but expressed their idea for one by the word etama1 meaning alone4 ,the ,tacanas of the same country have no numerals except those borrowed from ,spanish1 or from ,aymara or ,peno1 languages with which they have long been in contact4#b ,a few other ,south ,american languages are almost equally destitute of numeral words4 ,but even here1 rudimentary as the number sense undoubtedly is1 it is not wholly lacking2 and some indirect expression1 or some form of circumlocution1 shows a conception of the difference between one and two1 or at least1 between one and many4 ,these facts must of necessity deter the mathematician from seeking to push his investigation too far back toward the very origin of number4 ,philosophers have endeavoured to establish certain propositions concerning this subject1 but1 as might have been expected1 have failed to reach any common ground of agreement4 ,whewell has maintained that such propositions as that two and three make five are necessary truths1 containing in them an element of certainty beyond that which mere experience can give4 ,mill1 on the other hand1 argues that any such statement merely expresses a truth derived from early and constant experience2 and in this view he is heartily supported by ,tylor4#c ,but why this question should provoke controversy1 it is difficult for the mathematician to understand4 ,either view would seem to be correct1 according to the standpoint from which the question is approached4 ,we know of no language in which the suggestion of number does not appear1 and we must admit that the words which give expression to the number sense would be among the early words to be formed in any language4 ,they express ideas which are1 at first1 wholly concrete1 which are of the greatest possible simplicity1 and which seem in many ways to be clearly understood1 even by the higher orders of the brute creation4 ,the origin of number would in itself1 then1 appear to lie beyond the proper limits of inquiry2 and the primitive conception of number to be fundamental with human thought4 ,in connection with the assertion that the idea of number seems to be understood by the higher orders of animals1 the following brief quotation from a paper by ,sir ,john ,lubbock may not be out of place3 ,leroy 444 mentions a case in which a man was anxious to shoot a crow4 ',to deceive this suspicious bird1 the plan was hit upon of sending two men to the watch house1 one of whom passed on1 while the other remained2 but the crow counted and kept her distance4 ,the next day three went1 and again she perceived that only two retired4 ,in fine1 it was found necessary to send five or six men to the watch house to put her out in her calculation4 ,the crow1 thinking that this number of men had passed by1 lost no time in returning4' ,from this he inferred that crows could count up to four4 ,lichtenberg mentions a nightingale which was said to count up to three4 ,every day he gave it three mealworms1 one at a time4 ,when it had finished one it returned for another1 but after the third it knew that the feast was over4444 ,there is an amusing and suggestive remark in ,mr4 ,galton's interesting ,narrative of an ,explorer in ,tropical ,south ,africa4 ,after describing the ,demara's weakness in calculations1 he says3 ',once while ,i watched a ,demara floundering hopelessly in a calculation on one side of me1 ,i observed1 ,dinah1 my spaniel1 equally embarrassed on the other2 she was overlooking half a dozen of her new-born puppies1 which had been removed two or three times from her1 and her anxiety was excessive1 as she tried to find out if they were all present1 or if any were still missing4 ,she kept puzzling and running her eyes over them backwards and forwards1 but could not satisfy herself4 ,she evidently had a vague notion of counting1 but the figure was too large for her brain4 ,taking the two as they stood1 dog and ,demara1 the comparison reflected no great honour on the man4444' ,according to my bird-nesting recollections1 which ,i have refreshed by more recent experience1 if a nest contains four eggs1 one may safely be taken2 but if two are removed1 the bird generally deserts4 ,here1 then1 it would seem as if we had some reason for supposing that there is sufficient intelligence to distinguish three from four4 ,an interesting consideration arises with reference to the number of the victims allotted to each cell by the solitary wasps4 ,one species of ,ammophila considers one large caterpillar of ,noctua segetum enough2 one species of ,eumenes supplies its young with five victims2 another #aj1 #ae1 and even up to #bd4 ,the number appears to be constant in each species4 ,how does the insect know when her task is fulfilled8 ,not by the cell being filled1 for if some be removed1 she does not replace them4 ,when she has brought her complement she considers her task accomplished1 whether the victims are still there or not4 ,how1 then1 does she know when she has made up the number #bd8 ,perhaps it will be said that each species feels some mysterious and innate tendency to provide a certain number of victims4 ,this would1 under no circumstances1 be any explanation2 but it is not in accordance with the facts4 ,in the genus ,eumenes the males are much smaller than the females4444 ,if the egg is male1 she supplies five2 if female1 #aj victims4 ,does she count8 ,certainly this seems very like a commencement of arithmetic4#d ,many writers do not agree with the conclusions which ,lubbock reaches2 maintaining that there is1 in all such instances1 a perception of greater or less quantity rather than any idea of number4 ,but a careful consideration of the objections offered fails entirely to weaken the argument4 ,example after example of a nature similar to those just quoted might be given1 indicating on the part of animals a perception of the difference between #a and #b1 or between #b and #c and #d2 and any reasoning which tends to show that it is quantity rather than number which the animal perceives1 will apply with equal force to the ,demara1 the ,chiquito1 and the ,australian4 ,hence the actual origin of number may safely be excluded from the limits of investigation1 and1 for the present1 be left in the field of pure speculation4 ,a most inviting field for research is1 however1 furnished by the primitive methods of counting and of giving visible expression to the idea of number4 ,our starting-point must1 of course1 be the sign language1 which always precedes intelligible speech2 and which is so convenient and so expressive a method of communication that the human family1 even in its most highly developed branches1 never wholly lays it aside4 ,it may1 indeed1 be stated as a universal law1 that some practical method of numeration has1 in the childhood of every nation or tribe1 preceded the formation of numeral words4 ,practical methods of numeration are many in number and diverse in kind4 ,but the one primitive method of counting which seems to have been almost universal throughout all time is the finger method4 ,it is a matter of common experience and observation that every child1 when he begins to count1 turns instinctively to his fingers2 and1 with these convenient aids as counters1 tallies off the little number he has in mind4 ,this method is at once so natural and obvious that there can be no doubt that it has always been employed by savage tribes1 since the first appearance of the human race in remote antiquity4 ,all research among uncivilized peoples has tended to confirm this view1 were confirmation needed of anything so patent4 ,occasionally some exception to this rule is found2 or some variation1 such as is presented by the forest tribes of ,brazil1 who1 instead of counting on the fingers themselves1 count on the joints of their fingers4#e ,as the entire number system of these tribes appears to be limited to three1 this variation is no cause for surprise4 ,the variety in practical methods of numeration observed among savage races1 and among civilized peoples as well1 is so great that any detailed account of them would be almost impossible4 ,in one region we find sticks or splints used2 in another1 pebbles or shells2 in another1 simple scratches1 or notches cut in a stick1 ,robinson ,crusoe fashion2 in another1 kernels or little heaps of grain2 in another1 knots on a string2 and so on1 in diversity of method almost endless4 ,such are the devices which have been1 and still are1 to be found in the daily habit of great numbers of ,indian1 negro1 ,mongolian1 and ,malay tribes2 while1 to pass at a single step to the other extremity of intellectual development1 the ,german student keeps his beer score by chalk marks on the table or on the wall4 ,but back of all these devices1 and forming a common origin to which all may be referred1 is the universal finger method2 the method with which all begin1 and which all find too convenient ever to relinquish entirely1 even though their civilization be of the highest type4 ,any such mode of counting1 whether involving the use of the fingers or not1 is to be regarded simply as an extraneous aid in the expression or comprehension of an idea which the mind cannot grasp1 or cannot retain1 without assistance4 ,the ,german student scores his reckoning with chalk marks because he might otherwise forget2 while the ,andaman ,islander counts on his fingers because he has no other method of counting1--or1 in other words1 of grasping the idea of number4 ,a single illustration may be given which typifies all practical methods of numeration4 ,more than a century ago travellers in ,madagascar observed a curious but simple mode of ascertaining the number of soldiers in an army4#f ,each soldier was made to go through a passage in the presence of the principal chiefs2 and as he went through1 a pebble was dropped on the ground4 ,this continued until a heap of #aj was obtained1 when one was set aside and a new heap begun4 ,upon the completion of #aj heaps1 a pebble was set aside to indicate #ajj2 and so on until the entire army had been numbered4 ,another illustration1 taken from the very antipodes of ,madagascar1 recently found its way into print in an incidental manner1#g and is so good that it deserves a place beside de ,flacourt's time-honoured example4 ,mom ,cely1 a ,southern negro of unknown age1 finds herself in debt to the storekeeper2 and1 unwilling to believe that the amount is as great as he represents1 she proceeds to investigate the matter in her own peculiar way4 ,she had kept a tally of these purchases by means of a string1 in which she tied commemorative knots4 ,when her creditor undertook to make the matter clear to ,cely's comprehension1 he had to proceed upon a system of her own devising4 ,a small notch was cut in a smooth white stick for every dime she owed1 and a large notch when the dimes amounted to a dollar2 for every five dollars a string was tied in the fifth big notch1 ,cely keeping tally by the knots in her bit of twine2 thus1 when two strings were tied about the stick1 the ten dollars were seen to be an indisputable fact4 ,this interesting method of computing the amount of her debt1 whether an invention of her own or a survival of the ,african life of her parents1 served the old negro woman's purpose perfectly2 and it illustrates1 as well as a score of examples could1 the methods of numeration to which the children of barbarism resort when any number is to be expressed which exceeds the number of counters with which nature has provided them4 ,the fingers are1 however1 often employed in counting numbers far above the first decade4 ,after giving the ,il-,oigob numerals up to #fj1 ,mller adds3#h ,above #fj all numbers1 indicated by the proper figure pantomime1 are expressed by means of the word ipi4 ,we know1 moreover1 that many of the ,american ,indian tribes count one ten after another on their fingers2 so that1 whatever number they are endeavouring to indicate1 we need feel no surprise if the savage continues to use his fingers throughout the entire extent of his counts4 ,in rare instances we find tribes which1 like the ,mairassis of the interior of ,new ,guinea1 appear to use nothing but finger pantomime4#i ,this tribe1 though by no means destitute of the number sense1 is said to have no numerals whatever1 but to use the single word awari with each show of fingers1 no matter how few or how many are displayed4 ,in the methods of finger counting employed by savages a considerable degree of uniformity has been observed4 ,not only does he use his fingers to assist him in his tally1 but he almost always begins with the little finger of his left hand1 thence proceeding towards the thumb1 which is #e4 ,from this point onward the method varies4 ,sometimes the second #e also is told off on the left hand1 the same order being observed as in the first #e2 but oftener the fingers of the right hand are used1 with a reversal of the order previously employed2 i4e4 the thumb denotes #f1 the index finger #g1 and so on to the little finger1 which completes the count to #aj4 ,at first thought there would seem to be no good reason for any marked uniformity of method in finger counting4 ,observation among children fails to detect any such thing2 the child beginning1 with almost entire indifference1 on the thumb or on the little finger of the left hand4 ,my own observation leads to the conclusion that very young children have a slight1 though not decided preference for beginning with the thumb4 ,experiments in five different primary rooms in the public schools of ,worcester1 ,mass41 showed that out of a total of #bjf children1 #eg began with the little finger and #adi with the thumb4 ,but the fact that nearly three-fourths of the children began with the thumb1 and but one-fourth with the little finger1 is really far less significant than would appear at first thought4 ,children of this age1 four to eight years1 will count in either way1 and sometimes seem at a loss themselves to know where to begin4 ,in one school room where this experiment was tried the teacher incautiously asked one child to count on his fingers1 while all the other children in the room watched eagerly to see what he would do4 ,he began with the little finger--and so did every child in the room after him4 ,in another case the same error was made by the teacher1 and the child first asked began with the thumb4 ,every other child in the room did the same1 each following1 consciously or unconsciously1 the example of the leader4 ,the results from these two schools were of course rejected from the totals which are given above2 but they serve an excellent purpose in showing how slight is the preference which very young children have in this particular4 ,so slight is it that no definite law can be postulated of this age2 but the tendency seems to be to hold the palm of the hand downward1 and then begin with the thumb4 ,the writer once saw a boy about seven years old trying to multiply #c by #f2 and his method of procedure was as follows3 holding his left hand with its palm down1 he touched with the forefinger of his right hand the thumb1 forefinger1 and middle finger successively of his left hand4 ,then returning to his starting-point1 he told off a second three in the same manner4 ,this process he continued until he had obtained #f threes1 and then he announced his result correctly4 ,if he had been a few years older1 he might not have turned so readily to his thumb as a starting-point for any digital count4 ,the indifference manifested by very young children gradually disappears1 and at the age of twelve or thirteen the tendency is decidedly in the direction of beginning with the little finger4 ,fully three-fourths of all persons above that age will be found to count from the little finger toward the thumb1 thus reversing the proportion that was found to obtain in the primary school rooms examined4 ,with respect to finger counting among civilized peoples1 we fail1 then1 to find any universal law2 the most that can be said is that more begin with the little finger than with the thumb4 ,but when we proceed to the study of this slight but important particular among savages1 we find them employing a certain order of succession with such substantial uniformity that the conclusion is inevitable that there must lie back of this some well-defined reason1 or perhaps instinct1 which guides them in their choice4 ,this instinct is undoubtedly the outgrowth of the almost universal right-handedness of the human race4 ,in finger counting1 whether among children or adults1 the beginning is made on the left hand1 except in the case of left-handed individuals2 and even then the start is almost as likely to be on the left hand as on the right4 ,savage tribes1 as might be expected1 begin with the left hand4 ,not only is this custom almost invariable1 when tribes as a whole are considered1 but the little finger is nearly always called into requisition first4 ,to account for this uniformity1 ,lieutenant ,gushing gives the following theory1#aj which is well considered1 and is based on the results of careful study and observation among the ,zui ,indians of the ,southwest3 ,primitive man when abroad never lightly quit hold of his weapons4 ,if he wanted to count1 he did as the ,zui afield does to-day2 he tucked his instrument under his left arm1 thus constraining the latter1 but leaving the right hand free1 that he might check off with it the fingers of the rigidly elevated left hand4 ,from the nature of this position1 however1 the palm of the left hand was presented to the face of the counter1 so that he had to begin his score on the little finger of it1 and continue his counting from the right leftward4 ,an inheritance of this may be detected to-day in the confirmed habit the ,zui has of gesticulating from the right leftward1 with the fingers of the right hand over those of the left1 whether he be counting and summing up1 or relating in any orderly manner4 ,here1 then1 is the reason for this otherwise unaccountable phenomenon4 ,if savage man is universally right-handed1 he will almost inevitably use the index finger of his right hand to mark the fingers counted1 and he will begin his count just where it is most convenient4 ,in his case it is with the little finger of the left hand4 ,in the case of the child trying to multiply #c by #f1 it was with the thumb of the same hand4 ,he had nothing to tuck under his arm2 so1 in raising his left hand to a position where both eye and counting finger could readily run over its fingers1 he held the palm turned away from his face4 ,the same choice of starting-point then followed as with the savage--the finger nearest his right hand2 only in this case the finger was a thumb4 ,the deaf mute is sometimes taught in this manner1 which is for him an entirely natural manner4 ,a left-handed child might be expected to count in a left-to-right manner1 beginning1 probably1 with the thumb of his right hand4 ,to the law just given1 that savages begin to count on the little finger of the left hand1 there have been a few exceptions noted2 and it has been observed that the method of progression on the second hand is by no means as invariable as on the first4 ,the ,otomacs#aa of ,south ,america began their count with the thumb1 and to express the number #c would use the thumb1 forefinger1 and middle finger4 ,the ,maipures1#ab oddly enough1 seem to have begun1 in some cases at least1 with the forefinger2 for they are reported as expressing #c by means of the fore1 middle1 and ring fingers4 ,the ,andamans#ac begin with the little finger of either hand1 tapping the nose with each finger in succession4 ,if they have but one to express1 they use the forefinger of either hand1 pronouncing at the same time the proper word4 ,the ,bahnars1#ad one of the native tribes of the interior of ,cochin ,china1 exhibit no particular order in the sequence of fingers used1 though they employ their digits freely to assist them in counting4 ,among certain of the negro tribes of ,south ,africa#ae the little finger of the right hand is used for #a1 and their count proceeds from right to left4 ,with them1 #f is the thumb of the left hand1 #g the forefinger1 and so on4 ,they hold the palm downward instead of upward1 and thus form a complete and striking exception to the law which has been found to obtain with such substantial uniformity in other parts of the uncivilized world4 ,in ,melanesia a few examples of preference for beginning with the thumb may also be noticed4 ,in the ,banks ,islands the natives begin by turning down the thumb of the right hand1 and then the fingers in succession to the little finger1 which is #e4 ,this is followed by the fingers of the left hand1 both hands with closed fists being held up to show the completed #aj4 ,in ,lepers' ,island1 they begin with the thumb1 but1 having reached #e with the little finger1 they do not pass to the other hand1 but throw up the fingers they have turned down1 beginning with the forefinger and keeping the thumb for #aj4af ,in the use of the single hand this people is quite peculiar4 ,the second #e is almost invariably told off by savage tribes on the second hand1 though in passing from the one to the other primitive man does not follow any invariable law4 ,he marks #f with either the thumb or the little finger4 ,probably the former is the more common practice1 but the statement cannot be made with any degree of certainty4 ,among the ,zulus the sequence is from thumb to thumb1 as is the case among the other ,south ,african tribes just mentioned2 while the ,veis and numerous other ,african tribes pass from thumb to little finger4 ,the ,eskimo1 and nearly all the ,american ,indian tribes1 use the correspondence between #f and the thumb2 but this habit is by no means universal4 ,respecting progression from right to left or left to right on the toes1 there is no general law with which the author is familiar4 ,many tribes never use the toes in counting1 but signify the close of the first #aj by clapping the hands together1 by a wave of the right hand1 or by designating some object2 after which the fingers are again used as before4 ,one other detail in finger counting is worthy of a moment's notice4 ,it seems to have been the opinion of earlier investigators that in his passage from one finger to the next1 the savage would invariably bend down1 or close1 the last finger used2 that is1 that the count began with the fingers open and outspread4 ,this opinion is1 however1 erroneous4 ,several of the ,indian tribes of the ,west#ag begin with the hand clenched1 and open the fingers one by one as they proceed4 ,this method is much less common than the other1 but that it exists is beyond question4 ,in the ,muralug ,island1 in the western part of ,torres ,strait1 a somewhat remarkable method of counting formerly existed1 which grew out of1 and is to be regarded as an extension of1 the digital method4 ,beginning with the little finger of the left hand1 the natives counted up to #e in the usual manner1 and then1 instead of passing to the other hand1 or repeating the count on the same fingers1 they expressed the numbers from #f to #aj by touching and naming successively the left wrist1 left elbow1 left shoulder1 left breast1 and sternum4 ,then the numbers from #aa to #ai were indicated by the use1 in inverse order1 of the corresponding portions of the right side1 arm1 and hand1 the little finger of the right hand signifying #ai4 ,the words used were in each case the actual names of the parts touched2 the same word1 for example1 standing for #f and #ad2 but they were never used in the numerical sense unless accompanied by the proper gesture1 and bear no resemblance to the common numerals1 which are but few in number4 ,this method of counting is rapidly dying out among the natives of the island1 and is at the present time used only by old people4#ah ,variations on this most unusual custom have been found to exist in others of the neighbouring islands1 but none were exactly similar to it4 ,one is also reminded by it of a custom#ai which has for centuries prevailed among bargainers in the ,east1 of signifying numbers by touching the joints of each other's fingers under a cloth4 ,every joint has a special signification2 and the entire system is undoubtedly a development from finger counting4 ,the buyer or seller will by this method express #f or #fj by stretching out the thumb and little finger and closing the rest of the fingers4 ,the addition of the fourth finger to the two thus used signifies #g or #gj2 and so on4 ,it is said that between two brokers settling a price by thus snipping with the fingers1 cleverness in bargaining1 offering a little more1 hesitating1 expressing an obstinate refusal to go further1 etc41 are as clearly indicated as though the bargaining were being carried on in words4 ,the place occupied1 in the intellectual development of man1 by finger counting and by the many other artificial methods of reckoning1--pebbles1 shells1 knots1 the abacus1 etc41--seems to be this3 ,the abstract processes of addition1 subtraction1 multiplication1 division1 and even counting itself1 present to the mind a certain degree of difficulty4 ,to assist in overcoming that difficulty1 these artificial aids are called in2 and1 among savages of a low degree of development1 like the ,australians1 they make counting possible4 ,a little higher in the intellectual scale1 among the ,american ,indians1 for example1 they are employed merely as an artificial aid to what could be done by mental effort alone4 ,finally1 among semi-civilized and civilized peoples1 the same processes are retained1 and form a part of the daily life of almost every person who has to do with counting1 reckoning1 or keeping tally in any manner whatever4 ,they are no longer necessary1 but they are so convenient and so useful that civilization can never dispense with them4 ,the use of the abacus1 in the form of the ordinary numeral frame1 has increased greatly within the past few years2 and the time may come when the abacus in its proper form will again find in civilized countries a use as common as that of five centuries ago4 ,in the elaborate calculating machines of the present1 such as are used by life insurance actuaries and others having difficult computations to make1 we have the extreme of development in the direction of artificial aid to reckoning4 ,but instead of appearing merely as an extraneous aid to a defective intelligence1 it now presents itself as a machine so complex that a high degree of intellectual power is required for the mere grasp of its construction and method of working4 ,,chapter ,,ii4 ,,number ,,system ,,limits4 ,with respect to the limits to which the number systems of the various uncivilized races of the earth extend1 recent anthropological research has developed many interesting facts4 ,in the case of the ,chiquitos and a few other native races of ,bolivia we found no distinct number sense at all1 as far as could be judged from the absence1 in their language1 of numerals in the proper sense of the word4 ,how they indicated any number greater than one is a point still requiring investigation4 ,in all other known instances we find actual number systems1 or what may for the sake of uniformity be dignified by that name4 ,in many cases1 however1 the numerals existing are so few1 and the ability to count is so limited1 that the term number system is really an entire misnomer4 ,among the rudest tribes1 those whose mode of living approaches most nearly to utter savagery1 we find a certain uniformity of method4 ,the entire number system may consist of but two words1 one and many2 or of three words1 one1 two1 many4 ,or1 the count may proceed to #c1 #d1 #e1 #aj1 #bj1 or #ajj2 passing always1 or almost always1 from the distinct numeral limit to the indefinite many or several1 which serves for the expression of any number not readily grasped by the mind4 ,as a matter of fact1 most races count as high as #aj2 but to this statement the exceptions are so numerous that they deserve examination in some detail4 ,in certain parts of the world1 notably among the native races of ,south ,america1 ,australia1 and many of the islands of ,polynesia and ,melanesia1 a surprising paucity of numeral words has been observed4 ,the ,encabellada of the ,rio ,napo have but two distinct numerals2 tey1 #a1 and cayapa1 #b4bj ,the ,chaco languages#ba of the ,guaycuru stock are also notably poor in this respect4 ,in the ,mbocobi dialect of this language the only native numerals are ya tvak1 #a1 and yfioaca1 #b4 ,the ,puris#bb count omi1 #a1 curiri1 #b1 prica1 many2 and the ,botocudos#bc mokenam1 #a1 uruhu1 many4 ,the ,fuegans1#bd supposed to have been able at one time to count to #aj1 have but three numerals1--kaoueli1 #a1 compaipi1 #b1 maten1 #c4 ,the ,campas of ,peru#be possess only three separate words for the expression of number1--patrio1 #a1 pitteni1 #b1 mahuani1 #c4 ,above #c they proceed by combinations1 as #a and #c for #d1 #a and #a and #c for #e4 ,counting above #aj is1 however1 entirely inconceivable to them1 and any number beyond that limit they indicate by tohaine1 many4 ,the ,conibos1#bf of the same region1 had1 before their contact with the ,spanish1 only atchoupre1 #a1 and rrabui1 #b2 though they made some slight progress above #b by means of reduplication4 ,the ,orejones1 one of the low1 degraded tribes of the ,upper ,amazon1#bg have no names for number except nayhay1 #a1 nenacome1 #b1 feninichacome1 #c1 ononoeomere1 #d4 ,in the extensive vocabularies given by ,von ,martins1#bh many similar examples are found4 ,for the ,bororos he gives only couai1 #a1 maeouai1 #b1 ouai1 #c4 ,the last word1 with the proper finger pantomime1 serves also for any higher number which falls within the grasp of their comprehension4 ,the ,guachi manage to reach #e1 but their numeration is of the rudest kind1 as the following scale shows3 tamak1 #a1 eu-echo1 #b1 eu-echo-kailau1 #c1 eu-echo-way1 #d1 localau1 #e4 ,the ,carajas counted by a scale equally rude1 and their conception of number seemed equally vague1 until contact with the neighbouring tribes furnished them with the means of going beyond their original limit4 ,their scale shows clearly the uncertain1 feeble number sense which is so marked in the interior of ,south ,america4 ,it contains wadewo1 #a1 wadebothoa1 #b1 wadeboaheodo1 #c1 wadebojeodo1 #d1 wadewajouclay1 #e1 wadewasori1 #f1 or many4 ,turning to the languages of the extinct1 or fast vanishing1 tribes of ,australia1 we find a still more noteworthy absence of numeral expressions4 ,in the ,gudang dialect#bi but two numerals are found--pirman1 #a1 and ilabiu1 #b2 in the ,weedookarry1 ekkamurda1 #a1 and kootera1 #b2 and in the ,queanbeyan1 midjemban1 #a1 and bollan1 #b4 ,in a score or more of instances the numerals stop at #c4 ,the natives of ,keppel ,bay count webben1 #a1 booli1 #b1 koorel1 #c2 of the ,boyne ,river1 karroon1 #a1 boodla1 #b1 numma1 #c2 of the ,flinders ,river1 kooroin1 #a1 kurto1 #b1 kurto kooroin1 #c2 at the mouth of the ,norman ,river1 lum1 #a1 buggar1 #b1 orinch1 #c2 the ,eaw tribe1 koothea1 #a1 woother1 #b1 marronoo1 #c2 the ,moree1 mal1 #a1 boolar1 #b1 kooliba1 #c2 the ,port ,essington1#cj erad1 #a1 nargarick1 #b1 nargarickelerad1 #c2 the ,darnly ,islanders1#ca netat1 #a1 naes1 #b1 naesa netat1 #c2 and so on through a long list of tribes whose numeral scales are equally scanty4 ,a still larger number of tribes show an ability to count one step further1 to #d2 but beyond this limit the majority of ,australian and ,tasmanian tribes do not go4 ,it seems most remarkable that any human being should possess the ability to count to #d1 and not to #e4 ,the number of fingers on one hand furnishes so obvious a limit to any of these rudimentary systems1 that positive evidence is needed before one can accept the statement4 ,a careful examination of the numerals in upwards of a hundred ,australian dialects leaves no doubt1 however1 that such is the fact4 ,the ,australians in almost all cases count by pairs2 and so pronounced is this tendency that they pay but little attention to the fingers4 ,some tribes do not appear ever to count beyond #b--;a single pair4 ,many more go one step further2 but if they do1 they are as likely as not to designate their next numeral as two-one1 or possibly1 one-two4 ,if this step is taken1 we may or may not find one more added to it1 thus completing the second pair4 ,still1 the ,australian's capacity for understanding anything which pertains to number is so painfully limited that even here there is sometimes an indefinite expression formed1 as many1 heap1 or plenty1 instead of any distinct numeral2 and it is probably true that no ,australian language contains a pure1 simple numeral for #d4 ,curr1 the best authority on this subject1 believes that1 where a distinct word for #d is given1 investigators have been deceived in every case4#cb ,if counting is carried beyond #d1 it is always by means of reduplication4 ,a few tribes gave expressions for #e1 fewer still for #f1 and a very small number appeared able to reach #g4 ,possibly the ability to count extended still further2 but if so1 it consisted undoubtedly in reckoning one pair after another1 without any consciousness whatever of the sum total save as a larger number4 ,the numerals of a few additional tribes will show clearly that all distinct perception of number is lost as soon as these races attempt to count above #c1 or at most1 #d4 ,the ,yuckaburra#cc natives can go no further than wigsin1 #a1 bullaroo1 #b1 goolbora1 #c4 ,above here all is referred to as moorgha1 many4 ,the ,marachowies#cd have but three distinct numerals1--cooma1 #a1 cootera1 #b1 murra1 #c4 ,for #d they say minna1 many4 ,at ,streaky ,bay we find a similar list1 with the same words1 kooma and kootera1 for #a and #b1 but entirely different terms1 karboo and yalkata for #c and many4 ,the same method obtains in the ,minnal ,yungar tribe1 where the only numerals are kain1 #a1 kujal1 #b1 moa1 #c1 and bulla1 plenty4 ,in the ,pinjarra dialect we find doombart1 #a1 gugal1 #b1 murdine1 #c1 boola1 plenty2 and in the dialect described as belonging to ,eyre's ,sand ,patch1 three definite terms are given--kean1 #a1 koojal1 #b1 yalgatta1 #c1 while a fourth1 murna1 served to describe anything greater4 ,in all these examples the fourth numeral is indefinite2 and the same statement is true of many other ,australian languages4 ,but more commonly still we find #d1 and perhaps #c also1 expressed by reduplication4 ,in the ,port ,mackay dialect#ce the latter numeral is compound1 the count being warpur1 #a1 boolera1 #b1 boolera warpur1 #c4 ,for #d the term is not given4 ,in the dialect which prevailed between the ,albert and ,tweed rivers#cf the scale appears as yaburu1 #a1 boolaroo1 #b1 boolaroo yaburu1 #c1 and gurul for #d or anything beyond4 ,the ,wiraduroi#cg have numbai1 #a1 bula1 #b1 bula numbai1 #c1 bungu1 #d1 or many1 and bungu galan or bian galan1 #e1 or very many4 ,the ,kamilaroi#ch scale is still more irregular1 compounding above #d with little apparent method4 ,the numerals are mal1 #a1 bular1 #b1 guliba1 #c1 bular bular1 #d1 bular guliba1 #e1 guliba guliba1 #f4 ,the last two numerals show that #e is to these natives simply #b-c1 and #f is #c-c4 ,for additional examples of a similar nature the extended list of ,australian scales given in ,chapter ,v4 may be consulted4 ,taken as a whole1 the ,australian and ,tasmanian tribes seem to have been distinctly inferior to those of ,south ,america in their ability to use and to comprehend numerals4 ,in all but two or three cases the ,tasmanians#ci were found to be unable to proceed beyond #b2 and as the foregoing examples have indicated1 their ,australian neighbours were but little better off4 ,in one or two instances we do find ,australian numeral scales which reach #aj1 and perhaps we may safely say #bj4 ,one of these is given in full in a subsequent chapter1 and its structure gives rise to the suspicion that it was originally as limited as those of kindred tribes1 and that it underwent a considerable development after the natives had come in contact with the ,europeans4 ,there is good reason to believe that no ,australian in his wild state could ever count intelligently to #g4dj ,in certain portions of ,asia1 ,africa1 ,melanesia1 ,polynesia1 and ,north ,america1 are to be found races whose number systems are almost and sometimes quite as limited as are those of the ,south4 ,american and ,australian tribes already cited1 but nowhere else do we find these so abundant as in the two continents just mentioned1 where example after example might be cited of tribes whose ability to count is circumscribed within the narrowest limits4 ,the ,veddas#da of ,ceylon have but two numerals1 ekkamei1 #a1 dekkame1 #b4 ,beyond this they count otameeka1 otameeka1 otameeka1 etc42 i4e4 and one more1 and one more1 and one more1 and so on indefinitely4 ,the ,andamans1#db inhabitants of a group of islands in the ,bay of ,bengal1 are equally limited in their power of counting4 ,they have ubatulda1 #a1 and ikporda1 #b2 but they can go no further1 except in a manner similar to that of the ,veddas4 ,above two they proceed wholly by means of the fingers1 saying as they tap the nose with each successive finger1 anka1 and this4 ,only the more intelligent of the ,andamans can count at all1 many of them seeming to be as nearly destitute of the number sense as it is possible for a human being to be4 ,the ,bushmen#dc of ,south ,africa have but two numerals1 the pronunciation of which can hardly be indicated without other resources than those of the ,english alphabet4 ,their word for #c means1 simply1 many1 as in the case of some of the ,australian tribes4 ,the ,watchandies#dd have but two simple numerals1 and their entire number system is cooteon1 #a1 utaura1 #b1 utarra cooteoo1 #c1 atarra utarra1 #d4 ,beyond this they can only say1 booltha1 many1 and booltha bat1 very many4 ,although they have the expressions here given for #c and #d1 they are reluctant to use them1 and only do so when absolutely required4 ,the natives of ,lower ,california#de cannot count above #e4 ,a few of the more intelligent among them understand the meaning of #b fives1 but this number seems entirely beyond the comprehension of the ordinary native4 ,the ,comanches1 curiously enough1 are so reluctant to employ their number words that they appear to prefer finger pantomime instead1 thus giving rise to the impression which at one time became current1 that they had no numerals at all for ordinary counting4 ,aside from the specific examples already given1 a considerable number of sweeping generalizations may be made1 tending to show how rudimentary the number sense may be in aboriginal life4 ,scores of the native dialects of ,australia and ,south ,america have been found containing number systems but little more extensive than those alluded to above4 ,the negro tribes of ,africa give the same testimony1 as do many of the native races of ,central ,america1 ,mexico1 and the ,pacific coast of the ,united ,states and ,canada1 the northern part of ,siberia1 ,greenland1 ,labrador1 and the arctic archipelago4 ,in speaking of the ,eskimos of ,point ,barrow1 ,murdoch#df says3 ,it was not easy to obtain any accurate information about the numeral system of these people1 since in ordinary conversation they are not in the habit of specifying any numbers above five4 ,counting is often carried higher than this among certain of these northern tribes1 but1 save for occasional examples1 it is limited at best4 ,dr4 ,franz ,boas1 who has travelled extensively among the ,eskimos1 and whose observations are always of the most accurate nature1 once told the author that he never met an ,eskimo who could count above #ae4 ,their numerals actually do extend much higher2 and a stray numeral of ,danish origin is now and then met with1 showing that the more intelligent among them are able to comprehend numbers of much greater magnitude than this4 ,but as ,dr4 ,boas was engaged in active work among them for three years1 we may conclude that the ,eskimo has an arithmetic but little more extended than that which sufficed for the ,australians and the forest tribes of ,brazil4 ,early ,russian explorers among the northern tribes of ,siberia noticed the same difficulty in ordinary1 every-day reckoning among the natives4 ,at first thought we might1 then1 state it as a general law that those races which are lowest in the scale of civilization1 have the feeblest number sense also2 or in other words1 the least possible power of grasping the abstract idea of number4 ,but to this law there are many and important exceptions4 ,the concurrent testimony of explorers seems to be that savage races possess1 in the great majority of cases1 the ability to count at least as high as #aj4 ,this limit is often extended to #bj1 and not infrequently to #ajj4 ,again1 we find #ajjj as the limit2 or perhaps #aj1jjj2 and sometimes the savage carries his number system on into the hundreds of thousands or millions4 ,indeed1 the high limit to which some savage races carry their numeration is far more worthy of remark than the entire absence of the number sense exhibited by others of apparently equal intelligence4 ,if the life of any tribe is such as to induce trade and barter with their neighbours1 a considerable quickness in reckoning will be developed among them4 ,otherwise this power will remain dormant because there is but little in the ordinary life of primitive man to call for its exercise4 ,in giving #a1 #b1 #c1 #e1 #aj1 or any other small number as a system limit1 it must not be overlooked that this limit mentioned is in all cases the limit of the spoken numerals at the savage's command4 ,the actual ability to count is almost always1 and one is tempted to say always1 somewhat greater than their vocabularies would indicate4 ,the ,bushman has no number word that will express for him anything higher than #b2 but with the assistance of his fingers he gropes his way on as far as #aj4 ,the ,veddas1 the ,andamans1 the ,guachi1 the ,botocudos1 the ,eskimos1 and the thousand and one other tribes which furnish such scanty numeral systems1 almost all proceed with more or less readiness as far as their fingers will carry them4 ,as a matter of fact1 this limit is frequently extended to #bj2 the toes1 the fingers of a second man1 or a recount of the savage's own fingers1 serving as a tale for the second #aj4 ,allusion is again made to this in a later chapter1 where the subject of counting on the fingers and toes is examined more in detail4 ,in saying that a savage can count to #aj1 to #bj1 or to #ajj1 but little idea is given of his real mental conception of any except the smallest numbers4 ,want of familiarity with the use of numbers1 and lack of convenient means of comparison1 must result in extreme indefiniteness of mental conception and almost entire absence of exactness4 ,the experience of ,captain ,parry1#dg who found that the ,eskimos made mistakes before they reached #g1 and of ,humboldt1#dh who says that a ,chayma might be made to say that his age was either #ah or #fj1 has been duplicated by all investigators who have had actual experience among savage races4 ,nor1 on the other hand1 is the development of a numeral system an infallible index of mental power1 or of any real approach toward civilization4 ,a continued use of the trading and bargaining faculties must and does result in a familiarity with numbers sufficient to enable savages to perform unexpected feats in reckoning4 ,among some of the ,west ,african tribes this has actually been found to be the case2 and among the ,yorubas of ,abeokuta#di the extraordinary saying1 ,you may seem very clever1 but you can't tell nine times nine1 shows how surprisingly this faculty has been developed1 considering the general condition of savagery in which the tribe lived4 ,there can be no doubt that1 in general1 the growth of the number sense keeps pace with the growth of the intelligence in other respects4 ,but when it is remembered that the ,tonga ,islanders have numerals up to #ajj1jjj1 and the ,tembus1 the ,fingoes1 the ,pondos1 and a dozen other ,south ,african tribes go as high as #a1jjj1jjj2 and that ,leigh ,hunt never could learn the multiplication table1 one must confess that this law occasionally presents to our consideration remarkable exceptions4 ,while considering the extent of the savage's arithmetical knowledge1 of his ability to count and to grasp the meaning of number1 it may not be amiss to ask ourselves the question1 what is the extent of the development of our own number sense8 ,to what limit can we absorb the idea of number1 with a complete appreciation of the idea of the number of units involved in any written or spoken quantity8 ,our perfect system of numeration enables us to express without difficulty any desired number1 no matter how great or how small it be4 ,but how much of actually clear comprehension does the number thus expressed convey to the mind8 ,we say that one place is #ajj miles from another2 that ,a paid ,b #ajjj dollars for a certain piece of property2 that a given city contains #aj1jjj inhabitants2 that #ajj1jjj bushels of wheat were shipped from ,duluth or ,odessa on such a day2 that #a1jjj1jjj feet of lumber were destroyed by the fire of yesterday1--and as we pass from the smallest to the largest of the numbers thus instanced1 and from the largest on to those still larger1 we repeat the question just asked2 and we repeat it with a new sense of our own mental limitation4 ,the number #ajj unquestionably stands for a distinct conception4 ,perhaps the same may be said for #ajjj1 though this could not be postulated with equal certainty4 ,but what of #aj1jjj8 ,if that number of persons were gathered together into a single hall or amphitheatre1 could an estimate be made by the average onlooker which would approximate with any degree of accuracy the size of the assembly8 ,or if an observer were stationed at a certain point1 and #aj1jjj persons were to pass him in single file without his counting them as they passed1 what sort of an estimate would he make of their number8 ,the truth seems to be that our mental conception of number is much more limited than is commonly thought1 and that we unconsciously adopt some new unit as a standard of comparison when we wish to render intelligible to our minds any number of considerable magnitude4 ,for example1 we say that ,a has a fortune of #a1jjj1jjj4 ,the impression is at once conveyed of a considerable degree of wealth1 but it is rather from the fact that that fortune represents an annual income of #dj1jjj than1 from the actual magnitude of the fortune itself4 ,the number #a1jjj1jjj is1 in itself1 so greatly in excess of anything that enters into our daily experience that we have but a vague conception of it1 except as something very great4 ,we are not1 after all1 so very much better off than the child who1 with his arms about his mother's neck1 informs her with perfect gravity and sincerity that he loves her a million bushels4 ,his idea is merely of some very great amount1 and our own is often but little clearer when we use the expressions which are so easily represented by a few digits4 ,among the uneducated portions of civilized communities the limit of clear comprehension of number is not only relatively1 but absolutely1 very low4 ,travellers in ,russia have informed the writer that the peasants of that country have no distinct idea of a number consisting of but a few hundred even4 ,there is no reason to doubt this testimony4 ,the entire life of a peasant might be passed without his ever having occasion to use a number as great as #ejj1 and as a result he might have respecting that number an idea less distinct than a trained mathematician would have of the distance from the earth to the sun4 ,de ,quincey#ej incidentally mentions this characteristic in narrating a conversation which occurred while he was at ,carnarvon1 a little town in ,wales4 ,it was on this occasion1 he says1 that ,i learned how vague are the ideas of number in unpractised minds4 ',what number of people do you think1' ,i said to an elderly person1 'will be assembled this day at ,carnarvon8' ',what number8' rejoined the person addressed2 'what number8 ,well1 really1 now1 ,i should reckon--perhaps a matter of four million4' ,four millions of extra people in little ,carnarvon1 that could barely find accommodation 7,i should calculate7 for an extra four hundred6 ,so the ,eskimo and the ,south ,american ,indian are1 after all1 not so very far behind the elderly person of ,carnarvon1 in the distinct perception of a number which familiarity renders to us absurdly small4 ,,chapter ,,iii4 ,,the ,,origin ,,of ,,number ,,words4 ,in the comparison of languages and the search for primitive root forms1 no class of expressions has been subjected to closer scrutiny than the little cluster of words1 found in each language1 which constitutes a part of the daily vocabulary of almost every human being--the words with which we begin our counting4 ,it is assumed1 and with good reason1 that these are among the earlier words to appear in any language2 and in the mutations of human speech1 they are found to suffer less than almost any other portion of a language4 ,kinship between tongues remote from each other has in many instances been detected by the similarity found to exist among the every-day words of each2 and among these words one may look with a good degree of certainty for the #a1 #b1 #c1 etc41 of the number scale4 ,so fruitful has been this line of research1 that the attempt has been made1 even1 to establish a common origin for all the races of mankind by means of a comparison of numeral words4#ea ,but in this instance1 as in so many others that will readily occur to the mind1 the result has been that the theory has finally taken possession of the author and reduced him to complete subjugation1 instead of remaining his servant and submitting to the legitimate results of patient and careful investigation4 ,linguistic research is so full of snares and pitfalls that the student must needs employ the greatest degree of discrimination before asserting kinship of race because of resemblances in vocabulary2 or even relationship between words in the same language because of some chance likeness of form that may exist between them4 ,probably no one would argue that the ,english and the ,babusess of ,central ,africa were of the same primitive stock simply because in the language of the latter five atano means #e1 and ten kumi means #aj4eb ,but1 on the other hand1 many will argue that1 because the ,german zehn means #aj1 and zehen means toes1 the ancestors of the ,germans counted on their toes2 and that with them1 #aj was the complete count of the toes4 ,it may be so4 ,we certainly have no evidence with which to disprove this2 but1 before accepting it as a fact1 or even as a reasonable hypothesis1 we may be pardoned for demanding some evidence aside from the mere resemblance in the form of the words4 ,if1 in the study of numeral words1 form is to constitute our chief guide1 we must expect now and then to be confronted with facts which are not easily reconciled with any pet theory4 ,the scope of the present work will admit of no more than a hasty examination of numeral forms1 in which only actual and well ascertained meanings will be considered4 ,but here we are at the outset confronted with a class of words whose original meanings appear to be entirely lost4 ,they are what may be termed the numerals proper--the native1 uncompounded words used to signify number4 ,such words are the one1 two1 three1 etc41 of ,english2 the eins1 zwei1 drei1 etc41 of ,german2 words which must at some time1 in some prehistoric language1 have had definite meanings entirely apart from those which they now convey to our minds4 ,in savage languages it is sometimes possible to detect these meanings1 and thus to obtain possession of the clue that leads to the development1 in the barbarian's rude mind1 of a count scale--a number system4 ,but in languages like those of modern ,europe1 the pedigree claimed by numerals is so long that1 in the successive changes through which they have passed1 all trace of their origin seems to have been lost4 ,the actual number of such words is1 however1 surprisingly small in any language4 ,in ,english we count by simple words only to #aj4 ,from this point onward all our numerals except hundred and thousand are compounds and combinations of the names of smaller numbers4 ,the words we employ to designate the higher orders of units1 as million1 billion1 trillion1 etc41 are appropriated bodily from the ,italian2 and the native words pair1 tale1 brace1 dozen1 gross1 and score1 can hardly be classed as numerals in the strict sense of the word4 ,german possesses exactly the same number of native words in its numeral scale as ,english2 and the same may be said of the ,teutonic languages generally1 as well as of the ,celtic1 the ,latin1 the ,slavonic1 and the ,basque4 ,this is1 in fact1 the universal method observed in the formation of any numeral scale1 though the actual number of simple words may vary4 ,the ,chiquito language has but one numeral of any kind whatever2 ,english contains twelve simple terms2 ,sanskrit has twenty-seven1 while ,japanese possesses twenty-four1 and the ,chinese a number almost equally great4 ,very many languages1 as might be expected1 contain special numeral expressions1 such as the ,german dutzend and the ,french dizaine2 but these1 like the ,english dozen and score1 are not to be regarded as numerals proper4 ,the formation of numeral words shows at a glance the general method in which any number scale has been built up4 ,the primitive savage counts on his fingers until he has reached the end of one1 or more probably of both1 hands4 ,then1 if he wishes to proceed farther1 some mark is made1 a pebble is laid aside1 a knot tied1 or some similar device employed to signify that all the counters at his disposal have been used4 ,then the count begins anew1 and to avoid multiplication of words1 as well as to assist the memory1 the terms already used are again resorted to2 and the name by which the first halting-place was designated is repeated with each new numeral4 ,hence the thirteen1 fourteen1 fifteen1 etc41 which are contractions of the fuller expressions three-and-ten1 four-and-ten1 five-and-ten1 etc4 ,the specific method of combination may not always be the same1 as witness the eighteen1 or eight-ten1 in ,english1 and dix-huit1 or ten-eight1 in ,french2 forty-five1 or four-tens-five1 in ,english1 and fnf und vierzig1 or five and four tens in ,german4 ,but the general method is the same the world over1 presenting us with nothing but local variations1 which are1 relatively speaking1 entirely unimportant4 ,with this fact in mind1 we can cease to wonder at the small number of simple numerals in any language4 ,it might1 indeed1 be queried1 why do any languages1 ,english and ,german1 for example1 have unusual compounds for #aa and #ab8 ,it would seem as though the regular method of compounding should begin with #aj and #a1 instead of #aj and #c1 in any language using a system with #aj as a base4 ,an examination of several hundred numeral scales shows that the ,teutonic languages are somewhat exceptional in this respect4 ,the words eleven and twelve are undoubtedly combinations1 but not in the same direct sense as thirteen1 twenty-five1 etc4 ,the same may be said of the ,french onze1 douze1 treize1 quatorze1 quinze1 and seize1 which are obvious compounds1 but not formed in the same manner as the numerals above that point4 ,almost all civilized languages1 however1 except the ,teutonic1 and practically all uncivilized languages1 begin their direct numeral combinations as soon as they have passed their number base1 whatever that may be4 ,to give an illustration1 selected quite at random from among the barbarous tribes of ,africa1 the ,ki-,swahili numeral scale runs as follows3#ec #a4 moyyi1 #b4 mbiri1 #c4 tato1 #d4 ena1 #e4 tano1 #f4 seta1 #g4 saba1 #h4 nani1 #i4 kenda1 #aj4 kumi1 #aa4 kumi na moyyi1 #ab4 kumi na mbiri1 #ac4 kumi na tato1 etc4 ,the words for #aa1 #ab1 and #ac1 are seen at a glance to signify ten-and-one1 ten-and-two1 ten-and-three1 and the count proceeds1 as might be inferred1 in a similar manner as far as the number system extends4 ,our ,english combinations are a little closer than these1 and the combinations found in certain other languages are1 in turn1 closer than those of the ,english2 as witness the once1 #aa1 doce1 #ab1 trece1 #ac1 etc41 of ,spanish4 ,but the process is essentially the same1 and the law may be accepted as practically invariable1 that all numerals greater than the base of a system are expressed by compound words1 except such as are necessary to establish some new order of unit1 as hundred or thousand4 ,in the scale just given1 it will be noticed that the larger number precedes the smaller1 giving #aj #a1 #aj #b1 etc41 instead of #a #aj1 #b #aj1 etc4 ,this seems entirely natural1 and hardly calls for any comment whatever4 ,but we have only to consider the formation of our ,english teens to see that our own method is1 at its inception1 just the reverse of this4 ,thirteen1 #ad1 and the remaining numerals up to #ai are formed by prefixing the smaller number to the base2 and it is only when we pass #bj that we return to the more direct and obvious method of giving precedence to the larger4 ,in ,german and other ,teutonic languages the inverse method is continued still further4 ,here #be is fnf und zwanzig1 #e and #bj2 #ib is zwei und neunzig1 #b and #ij1 and so on to #ii4 ,above #ajj the order is made direct1 as in ,english4 ,of course1 this mode of formation between #bj and #ajj is permissible in ,english1 where five and twenty is just as correct a form as twenty-five4 ,but it is archaic1 and would soon pass out of the language altogether1 were it not for the influence of some of the older writings which have had a strong influence in preserving for us many of older and more essentially ,saxon forms of expression4 ,both the methods described above are found in all parts of the world1 but what ,i have called the direct is far more common than the other4 ,in general1 where the smaller number precedes the larger it signifies multiplication instead of addition4 ,thus1 when we say thirty1 i4e4 three-ten1 we mean #c #aj2 just as three hundred means #c #ajj4 ,when the larger precedes the smaller1 we must usually understand addition4 ,but to both these rules there are very many exceptions4 ,among higher numbers the inverse order is very rarely used2 though even here an occasional exception is found4 ,the ,taensa ,indians1 for example1 place the smaller numbers before the larger1 no matter how far their scale may extend4 ,to say #ahha they make a complete inversion of our own order1 beginning with #a and ending with #ajjj4 ,their full numeral for this is yeha av wabki mar-u-wab mar-u-haki1 which means1 literally1 #a #hj #ajj #h #ajj #aj4ed ,such exceptions are1 however1 quite rare4 ,one other method of combination1 that of subtraction1 remains to be considered4 ,every student of ,latin will recall at once the duodeviginti1 #b from #bj1 and undeviginti1 #a from #bj1 which in that language are the regular forms of expression for #ah and #ai4 ,at first they seem decidedly odd2 but familiarity soon accustoms one to them1 and they cease entirely to attract any special attention4 ,this principle of subtraction1 which1 in the formation of numeral words1 is quite foreign to the genius of ,english1 is still of such common occurrence in other languages that the ,latin examples just given cease to be solitary instances4 ,the origin of numerals of this class is to be found in the idea of reference1 not necessarily to the last1 but to the nearest1 halting-point in the scale4 ,many tribes seem to regard #i as almost #aj1 and to give it a name which conveys this thought4 ,in the ,mississaga1 one of the numerous ,algonquin languages1 we have1 for example1 the word cangaswi1 incomplete #aj1 for #i4ee ,in the ,kwakiutl of ,british ,columbia1 #h as well as #i is formed in this way2 these two numbers being matlguanatl1 #aj - #b1 and nanema1 #aj - #a1 respectively4#ef ,in many of the languages of ,british ,columbia we find a similar formation for #h and #i1 or for #i alone4 ,the same formation occurs in ,malay1 resulting in the numerals delapan1 #aj - #b1 and sambilan #aj - #a4eg ,in ,green ,island1 one of the ,new ,ireland group1 these become simply andra-lua1 less #b1 and andra-si1 less #a4eh ,in the ,admiralty ,islands this formation is carried back one step further1 and not only gives us shua-luea1 less #b1 and shu-ri1 less #a1 but also makes #g appear as sua-tolu1 less #c4ei ,surprising as this numeral is1 it is more than matched by the ,ainu scale1 which carries subtraction back still another step1 and calls #f1 #aj - #d4 ,the four numerals from #f to #i in this scale are respectively1 iwa1 #aj - #d1 arawa1 #aj - #c1 tupe-san1 #aj - #b1 and sinepe-san1 #aj - #a4fj ,numerous examples of this kind of formation will be found in later chapters of this work2 but they will usually be found to occur in one or both of the numerals1 #h and #i4 ,occasionally they appear among the higher numbers2 as in the ,maya languages1 where1 for example1 #ii years is one single year lacking from five score years1#fa and in the ,arikara dialects1 where #ih and #ii are #e men minus and #e men #a not4#fb ,the ,welsh1 ,danish1 and other languages less easily accessible than these to the general student1 also furnish interesting examples of a similar character4 ,more rarely yet are instances met with of languages which make use of subtraction almost as freely as addition1 in the composition of numerals4 ,within the past few years such an instance has been noticed in the case of the ,bellacoola language of ,british ,columbia4 ,in their numeral scale #ae1 one foot1 is followed by #af1 one man less #d2 #ag1 one man less #c2 #ah1 one man less #b2 #ai1 one man less #a2 and #bj1 one man4 ,twenty-five is one man and one hand2 #bf1 one man and two hands less #d2 #cf1 two men less #d2 and so on4 ,this method of formation prevails throughout the entire numeral scale4#fc ,one of the best known and most interesting examples of subtraction as a well-defined principle of formation is found in the ,maya scale4 ,up to #dj no special peculiarity appears2 but as the count progresses beyond that point we find a succession of numerals which one is almost tempted to call #fj - #ai1 #fj - #ah1 #fj - #ag1 etc4 ,literally translated the meanings seem to be #a to #fj1 #b to #fj1 #c to #fj1 etc4 ,the point of reference is #fj1 and the thought underlying the words may probably be expressed by the paraphrases1 #a on the third score1 #b on the third score1 #c on the third score1 etc4 ,similarly1 #fa is #a on the fourth score1 #ha is one on the fifth score1 #cha is #a on the nineteenth score1 and so on to #djj4 ,at #dda the same formation reappears2 and it continues to characterize the system in a regular and consistent manner1 no matter how far it is extended4#fd ,the ,yoruba language of ,africa is another example of most lavish use of subtraction2 but it here results in a system much less consistent and natural than that just considered4 ,here we find not only #e1 #aj1 and #bj subtracted from the next higher unit1 but also #dj1 and even #ajj4 ,for example1 #cfj is #djj - #dj2 #dfj is #ejj - #dj2 #ejj is #fjj - #ajj2 #acjj is #adjj - #ajj1 etc4 ,one of the ,yoruba units is #bjj2 and all the odd hundreds up to #bjjj1 the next higher unit1 are formed by subtracting #ajj from the next higher multiple of #bjj4 ,the system is quite complex1 and very artificial2 and seems to have been developed by intercourse with traders4#fe ,it has already been stated that the primitive meanings of our own simple numerals have been lost4 ,this is also true of the languages of nearly all other civilized peoples1 and of numerous savage races as well4 ,we are at liberty to suppose1 and we do suppose1 that in very many cases these words once expressed meanings closely connected with the names of the fingers1 or with the fingers themselves1 or both4 ,now and then a case is met with in which the numeral word frankly avows its meaning--as in the ,botocudo language1 where #a is expressed by podzik1 finger1 and #b by kripo1 double finger2#ff and in the ,eskimo dialect of ,hudson's ,bay1 where eerkitkoka means both #aj and little finger4#fg ,such cases are1 however1 somewhat exceptional4 ,in a few noteworthy instances1 the words composing the numeral scale of a language have been carefully investigated and their original meanings accurately determined4 ,the simple structure of many of the rude languages of the world should render this possible in a multitude of cases2 but investigators are too often content with the mere numerals themselves1 and make no inquiry respecting their meanings4 ,but the following exposition of the ,zui scale1 given by ,lieutenant ,gushing#fh leaves nothing to be desired3 #a4 tpinte taken to start with4 #b4 kwilli put down together with4 #c4 ha'i the equally dividing finger4 #d4 awite all the fingers all but done with4 #e4 pte the notched off4 ,this finishes the list of original simple numerals1 the ,zui stopping1 or notching off1 when he finishes the fingers of one hand4 ,compounding now begins4 #f4 topalk'ya another brought to add to the done with4 #g4 kwillilk'ya two brought to and held up with the rest4 #h4 hailk'ye three brought to and held up with the rest4 #i4 tenalk'ya all but all are held up with the rest4 #aj4 stem'thila all the fingers4 #aa4 stem'thla topay'thl'tona all the fingers and another over above held4 ,the process of formation indicated in #aa is used in the succeeding numerals up to #ai4 #bj4 kwillik'ynstem'thlan two times all the fingers4 #ajj4 ssistem'thlak'ya the fingers all the fingers4 #ajjj4 ssistem'thlanak'ynstem'thla the fingers all the fingers times all the fingers4 ,the only numerals calling for any special note are those for #aa and #i4 ,for #i we should naturally expect a word corresponding in structure and meaning to the words for #g and #h4 ,but instead of the four brought to and held up with the rest1 for which we naturally look1 the ,zui1 to show that he has used all of his fingers but one1 says all but all are held up with the rest4 ,to express #aa he cannot use a similar form of composition1 since he has already used it in constructing his word for #f1 so he says all the fingers and another over above held4 ,the one remarkable point to be noted about the ,zui scale is1 after all1 the formation of the words for #a and #b4 ,while the savage almost always counts on his fingers1 it does not seem at all certain that these words would necessarily be of finger formation4 ,the savage can always distinguish between one object and two objects1 and it is hardly reasonable to believe that any external aid is needed to arrive at a distinct perception of this difference4 ,the numerals for #a and #b would be the earliest to be formed in any language1 and in most1 if not all1 cases they would be formed long before the need would be felt for terms to describe any higher number4 ,if this theory be correct1 we should expect to find finger names for numerals beginning not lower than #c1 and oftener with #e than with any other number4 ,the highest authority has ventured the assertion that all numeral words have their origin in the names of the fingers2#fi substantially the same conclusion was reached by ,professor ,pott1 of ,halle1 whose work on numeral nomenclature led him deeply into the study of the origin of these words4 ,but we have abundant evidence at hand to show that1 universal as finger counting has been1 finger origin for numeral words has by no means been universal4 ,that it is more frequently met with than any other origin is unquestionably true2 but in many instances1 which will be more fully considered in the following chapter1 we find strictly non-digital derivations1 especially in the case of the lowest members of the scale4 ,but in nearly all languages the origin of the words for #a1 #b1 #c1 and #d are so entirely unknown that speculation respecting them is almost useless4 ,an excellent illustration of the ordinary method of formation which obtains among number scales is furnished by the ,eskimos of ,point ,barrow1#gj who have pure numeral words up to #e1 and then begin a systematic course of word formation from the names of their fingers4 ,if the names of the first five numerals are of finger origin1 they have so completely lost their original form1 or else the names of the fingers themselves have so changed1 that no resemblance is now to be detected between them4 ,this scale is so interesting that it is given with considerable fulness1 as follows3 #a4 atauzik4 #b4 madro4 #c4 pinasun4 #d4 sisaman4 #e4 tudlemut4 #f4 atautyimin akbinigin tudlimu7t7 #e and #a on the next4 #g4 madronin akbinigin twice on the next4 #h4 pinasunin akbinigin three times on the next4 #i4 kodlinotaila that which has not its #aj4 #aj4 kodlin the upper part--i4e4 the fingers4 #ad4 akimiaxotaityuna ,i have not #ae4 #ae4 akimia4 ,this seems to be a real numeral word4 #bj4 inyuina a man come to an end4 #be4 inyuina tudlimunin akbinidigin a man come to an end and #e on the next4 #cj4 inyuina kodlinin akbinidigin a man come to an end and #aj on the next4 #ce4 inyuina akimiamin aipalin a man come to an end accompanied by #a fifteen times4 #dj4 madro inyuina #b men come to an end4 ,in this scale we find the finger origin appearing so clearly and so repeatedly that one feels some degree of surprise at finding #e expressed by a pure numeral instead of by some word meaning hand or fingers of one hand4 ,in this respect the ,eskimo dialects are somewhat exceptional among scales built up of digital words4 ,the system of the ,greenland ,eskimos1 though differing slightly from that of their ,point ,barrow cousins1 shows the same peculiarity4 ,the first ten numerals of this scale are3#ga #a4 atausek4 #b4 mardluk4 #c4 pingasut4 #d4 sisamat4 #e4 tatdlimat4 #f4 arfinek-atausek to the other hand #a4 #g4 arfinek-mardluk to the other hand #b4 #h4 arfinek-pingasut to the other hand #c4 #i4 arfinek-sisamat to the other hand #d4 #aj4 kulit4 ,the same process is now repeated1 only the feet instead of the hands are used2 and the completion of the second #aj is marked by the word innuk1 man4 ,it may be that the ,eskimo word for #e is1 originally1 a digital word1 but if so1 the fact has not yet been detected4 ,from the analogy furnished by other languages we are justified in suspecting that this may be the case2 for whenever a number system contains digital words1 we expect them to begin with five1 as1 for example1 in the ,arawak scale1#gb which runs3 #a4 abba4 #b4 biama4 #c4 kabbuhin4 #d4 bibiti4 #e4 abbatekkbe #a hand4 #f4 abbatiman #a of the other4 #g4 biamattiman #b of the other4 #h4 kabbuhintiman #c of the other4 #i4 bibitiman #d of the other4 #aj4 biamantekbbe #b hands4 #aa4 abba kutihibena #a from the feet4 #bj4 abba lukku hands feet4 ,the four sets of numerals just given may be regarded as typifying one of the most common forms of primitive counting2 and the words they contain serve as illustrations of the means which go to make up the number scales of savage races4 ,frequently the finger and toe origin of numerals is perfectly apparent1 as in the ,arawak system just given1 which exhibits the simplest and clearest possible method of formation4 ,another even more interesting system is that of the ,montagnais of northern ,canada4#gc ,here1 as in the ,zui scale1 the words are digital from the outset4 #a4 inl'are the end is bent4 #b4 nak'e another is bent4 #c4 t'are the middle is bent4 #d4 dinri there are no more except this4 #e4 se-sunla-re the row on the hand4 #f4 elkke-t'are #c from each side4 #g4 t'a-ye-oyertan there are still #c of them4 inl'as dinri on one side there are #d of them4 #h4 elkke-dinri #d on each side4 #i4 inl'a-ye-oyert'an there is still #a more4 #aj4 onernan finished on each side4 #aa4 onernan inl'are ttcharidhel #a complete and #a4 #ab4 onernan nak'e ttcharidhel #a complete and #b1 etc4 ,the formation of #f1 #g1 and #h of this scale is somewhat different from that ordinarily found4 ,to express #f1 the ,montagnais separates the thumb and forefinger from the three remaining fingers of the left hand1 and bringing the thumb of the right hand close to them1 says3 #c from each side4 ,for #g he either subtracts from #aj1 saying3 there are still #c of them1 or he brings the thumb and forefinger of the right hand up to the thumb of the left1 and says3 on one side there are #d of them4 ,he calls #h by the same name as many of the other ,canadian tribes1 that is1 two #d's2 and to show the proper number of fingers1 he closes the thumb and little finger of the right hand1 and then puts the three remaining fingers beside the thumb of the left hand4 ,this method is1 in some of these particulars1 different from any other ,i have ever examined4 ,it often happens that the composition of numeral words is less easily understood1 and the original meanings more difficult to recover1 than in the examples already given4 ,but in searching for number systems which show in the formation of their words the influence of finger counting1 it is not unusual to find those in which the derivation from native words signifying finger1 hand1 toe1 foot1 and man1 is just as frankly obvious as in the case of the ,zui1 the ,arawak1 the ,eskimo1 or the ,montagnais scale4 ,among the ,tamanacs1#gd one of the numerous ,indian tribes of the ,orinoco1 the numerals are as strictly digital as in any of the systems already examined4 ,the general structure of the ,tamanac scale is shown by the following numerals3 #e4 amgnaitone #a hand complete4 #f4 itacono amgna pona tevinitpe #a on the other hand4 #aj4 amgna aceponare all of the #b hands4 #aa4 puitta pona tevinitpe #a on the foot4 #af4 itacono puitta pona tevinitpe #a on the other foot4 #bj4 tevin itoto #a man4 #ba4 itacono itoto jamgnar bona tevinitpe #a on the hands of another man4 ,in the ,guarani#ge language of ,paraguay the same method is found1 with a different form of expression for #bj4 ,here the numerals in question are #e4 asepopetei one hand4 #aj4 asepomokoi two hands4 #bj4 asepo asepi abe hands and feet4 ,another slight variation is furnished by the ,kiriri language1#gf which is also one of the numerous ,south ,american ,indian forms of speech1 where we find the words to be #e4 mi biche misa one hand4 #aj4 mikriba misa sai both hands4 #bj4 mikriba misa idecho ibi sai both hands together with the feet4 ,illustrations of this kind might be multiplied almost indefinitely2 and it is well to note that they may be drawn from all parts of the world4 ,south ,america is peculiarly rich in native numeral words of this kind2 and1 as the examples above cited show1 it is the field to which one instinctively turns when this subject is under discussion4 ,the ,zamuco numerals are1 among others1 exceedingly interesting1 giving us still a new variation in method4 ,they are#gg #a4 tsomara4 #b4 gar4 #c4 gadiok4 #d4 gahagani4 #e4 tsuena yimana-ite ended #a hand4 #f4 tsomara-hi #a on the other4 #g4 gari-hi #b on the other4 #h4 gadiog-ihi #c on the other4 #i4 gahagani-hi #d on the other4 #aj4 tsuena yimana-die ended both hands4 #aa4 tsomara yiri-tie #a on the foot4 #ab4 gar yiritie #b on the foot4 #bj4 tsuena yiri-die ended both feet4 ,as is here indicated1 the form of progression from #e to #aj1 which we should expect to be hand-#a1 or hand-and-#a1 or some kindred expression1 signifying that one hand had been completed1 is simply #a on the other4 ,again1 the expressions for #aa1 #ab1 etc41 are merely #a on the foot1 #b on the foot1 etc41 while #bj is both feet ended4 ,an equally interesting scale is furnished by the language of the ,maipures#gh of the ,orinoco1 who count #a4 papita4 #b4 avanume4 #c4 apekiva4 #d4 apekipaki4 #e4 papitaerri capiti #a only hand4 #f4 papita yana pauria capiti purena #a of the other hand we take4 #aj4 apanumerri capiti #b hands4 #aa4 papita yana kiti purena #a of the toes we take4 #bj4 papita camonee #a man4 #dj4 avanume camonee #b men4 #fj4 apekiva camonee #c men1 etc4 ,in all the examples thus far given1 #bj is expressed either by the equivalent of man or by some formula introducing the word feet4 ,both these modes of expressing what our own ancestors termed a score1 are so common that one hesitates to say which is of the more frequent use4 ,the following scale1 from one of the ,betoya dialects#gi of ,south ,america1 is quite remarkable among digital scales1 making no use of either man or foot1 but reckoning solely by fives1 or hands1 as the numerals indicate4 #a4 tey4 #b4 cayapa4 #c4 toazumba4 #d4 cajezea #b with plural termination4 #e4 teente hand4 #f4 teyentetey hand #a4 #g4 teyente cayapa hand #b4 #h4 teyente toazumba hand #c4 #i4 teyente caesea hand #d4 #aj4 caya ente1 or caya huena #b hands4 #aa4 caya ente-tey #b hands #a4 #ae4 toazumba-ente #c hands4 #af4 toazumba-ente-tey #c hands #a4 #bj4 caesea ente #d hands4 ,in the last chapter mention was made of the scanty numeral systems of the ,australian tribes1 but a single scale was alluded to as reaching the comparatively high limit of #bj4 ,this system is that belonging to the ,pikumbuls1#hj and the count runs thus3 #a4 mal4 #b4 bular4 #c4 guliba4 #d4 bularbular #b-b4 #e4 mulanbu4 #f4 malmulanbu mummi #a and #e added on4 #g4 bularmulanbu mummi #b and #e added on4 #h4 gulibamulanbu mummi #c and #e added on4 #i4 bularbularmulanbu mummi #d and #e added on4 #aj4 bularin murra belonging to the #b hands4 #aa4 maldinna mummi #a of the toes added on 7to the #aj fingers74 #ab4 bular dinna mummi #b of the toes added on4 #ac4 guliba dinna mummi #c of the toes added on4 #ad4 bular bular dinna mummi #d of the toes added on4 #ae4 mulanba dinna #e of the toes added on4 #af4 mal dinna mulanbu #a and #e toes4 #ag4 bular dinna mulanbu #b and #e toes4 #ah4 guliba dinna mulanbu #c and #e toes4 #ai4 bular bular dinna mulanbu #d and #e toes4 #bj4 bularin dinna belonging to the #b feet4 ,as has already been stated1 there is good ground for believing that this system was originally as limited as those obtained from other ,australian tribes1 and that its extension from #d1 or perhaps from #e onward1 is of comparatively recent date4 ,a somewhat peculiar numeral nomenclature is found in the language of the ,klamath ,indians of ,oregon4 ,the first ten words in the ,klamath scale are3#ha #a4 nash1 or nas4 #b4 lap hand4 #c4 ndan4 #d4 vunep hand up4 #e4 tunep hand away4 #f4 nadshkshapta #a ,i have bent over4 #g4 lapkshapta #b ,i have bent over4 #h4 ndankshapta #c ,i have bent over4 #i4 nadshskeksh #a left over4 #aj4 taunep hand hand8 ,in describing this system ,mr4 ,gatschet says3 ,if the origin of the ,klamath numerals is thus correctly traced1 their inventors must have counted only the four long fingers without the thumb1 and #e was counted while saying hand away6 hand off6 ,the 'four1' or hand high6 hand up6 intimates that the hand was held up high after counting its four digits2 and some term expressing this gesture was1 in the case of nine1 substituted by 'one left over' 444 which means to say1 'only one is left until all the fingers are counted4' ,it will be observed that the ,klamath introduces not only the ordinary finger manipulation1 but a gesture of the entire hand as well4 ,it is a common thing to find something of the kind to indicate the completion of #e or #aj1 and in one or two instances it has already been alluded to4 ,sometimes one or both of the closed fists are held up2 sometimes the open hand1 with all the fingers extended1 is used2 and sometimes an entirely independent gesture is introduced4 ,these are1 in general1 of no special importance2 but one custom in vogue among some of the prairie tribes of ,indians1 to which my attention was called by ,dr4 ,j4 ,owen ,dorsey1#hb should be mentioned4 ,it is a gesture which signifies multiplication1 and is performed by throwing the hand to the left4 ,thus1 after counting #e1 a wave of the hand to the left means #ej4 ,as multiplication is rather unusual among savage tribes1 this is noteworthy1 and would seem to indicate on the part of the ,indian a higher degree of intelligence than is ordinarily possessed by uncivilized races4 ,in the numeral scale as we possess it in ,english1 we find it necessary to retain the name of the last unit of each kind used1 in order to describe definitely any numeral employed4 ,thus1 fifteen1 one hundred forty-two1 six thousand seven hundred twenty-seven1 give in full detail the numbers they are intended to describe4 ,in primitive scales this is not always considered necessary2 thus1 the ,zamucos express their teens without using their word for #aj at all4 ,they say simply1 #a on the foot1 #b on the foot1 etc4 ,corresponding abbreviations are often met2 so often1 indeed1 that no further mention of them is needed4 ,they mark one extreme1 the extreme of brevity1 found in the savage method of building up hand1 foot1 and finger names for numerals2 while the ,zui scale marks the extreme of prolixity in the formation of such words4 ,a somewhat ruder composition than any yet noticed is shown in the numerals of the ,vilelo scale1#hc which are3 #a4 agit1 or yaagit4 #b4 uke4 #c4 nipetuei4 #d4 yepkatalet4 #e4 isig-nisle-yaagit hand fingers #a4 #f4 isig-teet-yaagit hand with #a4 #g4 isig-teet-uke hand with #b4 #h4 isig-teet-nipetuei hand with #c4 #i4 isig-teet-yepkatalet hand with #d4 #aj4 isig-uke-nisle second hand fingers 7lit4 hand-two-fingers74 #aa4 isig-uke-nisle-teet-yaagit second hand fingers with #a4 #bj4 isig-ape-nisle-lauel hand foot fingers all4 ,in the examples thus far given1 it will be noticed that the actual names of individual fingers do not appear4 ,in general1 such words as thumb1 forefinger1 little finger1 are not found1 but rather the hand-#a1 #a on the next1 or #a over and above1 which we have already seen1 are the type forms for which we are to look4 ,individual finger names do occur1 however1 as in the scale of the ,hudson's ,bay ,eskimos1#hd where the three following words are used both as numerals and as finger names3 #h4 kittukleemoot middle finger4 #i4 mikkeelukkamoot fourth finger4 #aj4 eerkitkoka little finger4 ,words of similar origin are found in the original ,jiviro scale1#he where the native numerals are3 #a4 ala4 #b4 catu4 #c4 cala4 #d4 encatu4 #e4 alactegladu #a hand4 #f4 intimutu thumb 7of second hand74 #g4 tannituna index finger4 #h4 tannituna cabiasu the finger next the index finger4 #i4 bitin tegla cabiasu hand next to complete4 #aj4 catgladu #b hands4 ,as if to emphasize the rarity of this method of forming numerals1 the ,jiviros afterward discarded the last five of the above scale1 replacing them by words borrowed from the ,quichuas1 or ancient ,peruvians4 ,the same process may have been followed by other tribes1 and in this way numerals which were originally digital may have disappeared4 ,but we have no evidence that this has ever happened in any extensive manner4 ,we are1 rather1 impelled to accept the occasional numerals of this class as exceptions to the general rule1 until we have at our disposal further evidence of an exact and critical nature1 which would cause us to modify this opinion4 ,an elaborate philological study by ,dr4 ,j4,h4 ,trumbull#hf of the numerals used by many of the ,north ,american ,indian tribes reveals the presence in the languages of these tribes of a few1 but only a few1 finger names which are used without change as numeral expressions also4 ,sometimes the finger gives a name not its own to the numeral with which it is associated in counting--as in the ,chippeway dialect1 which has nawi-nindj1 middle of the hand1 and nisswi1 #c2 and the ,cheyenne1 where notoyos1 middle finger1 and na-nohhtu1 #h1 are closely related4 ,in other parts of the world isolated examples of the transference of finger names to numerals are also found4 ,of these a well-known example is furnished by the ,zulu numerals1 where tatisitupa1 taking the thumb1 becomes a numeral for six4 ,then the verb komba1 to point1 indicating the forefinger1 or 'pointer1' makes the next numeral1 seven4 ,thus1 answering the question1 ',how much did your master give you8' a ,zulu would say1 ',u kombile1' ',he pointed with his forefinger1' i4e4 ',he gave me seven'2 and this curious way of using the numeral verb is also shown in such an example as 'amahasi akombile1' 'the horses have pointed1' i4e4 'there were seven of them4' ,in like manner1 ,kijangalobili1 'keep back two fingers1' i4e4 eight1 and ,kijangalolunje1 'keep back one finger1' i4e4 nine1 lead on to kumi1 ten4#hg ,returning for a moment to the consideration of number systems in the formation of which the influence of the hand has been paramount1 we find still further variations of the method already noticed of constructing names for the fives1 tens1 and twenties1 as well as for the intermediate numbers4 ,instead of the simple words hand1 foot1 etc41 we not infrequently meet with some paraphrase for one or for all these terms1 the derivation of which is unmistakable4 ,the ,nengones1#hh an island tribe of the ,indian ,ocean1 though using the word man for #bj1 do not employ explicit hand or foot words1 but count #a4 sa4 #b4 rewe4 #c4 tini4 #d4 etse4 #e4 se dono the end 7of the first hand74 #f4 dono ne sa end and #a4 #g4 dono ne rewe end and #b4 #h4 dono ne tini end and #c4 #i4 dono ne etse end and #d4 #aj4 rewe tubenine #b series 7of fingers74 #aa4 rewe tubenine ne sa re tsemene #b series and #a on the next8 #bj4 sa re nome #a man4 #cj4 sa re nome ne rewe tubenine #a man and #b series4 #dj4 rewe ne nome #b men4 ,examples like the above are not infrequent4 ,the ,aztecs used for #aj the word matlactli1 hand-half1 i4e4 the hand half of a man1 and for #bj cempoalli1 one counting4#hi ,the ,point ,barrow ,eskimos call #aj kodlin1 the upper part1 i4e4 of a man4 ,one of the ,ewe dialects of ,western ,africa#ij has ewo1 done1 for #aj2 while1 curiously enough1 #i1 asieke1 is a digital word1 meaning to part 7from7 the hand4 ,in numerous instances also some characteristic word not of hand derivation is found1 like the ,yoruba ogodzi1 string1 which becomes a numeral for #dj1 because #dj cowries made a string2 and the ,maori tekau1 bunch1 which signifies #aj4 ,the origin of this seems to have been the custom of counting yams and fish by bunches of ten each4#ia ,another method of forming numeral words above #e or #aj is found in the presence of such expressions as second #a1 second #b1 etc4 ,in languages of rude construction and incomplete development the simple numeral scale is often found to end with #e1 and all succeeding numerals to be formed from the first #e4 ,the progression from that point may be #e-a1 #e-b1 etc41 as in the numerous quinary scales to be noticed later1 or it may be second #a1 second #b1 etc41 as in the ,niam ,niam dialect of ,central ,africa1 where the 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 ,that this method of progression is not confined to the least developed languages1 however1 is shown by a most cursory examination of the numerals of our ,american ,indian tribes1 where numeral formation like that exhibited above is exceedingly common4 ,in the ,kootenay dialect1#ic of ,british ,columbia1 qaetsa1 #d1 and wo-qaetsa1 #h1 are obviously related1 the latter word probably meaning a second #d4 ,most of the native languages of ,british ,columbia form their words for #g and #h from those which signify #b and #c2 as1 for example1 the ,heiltsuk1#id which shows in the following words a most obvious correspondence3 #b4 matl4 #g4 matlaaus4 #c4 yutq4 #h4 yutquaus4 ,in the ,choctaw language#ie the relation between #b and #g1 and #c and #h1 is no less clear4 ,here the words are3 #b4 tuklo4 #g4 untuklo4 #c4 tuchina4 #h4 untuchina4 ,the ,nez ,percs#if repeat the first three words of their scale in their #f1 #g1 and #h respectively1 as a comparison of these numerals will show4 #a4 naks4 #f4 oilaks4 #b4 lapit4 #g4 oinapt4 #c4 mitat4 #h4 oimatat4 ,in all these cases the essential point of the method is contained in the repetition1 in one way or another1 of the numerals of the second quinate1 without the use with each one of the word for #e4 ,this may make #f1 #g1 #h1 and #i appear as second #a1 second #b1 etc41 or another #a1 another #b1 etc42 or1 more simply still1 as #a more1 #b more1 etc4 ,it is the method which was briefly discussed in the early part of the present chapter1 and is by no means uncommon4 ,in a decimal scale this repetition would begin with #aa instead of #f2 as in the system found in use in ,tagala and ,pampanaga1 two of the ,philippine ,islands1 where1 for example1 #aa1 #ab1 and #ac are3#ig #aa4 labi-n-isa over #a4 #ab4 labi-n-dalaua over #b4 #ac4 labi-n-tatlo over #c4 ,a precisely similar method of numeral building is used by some of our ,western ,indian tribes4 ,selecting a few of the ,assiniboine numerals#ih as an illustration1 we have #aa4 ak kai washe more #a4 #ab4 ak kai noom pah more #b4 #ac4 ak kai yam me nee more #c4 #ad4 ak kai to pah more #d4 #ae4 ak kai zap tah more #e4 #af4 ak kai shak pah more #f1 etc4 ,a still more primitive structure is shown in the numerals of the ,mboushas#ii of ,equatorial ,africa4 ,instead of using #e-a1 #e-b1 #e-c1 #e-d1 or #b;d #a1 #b;d #b1 #b;d #c1 #b;d #d1 in forming their numerals from #f to #i1 they proceed in the following remarkable and1 at first thought1 inexplicable manner to form their compound numerals3 #a4 ivoco4 #b4 beba4 #c4 belalo4 #d4 benai4 #e4 betano4 #f4 ivoco beba #a-b4 #g4 ivoco belalo #a-c4 #h4 ivoco benai #a-d4 #i4 ivoco betano #a-e4 #aj4 dioum4 ,no explanation is given by ,mr4 du ,chaillu for such an apparently incomprehensible form of expression as1 for example1 #a-c1 for #g4 ,some peculiar finger pantomime may accompany the counting1 which1 were it known1 would enlighten us on the ,mbousha's method of arriving at so anomalous a scale4 ,mere repetition in the second quinate of the words used in the first might readily be explained by supposing the use of fingers absolutely indispensable as an aid to counting1 and that a certain word would have one meaning when associated with a certain finger of the left hand1 and another meaning when associated with one of the fingers of the right4 ,such scales are1 if the following are correct1 actually in existence among the islands of the ,pacific4 ,,balad4#ajj ,,uea4#ajj #a4 parai4 #a4 tahi4 #b4 paroo4 #b4 lua4 #c4 pargen4 #c4 tolu4 #d4 parbai4 #d4 fa4 #e4 panim4 #e4 lima4 #f4 parai4 #f4 tahi4 #g4 paroo4 #g4 lua4 #h4 pargen4 #h4 tolu4 #i4 parbai4 #i4 fa4 #aj4 panim4 #aj4 lima4 ,such examples are1 ,i believe1 entirely unique among primitive number systems4 ,in numeral scales where the formative process has been of the general nature just exhibited1 irregularities of various kinds are of frequent occurrence4 ,hand numerals may appear1 and then suddenly disappear1 just where we should look for them with the greatest degree of certainty4 ,in the ,ende1#aja a dialect of the ,flores ,islands1 #e1 #f1 and #g are of hand formation1 while #h and #i are of entirely different origin1 as the scale shows4 #a4 sa4 #b4 zua4 #c4 telu4 #d4 wutu4 #e4 lima #f4 lima sa hand #a4 #g4 lima zua hand #b4 #h4 rua butu #b #d4 #i4 trasa #aj - #a8 #aj4 sabulu4 ,one special point to be noticed in this scale is the irregularity that prevails between #g1 #h1 #i4 ,the formation of #g is of the most ordinary kind2 #h is #b fours--common enough duplication2 while #i appears to be #aj - #a4 ,all of these modes of compounding are1 in their own way1 regular2 but the irregularity consists in using all three of them in connective numerals in the same system4 ,but1 odd as this jumble seems1 it is more than matched by that found in the scale of the ,karankawa ,indians1#ajb an extinct tribe formerly inhabiting the coast region of ,texas4 ,the first ten numerals of this singular array are3 #a4 natsa4 #b4 haikia4 #c4 kachayi4 #d4 hayo hakn #b #b4 #e4 natsa behema #a father1 i4e4 of the fingers4 #f4 hayo haikia #c #b8 #g4 haikia natsa #b #e8 #h4 haikia behema #b fathers8 #i4 haikia doatn #b;d from #aj8 #aj4 doatn habe4 ,systems like the above1 where chaos instead of order seems to be the ruling principle1 are of occasional occurrence1 but they are decidedly the exception4 ,in some of the cases that have been adduced for illustration it is to be noticed that the process of combination begins with #g instead of with #f4 ,among others1 the scale of the ,pigmies of ,central ,africa#ajc and that of the ,mosquitos#ajd of ,central ,america show this tendency4 ,in the ,pigmy scale the words for #a and #f are so closely akin that one cannot resist the impression that #f was to them a new #a1 and was thus named4 ,,mosquito4 ,,pigmy4 #a4 kumi4 ujju4 #b4 wal4 ibari4 #c4 niupa4 ikaro4 #d4 wal-wal #b-b4 ikwanganya4 #e4 mata-sip fingers of #a hand4 bumuti4 #f4 matlalkabe4 ijju4 #g4 matlalkabe pura kumi #f and #a4 bumutti-na-ibali #e and #b4 #h4 matlalkabe pura wal #f and #b4 bumutti-na-ikaro #e and #c4 #i4 matlalkabe pura niupa #f and #c4 bumutti-na-ikwanganya #e and #d4 #aj4 mata wal sip fingers of #b hands4 mabo half man4 ,the ,mosquito scale is quite exceptional in forming #g1 #h1 and #i from #f1 instead of from #e4 ,the usual method1 where combinations appear between #f and #aj1 is exhibited by the ,pigmy scale4 ,still another species of numeral form1 quite different from any that have already been noticed1 is found in the ,yoruba#aje scale1 which is in many respects one of the most peculiar in existence4 ,here the words for #aa1 #ab1 etc41 are formed by adding the suffix -la1 great1 to the words for #a1 #b1 etc41 thus3 #a4 eni1 or okan4 #b4 edzi4 #c4 eta4 #d4 erin4 #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 erinla great #d1 etc4 #dj4 ogodzi string4 #bjj4 igba heap4 ,the word for #dj was adopted because cowrie shells1 which are used for counting1 were strung by forties2 and igba1 #bjj1 because a heap of #bjj shells was five strings1 and thus formed a convenient higher unit for reckoning4 ,proceeding in this curious manner1#ajf they called #ej strings #a afo or head2 and to illustrate their singular mode of reckoning--the king of the ,dahomans1 having made war on the ,yorubans1 and attacked their army1 was repulsed and defeated with a loss of two heads1 twenty strings1 and twenty cowries of men1 or #dhbj4 ,the number scale of the ,abipones1#ajg one of the low tribes of the ,paraguay region1 contains two genuine curiosities1 and by reason of those it deserves a place among any collection of numeral scales designed to exhibit the formation of this class of words4 ,it is3 #a4 initara #a alone4 #b4 inoaka4 #c4 inoaka yekaini #b and #a4 #d4 geyenknate toes of an ostrich4 #e4 neenhalek a five coloured1 spotted hide1 or hanambegen fingers of #a hand4 #aj4 lanamrihegem fingers of both hands4 #bj4 lanamrihegem cat gracherhaka anamichirihegem fingers of both hands together with toes of both feet4 ,that the number sense of the ,abipones is but little1 if at all1 above that of the native ,australian tribes1 is shown by their expressing #c by the combination #b and #a4 ,this limitation1 as we have already seen1 is shared by the ,botocudos1 the ,chiquitos1 and many of the other native races of ,south ,america4 ,but the ,abipones1 in seeking for words with which to enable themselves to pass beyond the limit #c1 invented the singular terms just given for #d and #e4 ,the ostrich1 having three toes in front and one behind on each foot presented them with a living example of #c #a2 hence toes of an ostrich became their numeral for #d4 ,similarly1 the number of colours in a certain hide being five1 the name for that hide was adopted as their next numeral4 ,at this point they began to resort to digital numeration also2 and any higher number is expressed by that method4 ,in the sense in which the word is defined by mathematicians1 number is a pure1 abstract concept4 ,but a moment's reflection will show that1 as it originates among savage races1 number is1 and from the limitations of their intellect must be1 entirely concrete4 ,an abstract conception is something quite foreign to the essentially primitive mind1 as missionaries and explorers have found to their chagrin4 ,the savage can form no mental concept of what civilized man means by such a word as soul2 nor would his idea of the abstract number #e be much clearer4 ,when he says five1 he uses1 in many cases at least1 the same word that serves him when he wishes to say hand2 and his mental concept when he says five is of a hand4 ,the concrete idea of a closed fist or an open hand with outstretched fingers1 is what is upper-most in his mind4 ,he knows no more and cares no more about the pure number #e than he does about the law of the conservation of energy4 ,he sees in his mental picture only the real1 material image1 and his only comprehension of the number is1 these objects are as many as the fingers on my hand4 ,then1 in the lapse of the long interval of centuries which intervene between lowest barbarism and highest civilization1 the abstract and the concrete become slowly dissociated1 the one from the other4 ,first the actual hand picture fades away1 and the number is recognized without the original assistance furnished by the derivation of the word4 ,but the number is still for a long time a certain number of objects1 and not an independent concept4 ,it is only when the savage ceases to be wholly an animal1 and becomes a thinking human being1 that number in the abstract can come within the grasp of his mind4 ,it is at this point that mere reckoning ceases1 and arithmetic begins4 ,,chapter ,,iv4 ,,the ,,origin ,,of ,,number ,,words4 7,,continued47 ,by the slow1 and often painful1 process incident to the extension and development of any mental conception in a mind wholly unused to abstractions1 the savage gropes his way onward in his counting from #a1 or more probably from #b1 to the various higher numbers required to form his scale4 ,the perception of unity offers no difficulty to his mind1 though he is conscious at first of the object itself rather than of any idea of number associated with it4 ,the concept of duality1 also1 is grasped with perfect readiness4 ,this concept is1 in its simplest form1 presented to the mind as soon as the individual distinguishes himself from another person1 though the idea is still essentially concrete4 ,perhaps the first glimmering of any real number thought in connection with #b comes when the savage contrasts one single object with another--or1 in other words1 when he first recognizes the pair4 ,at first the individuals composing the pair are simply this one1 and that one1 or this and that2 and his number system now halts for a time at the stage when he can1 rudely enough it may be1 count #a1 #b1 many4 ,there are certain cases where the forms of #a and #b are so similar than one may readily imagine that these numbers really were this and that in the savage's original conception of them2 and the same likeness also occurs in the words for #c and #d1 which may readily enough have been a second this and a second that4 ,in the ,lushu tongue the words for #a and #b are tizi and tazi respectively4 ,in ,koriak we find ngroka1 #c1 and ngraka1 #d2 in ,kolyma1 niyokh1 #c1 and niyakh1 #d2 and in ,kamtschatkan1 tsuk1 #c1 and tsaak1 #d4ajh ,sometimes1 as in the case of the ,australian races1 the entire extent of the count is carried through by means of pairs4 ,but the natural theory one would form is1 that #b is the halting place for a very long time2 that up to this point the fingers may or may not have been used--probably not2 and that when the next start is made1 and #c1 #d1 #e1 and so on are counted1 the fingers first come into requisition4 ,if the grammatical structure of the earlier languages of the world's history is examined1 the student is struck with the prevalence of the dual number in them--something which tends to disappear as language undergoes extended development4 ,the dual number points unequivocally to the time when #a and #b were the numbers at mankind's disposal2 to the time when his three numeral concepts1 #a1 #b1 many1 each demanded distinct expression4 ,with increasing knowledge the necessity for this differentiatuin would pass away1 and but two numbers1 singular and plural1 would remain4 ,incidentally it is to be noticed that the ,indo-,european words for #c--three1 trois1 drei1 tres1 tri1 etc41 have the same root as the ,latin trans1 beyond1 and give us a hint of the time when our ,aryan ancestors counted in the manner ,i have just described4 ,the first real difficulty which the savage experiences in counting1 the difficulty which comes when he attempts to pass beyond #b1 and to count #c1 #d1 and #e1 is of course but slight2 and these numbers are commonly used and readily understood by almost all tribes1 no matter how deeply sunk in barbarism we find them4 ,but the instances that have already been cited must not be forgotten4 ,the ,chiquitos do not1 in their primitive state1 properly count at all2 the ,andamans1 the ,veddas1 and many of the ,australian tribes have no numerals higher than #b2 others of the ,australians and many of the ,south ,americans stop with #c or #d2 and tribes which make #e their limit are still more numerous4 ,hence it is safe to assert that even this insignificant number is not always reached with perfect ease4 ,beyond #e primitive man often proceeds with the greatest difficulty4 ,most savages1 even those of the tribes just mentioned1 can really count above here1 even though they have no words with which to express their thought4 ,but they do it with reluctance1 and as they go on they quickly lose all sense of accuracy4 ,this has already been commented on1 but to emphasize it afresh the well-known example given by ,mr4 ,oldfield from his own experience among the ,watchandies may be quoted4#aji ,i once wished to ascertain the exact number of natives who had been slain on a certain occasion4 ,the individual of whom ,i made the inquiry began to think over the names 444 assigning one of his fingers to each1 and it was not until after many failures1 and consequent fresh starts1 that he was able to express so high a number1 which he at length did by holding up his hand three times1 thus giving me to understand that fifteen was the answer to this most difficult arithmetical question4 ,this meagreness of knowledge in all things pertaining to numbers is often found to be sharply emphasized in the names adopted by savages for their numeral words4 ,while discussing in a previous chapter the limits of number systems1 we found many instances where anything above #b or #c was designated by some one of the comprehensive terms much1 many1 very many2 these words1 or such equivalents as lot1 heap1 or plenty1 serving as an aid to the finger pantomime necessary to indicate numbers for which they have no real names4 ,the low degree of intelligence and civilization revealed by such words is brought quite as sharply into prominence by the word occasionally found for #e4 ,whenever the fingers and hands are used at all1 it would seem natural to expect for #e some general expression signifying hand1 for #aj both hands1 and for #bj man4 ,such is1 as we have already seen1 the ordinary method of progression1 but it is not universal4 ,a drop in the scale of civilization takes us to a point where #aj1 instead of #bj1 becomes the whole man4 ,the ,kusaies1#aaj of ,strong's ,island1 call #aj sie-nul1 #a man1 #cj tol-nul1 #c men1 #dj a naul1 #d men1 etc42 and the ,ku-,mbutti#aaa of central ,africa have mukko1 #aj1 and moku1 man4 ,if #aj is to be expressed by reference to the man1 instead of his hands1 it might appear more natural to employ some such expression as that adopted by the ,african ,pigmies1#aab who call #aj mabo1 and man mabo-mabo4 ,with them1 then1 #aj is perhaps half a man1 as it actually is among the ,towkas of ,south ,america2 and we have already seen that with the ,aztecs it was matlactli1 the hand half of a man4#aac ,the same idea crops out in the expression used by the ,nicobar ,islanders for #cj--;heam-umdjome ruktei1 #a man 7and a7 half4#aad ,such nomenclature is entirely natural1 and it accords with the analogy offered by other words of frequent occurrence in the numeral scales of savage races4 ,still1 to find #aj expressed by the term man always conveys an impression of mental poverty2 though it may1 of course1 be urged that this might arise from the fact that some races never use the toes in counting1 but go over the fingers again1 or perhaps bring into requisition the fingers of a second man to express the second #aj4 ,it is not safe to postulate an extremely low degree of civilization from the presence of certain peculiarities of numeral formation4 ,only the most general statements can be ventured on1 and these are always subject to modification through some circumstance connected with environment1 mode of living1 or intercourse with other tribes4 ,two ,south ,american races may be cited1 which seem in this respect to give unmistakable evidence of being sunk in deepest barbarism4 ,these are the ,juri and the ,cayriri1 who use the same word for man and for #e4 ,the former express #e by ghomen apa1 #a man1#aae and the latter by ibicho1 person4#aaf ,the ,tasmanians of ,oyster ,bay use the native word of similar meaning1 puggana1 man1#aag for #e4 ,wherever the numeral #bj is expressed by the term man1 it may be expected that #dj will be #b men1 #fj1 #c men1 etc4 ,this form of numeration is usually1 though not always1 carried as far as the system extends2 and it sometimes leads to curious terms1 of which a single illustration will suffice4 ,the ,san ,blas ,indians1 like almost all the other ,central and ,south ,american tribes1 count by digit numerals1 and form their twenties as follows3#aah #bj4 tula guena man #a4 #dj4 tula pogua man #b4 #ajj4 tula atala man #e4 #abj4 tula nergua man #f4 #ajjj4 tula wala guena great #a man4 ,the last expression may1 perhaps1 be translated great hundred1 though the literal meaning is the one given4 ,if #aj1 instead of #bj1 is expressed by the word man1 the multiples of #aj follow the law just given for multiples of #bj4 ,this is sufficiently indicated by the ,kusaie scale2 or equally well by the ,api words for #ajj and #bjj1 which are#aai duulimo toromomo #aj times the whole man4 duulimo toromomo va juo #aj times the whole man taken #b times4 ,as an illustration of the legitimate result which is produced by the attempt to express high numbers in this manner the term applied by educated native ,greenlanders#abj for a thousand may be cited4 ,this numeral1 which is1 of course1 not in common use1 is inuit kulit tatdlima nik kuleriartut navdlugit #aj men #e times #aj times come to an end4 ,it is worth noting that the word great1 which appears in the scale of the ,san ,blas ,indians1 is not infrequently made use of in the formation of higher numeral words4 ,the ,african ,mabas#aba call #aj atuk1 great #a2 the ,hottentots#abb and the ,hidatsa ,indians call #ajj great #aj1 their words being gei disi and pitikitstia respectively4 ,the ,nicaraguans#abc express #ajj by guhamba1 great #aj1 and #djj by dinoamba1 great #bj2 and our own familiar word million1 which so many modern languages have borrowed from the ,italian1 is nothing more nor less than a derivative of the ,latin mille1 and really means great thousand4 ,the ,dakota#abd language shows the same origin for its expression of #a1jjj1jjj1 which is kick ta opong wa tunkah1 great #ajjj4 ,the origin of such terms can hardly be ascribed to poverty of language4 ,it is found1 rather1 in the mental association of the larger with the smaller unit1 and the consequent repetition of the name of the smaller4 ,any unit1 whether it be a single thing1 a dozen1 a score1 a hundred1 a thousand1 or any other unit1 is1 whenever used1 a single and complete group2 and where the relation between them is sufficiently close1 as in our gross and great gross1 this form of nomenclature is natural enough to render it a matter of some surprise that it has not been employed more frequently4 ,an old ,english nursery rhyme makes use of this association1 only in a manner precisely the reverse of that which appears now and then in numeral terms4 ,in the latter case the process is always one of enlargement1 and the associative word is great4 ,in the following rhyme1 constructed by the mature for the amusement of the childish mind1 the process is one of diminution1 and the associative word is little3 ,one's none1 ,two's some1 ,three's a many1 ,four's a penny1 ,five's a little hundred4#abe ,any real numeral formation by the use of little1 with the name of some higher unit1 would1 of course1 be impossible4 ,the numeral scale must be complete before the nursery rhyme can be manufactured4 ,it is not to be supposed from the observations that have been made on the formation of savage numeral scales that all1 or even the majority of tribes1 proceed in the awkward and faltering manner indicated by many of the examples quoted4 ,some of the ,north ,american ,indian tribes have numeral scales which are1 as far as they go1 as regular and almost as simple as our own4 ,but where digital numeration is extensively resorted to1 the expressions for higher numbers are likely to become complex1 and to act as a real bar to the extension of the system4 ,the same thing is true1 to an even greater degree1 of tribes whose number sense is so defective that they begin almost from the outset to use combinations4 ,if a savage expresses the number #c by the combination #b-a1 it will at once be suspected that his numerals will1 by the time he reaches #aj or #bj1 become so complex and confused that numbers as high as these will be expressed by finger pantomime rather than by words4 ,such is often the case2 and the comment is frequently made by explorers that the tribes they have visited have no words for numbers higher than #c1 #d1 #e1 #aj1 or #bj1 but that counting is carried beyond that point by the aid of fingers or other objects4 ,so reluctant1 in many cases1 are savages to count by words1 that limits have been assigned for spoken numerals1 which subsequent investigation proved to fall far short of the real extent of the number systems to which they belonged4 ,one of the south-western ,indian tribes of the ,united ,states1 the ,comanches1 was for a time supposed to have no numeral words below #aj1 but to count solely by the use of fingers4 ,but the entire scale of this taciturn tribe was afterward discovered and published4 ,to illustrate the awkward and inconvenient forms of expression which abound in primitive numeral nomenclature1 one has only to draw from such scales as those of the ,zui1 or the ,point ,barrow ,eskimos1 given in the last chapter4 ,terms such as are found there may readily be duplicated from almost any quarter of the globe4 ,the ,soussous of ,sierra ,leone#abf call #ii tongo solo manani nun solo manani1 i4e4 to take 7#aj understood7 #e #d times and #e #d4 ,the ,malagasy expression for #ahcb is#abg roambistelo polo amby valonjato amby arivo1 #b #cj #hjj #ajjj4 ,the ,aztec equivalent for #cii is#abh caxtolli onnauh poalli ipan caxtolli onnaui1 7#ae #d7 #bj #ae #d2 and the ,sioux require for #bi the ponderous combination#abi wick a chimen ne nompah sam pah nep e chu wink a4 ,these terms1 long and awkward as they seem1 are only the legitimate results which arise from combining the names of the higher and lower numbers1 according to the peculiar genius of each language4 ,from some of the ,australian tribes are derived expressions still more complex1 as for #f1 marh-jin-bang-ga-gudjir-gyn1 half the hands and #a2 and for #ae1 marh-jin-belli-belli-gudjir-jina-bang-ga 1 the hand on either side and half the feet4#acj ,the ,mar tribe1 one of the numerous island tribes of ,melanesia1#aca required for a translation of the numeral #ch1 which occurs in ,john v4 #e1 had an infirmity thirty and eight years1 the circumlocution1 one man and both sides five and three4 ,such expressions1 curious as they seem at first thought1 are no more than the natural outgrowth of systems built up by the slow and tedious process which so often obtains among primitive races1 where digit numerals are combined in an almost endless variety of ways1 and where mere reduplication often serves in place of any independent names for higher units4 ,to what extent this may be carried is shown by the language of the ,cayubabi1#acb who have for #aj the word tunca1 and for #ajj and #ajjj the compounds tunca tunca1 and tunca tunca tunca respectively2 or of the ,sapibocones1 who call #aj bururuche1 hand hand1 and #ajj buruche buruche1 hand hand hand hand4#acc ,more remarkable still is the ,ojibwa language1 which continues its numeral scale without limit1 furnishing combinations which are really remarkable2 as1 e4g41 that for #a1jjj1jjj1jjj1 which is me das wac me das wac as he me das wac1#acd #ajjj #ajjj #ajjj4 ,the ,winnebago expression for the same number1#ace ho ke he hhuta hhu chen a ho ke he ka ra pa ne za is no less formidable1 but it has every appearance of being an honest1 native combination4 ,all such primitive terms for larger numbers must1 however1 be received with caution4 ,savages are sometimes eager to display a knowledge they do not possess1 and have been known to invent numeral words on the spot for the sake of carrying their scales to as high a limit as possible4 ,the ,choctaw words for million and billion are obvious attempts to incorporate the corresponding ,english terms into their own language4#acf ,for million they gave the vocabulary-hunter the phrase mil yan chuffa1 and for billion1 bil yan chuffa4 ,the word chuffa signifies #a1 hence these expressions are seen at a glance to be coined solely for the purpose of gratifying a little harmless ,choctaw vanity4 ,but this is innocence itself compared with the fraud perpetrated on ,labillardire by the ,tonga ,islanders1 who supplied the astonished and delighted investigator with a numeral vocabulary up to quadrillions4 ,their real limit was afterward found to be #ajj1jjj1 and above that point they had palmed off as numerals a tolerably complete list of the obscene words of their language1 together with a few nonsense terms4 ,these were all accepted and printed in good faith1 and the humiliating truth was not discovered until years afterward4#acg ,one noteworthy and interesting fact relating to numeral nomenclature is the variation in form which words of this class undergo when applied to different classes of objects4 ,to one accustomed as we are to absolute and unvarying forms for numerals1 this seems at first a novel and almost unaccountable linguistic freak4 ,but it is not uncommon among uncivilized races1 and is extensively employed by so highly enlightened a people1 even1 as the ,japanese4 ,this variation in form is in no way analogous to that produced by inflectional changes1 such as occur in ,hebrew1 ,greek1 ,latin1 etc4 ,it is sufficient in many cases to produce almost an entire change in the form of the word2 or to result in compounds which require close scrutiny for the detection of the original root4 ,for example1 in the ,carrier1 one of the ,dn dialects of western ,canada1 the word tha means #c things2 thane1 #c persons2 that1 #c times2 thatoen1 in #c places2 thauh1 in #c ways2 thailtoh1 all of the #c things2 thahoeltoh1 all of the #c persons2 and thahultoh1 all of the #c times4#ach ,in the ,tsimshian language of ,british ,columbia we find seven distinct sets of numerals which are used for various classes of objects that are counted4 ,the first set is used in counting where there is no definite object referred to2 the second class is used for counting flat objects and animals2 the third for counting round objects and divisions of time2 the fourth for counting men2 the fifth for counting long objects1 the numerals being composed with kan1 tree2 the sixth for counting canoes2 and the seventh for measures4 ,the last seem to be composed with anon1 hand4#aci ,the first ten numerals of each of these classes is given in the following table3 ---------------------------------------- --------------------------------------- ,no4 ,counting ,flat ,round ,men ,long ,canoes ,measures ,objects ,objects ,objects ---------------------------------------- --------------------------------------- #a gyak gak g'erel k'al k'awutskank'amaet k'al #b t'epqat t'epqat goupel t'epqadal gaopskan g'alpeeltkgulbel #c guant guant gutle gulal galtskan galtskantk guleont #d tqalpq tqalpq tqalpq tqalpqdal tqaapskan tqalpqsk tqalpqalont #e kctonckctonckctonckcenecal k'etoentskankctoonsk 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 guandalt yuktalt yuktalt yuktleadalek'tlaedskanyuktaltk yuktaldelont #i kctemac kctemac kctemac kctemacal kctemaestkankctemack kctemasilont #aj gy'ap gy'ap kpeel kpal kpeetskangy'apsk kpeont ---------------------------------------- --------------------------------------- ,remarkable as this list may appear1 it is by no means as extensive as that derived from many of the other ,british ,columbian tribes4 ,the numerals of the ,shushwap1 ,stlatlumh1 ,okanaken1 and other languages of this region exist in several different forms1 and can also be modified by any of the innumerable suffixes of these tongues4#adj ,to illustrate the almost illimitable number of sets that may be formed1 a table is given of a few classes1 taken from the ,heiltsuk dialect4#ada ,it appears from these examples that the number of classes is unlimited4 ---------------------------------------- ------------------------ ,one4 ,two4 ,three4 ---------------------------------------- ------------------------ ,animate4 menok maalok yutuk ,round4 menskam masem yutqsem ,long4 ments'ak mats'ak yututs'ak ,flat4 menaqsa matlqsa yutqsa ,day4 op'enequls matlp'enequls yutqp'enequls ,fathom4 op'enkh matlp'enkh yutqp'enkh ,grouped together4 ---- matloutl yutoutl ,groups of objects4 nemtsmots'utlmatltsmots'utlyutqtsmots'ut l ,filled cup4 menqtlala matl'aqtlala yutqtlala ,empty cup4 menqtla matl'aqtla yutqtla ,full box4 menskamala masemala yutqsemala ,empty box4 menskam masem yutqsem ,loaded canoe4 mentsake mats'ake yututs'ake ,canoe with crew4 ments'akis mats'akla yututs'akla ,together on beach4 ---- maalis ---- ,together in house1 etc4---- maalitl ---- ---------------------------------------- ------------------------ ,variation in numeral forms such as is exhibited in the above tables is not confined to any one quarter of the globe2 but it is more universal among the ,british ,columbian ,indians than among any other race1 and it is a more characteristic linguistic peculiarity of this than of any other region1 either in the ,old ,world or in the ,new4 ,it was to some extent employed by the ,aztecs1#adb and its use is current among the ,japanese2 in whose language ,crawfurd finds fourteen different classes of numerals without exhausting the list4#adc ,in examining the numerals of different languages it will be found that the tens of any ordinary decimal scale are formed in the same manner as in ,english4 ,twenty is simply #b times #aj2 #cj is #c times #aj1 and so on4 ,the word times is1 of course1 not expressed1 any more than in ,english2 but the expressions briefly are1 #b tens1 #c tens1 etc4 ,but a singular exception to this method is presented by the ,hebrew1 and other of the ,semitic languages4 ,in ,hebrew the word for #bj is the plural of the word for #aj2 and #cj1 #dj1 #ej1 etc4 to #ij are plurals of #c1 #d1 #e1 #f1 #g1 #h1 #i4 ,these numerals are as follows3#add #aj1 eser1 #bj1 eserim1 #c1 shalosh1 #cj1 shaloshim1 #d1 arba1 #dj1 arbaim1 #e1 chamesh1 #ej1 chamishshim1 #f1 shesh1 #fj1 sheshshim1 #g1 sheba1 #gj1 shibim1 #h1 shemoneh #hj1 shemonim1 #i1 tesha1 #ij1 tishim4 ,the same formation appears in the numerals of the ancient ,phoenicians1#ade and seems1 indeed1 to be a well-marked characteristic of the various branches of this division of the ,caucasian race4 ,an analogous method appears in the formation of the tens in the ,bisayan1#adf one of the ,malay numeral scales1 where #cj1 #dj1 444 #ij1 are constructed from #c1 #d1 444 #i1 by adding the termination -an4 ,no more interesting contribution has ever been made to the literature of numeral nomenclature than that in which ,dr4 ,trumbull embodies the results of his scholarly research among the languages of the native ,indian tribes of this country4#adg ,as might be expected1 we are everywhere confronted with a digital origin1 direct or indirect1 in the great body of the words examined4 ,but it is clearly shown that such a derivation cannot be established for all numerals2 and evidence collected by the most recent research fully substantiates the position taken by ,dr4 ,trumbull4 ,nearly all the derivations established are such as to remind us of the meanings we have already seen recurring in one form or another in language after language4 ,five is the end of the finger count on one hand--as1 the ,micmac nan1 and ,mohegan nunon1 gone1 or spent2 the ,pawnee sihuks1 hands half2 the ,dakota zaptan1 hand turned down2 and the ,massachusetts napanna1 on one side4 ,ten is the end of the finger count1 but is not always expressed by the both hands formula so commonly met with4 ,the ,cree term for this number is mitatat1 no further2 and the corresponding word in ,delaware is m'tellen1 no more4 ,the ,dakota #aj is1 like its #e1 a straightening out of the fingers which have been turned over in counting1 or wickchemna1 spread out unbent4 ,the same is true of the ,hidatsa pitika1 which signifies a smoothing out1 or straightening4 ,the ,pawnee #d1 skitiks1 is unusual1 signifying as it does all the fingers1 or more properly1 the fingers of the hand4 ,the same meaning attaches to this numeral in a few other languages also1 and reminds one of the habit some people have of beginning to count on the forefinger and proceeding from there to the little finger4 ,can this have been the habit of the tribes in question8 ,a suggestion of the same nature is made by the ,illinois and ,miami words for #h1 parare and polane1 which signify nearly ended4 ,six is almost always digital in origin1 though the derivation may be indirect1 as in the ,illinois kakatchui1 passing beyond the middle2 and the ,dakota shakpe1 #a in addition4 ,some of these significations are well matched by numerals from the ,ewe scales of western ,africa1 where we find the following3#adh #a4 de a going1 i4e4 a beginning4 7,cf4 the ,zui tpinte1 taken to start with47 #c4 eto the father 7from the middle1 or longest finger74 #f4 ade the other going4 #i4 asieke parting with the hands4 #aj4 ewo done4 ,in studying the names for #b we are at once led away from a strictly digital origin for the terms by which this number is expressed4 ,these names seem to come from four different sources3 7#a7 roots denoting separation or distinction2 7#b7 likeness1 equality1 or opposition2 7#c7 addition1 i4e4 putting to1 or putting with2 7#d7 coupling1 pairing1 or matching4 ,they are often related to1 and perhaps derived from1 names of natural pairs1 as feet1 hands1 eyes1 arms1 or wings4 ,in the ,dakota and ,algonkin dialects #b is almost always related to arms or hands1 and in the ,athapaskan to feet4 ,but the relationship is that of common origin1 rather than of derivation from these pair-names4 ,in the ,puri and ,hottentot languages1 #b and hand are closely allied2 while in ,sanskrit1 #b may be expressed by any one of the words kara1 hand1 bahu1 arm1 paksha1 wing1 or netra1 eye4#adi ,still more remote from anything digital in their derivation are the following1 taken at random from a very great number of examples that might be cited to illustrate this point4 ,the ,assiniboines call #g1 shak ko we1 or u she nah1 the odd number4#aej ,the ,crow #a1 hamat1 signifies the least2#aea the ,mississaga #a1 pecik1 a very small thing4#aeb ,in ,javanese1 ,malay1 and ,manadu1 the words for #a1 which are respectively siji1 satu1 and sabuah1 signify #a seed1 #a pebble1 and #a fruit respectively#aec--words as natural and as much to be expected at the beginning of a number scale as any finger name could possibly be4 ,among almost all savage races one form or another of palpable arithmetic is found1 such as counting by seeds1 pebbles1 shells1 notches1 or knots2 and the derivation of number words from these sources can constitute no ground for surprise4 ,the ,marquesan word for #d is pona1 knot1 from the practice of tying breadfruit in knots of #d4 ,the ,maori #aj is tekau1 bunch1 or parcel1 from the counting of yams and fish by parcels of #aj4aed ,the ,javanese call #be1 lawe1 a thread1 or string2 #ej1 ekat1 a skein of thread2 #djj1 samas1 a bit of gold2 #hjj1 domas1 #b bits of gold4#aee ,the ,macassar and ,butong term for #ajj is bilangan1 #a tale or reckoning4#aef ,the ,aztec #bj is cem pohualli1 #a count2 #djj is centzontli1 #a hair of the head2 and #hjjj is xiquipilli1 sack4#aeg ,this sack was of such a size as to contain #hjjj cacao nibs1 or grains1 hence the derivation of the word in its numeral sense is perfectly natural4 ,in ,japanese we find a large number of terms which1 as applied to the different units of the number scale1 seem almost purely fanciful4 ,these words1 with their meanings as given by a ,japanese lexicon1 are as follows3 #aj1jjj1 or #ajd1 mn enormous number4 #ajh1 oku a compound of the words man and mind4 #ajab1 chio indication1 or symptom4 #ajaf1 kei capital city4 #ajbj1 si a term referring to grains4 #ajbd1 owi ---- #ajbh1 jio extent of land4 #ajcb1 ko canal4 #ajcf1 kan some kind of a body of water4 #ajdj1 sai justice4 #ajdd1 sa support4 #ajdh1 kioku limit1 or more strictly1 ultimate4 4#jab1 rin ---- 4#jac1 mo hair 7of some animal74 4#jad1 shi thread4 ,in addition to these1 some of the lower fractional values are described by words meaning very small1 very fine thread1 sand grain1 dust1 and very vague4 ,taken altogether1 the ,japanese number system is the most remarkable ,i have ever examined1 in the extent and variety of the higher numerals with well-defined descriptive names4 ,most of the terms employed are such as to defy any attempt to trace the process of reasoning which led to their adoption4 ,it is not improbable that the choice was1 in some of these cases at least1 either accidental or arbitrary2 but still1 the changes in word meanings which occur with the lapse of time may have differentiated significations originally alike1 until no trace of kinship would appear to the casual observer4 ,our numerals score and gross are never thought of as having any original relation to what is conveyed by the other meanings which attach to these words4 ,but the origin of each1 which is easily traced1 shows that1 in the beginning1 there existed a well-defined reason for the selection of these1 rather than other terms1 for the numbers they now describe4 ,possibly these remarkable ,japanese terms may be accounted for in the same way1 though the supposition is1 for some reasons1 quite improbable4 ,the same may be said for the ,malagasy #ajjj1 alina1 which also means night1 and the ,hebrew #f1 shesh1 which has the additional signification white marble1 and the stray exceptions which now and then come to the light in this or that language4 ,such terms as these may admit of some logical explanation1 but for the great mass of numerals whose primitive meanings can be traced at all1 no explanation whatever is needed2 the words are self-explanatory1 as the examples already cited show4 ,a few additional examples of natural derivation may still further emphasize the point just discussed4 ,in ,bambarese the word for #aj1 tank1 is derived directly from adang1 to count4#aeh ,in the language of ,mota1 one of the islands of ,melanesia1 #ajj is mel nol1 used and done with1 referring to the leaves of the cycas tree1 with which the count had been carried on4#aei ,in many other ,melanesian dialects#afj #ajj is rau1 a branch or leaf4 ,in the ,torres ,straits we find the same number expressed by na won1 the close2 and in ,eromanga it is narolim narolim 7#b #e77b #e74afa ,this combination deserves remark only because of the involved form which seems to have been required for the expression of so small a number as #ajj4 ,a compound instead of a simple term for any higher unit is never to be wondered at1 so rude are some of the savage methods of expressing number2 but two fives 7times7 two fives is certainly remarkable4 ,some form like that employed by the ,nusqually#afb of ,puget ,sound for #ajjj1 i4e4 paduts-subqutche1 ten hundred1 is more in accordance with primitive method4 ,but we are equally likely to find such descriptive phrases for this numeral as the dor paka1 banyan roots1 of the ,torres ,islands2 rau na hai1 leaves of a tree1 of ,vaturana2 or udolu1 all1 of the ,fiji ,islands4 ,and two curious phrases for #ajjj are those of the ,banks' ,islands1 tar mataqelaqela1 eye blind thousand1 i4e4 many beyond count2 and of ,malanta1 warehune huto1 opossum's hairs1 or idumie one1 count the sand4#afc ,the native languages of ,india1 ,thibet1 and portions of the ,indian archipelago furnish us with abundant instances of the formation of secondary numeral scales1 which were used only for special purposes1 and without in any way interfering with the use of the number words already in use4 ,thus the scholars of ,india1 ages ago1 selected a set of words for a memoria technica1 in order to record dates and numbers4 ,these words they chose for reasons which are still in great measure evident2 thus 'moon' or 'earth' expressed #a1 there being but one of each2 #b might be called 'eye1' 'wing1' 'arm1' 'jaw1' as going in pairs2 for #c they said ',rama1' 'fire1' or 'quality1' there being considered to be three ,ramas1 three kinds of fire1 three qualities 7guna72 for #d were used 'veda1' 'age1' or 'ocean1' there being four of each recognized2 'season' for #f1 because they reckoned six seasons2 'sage' or 'vowel1' for #g1 from the seven sages and the seven vowels2 and so on with higher numbers1 'sun' for #ab1 because of his twelve annual denominations1 or 'zodiac' from his twelve signs1 and 'nail' for #bj1 a word incidentally bringing in finger notation4 ,as ,sanskrit is very rich in synonyms1 and as even the numerals themselves might be used1 it became very easy to draw up phrases or nonsense verses to record series of numbers by this system of artificial memory4#afd ,more than enough has been said to show how baseless is the claim that all numeral words are derived1 either directly or indirectly1 from the names of fingers1 hands1 or feet4 ,connected with the origin of each number word there may be some metaphor1 which cannot always be distinctly traced2 and where the metaphor was born of the hand or of the foot1 we inevitably associate it with the practice of finger counting4 ,but races as fond of metaphor and of linguistic embellishment as are those of the ,east1 or as are our ,american ,indians even1 might readily resort to some other source than that furnished by the members of the human body1 when in want of a term with which to describe the #e1 #aj1 or any other number of the numeral scale they were unconsciously forming4 ,that the first numbers of a numeral scale are usually derived from other sources1 we have some reason to believe2 but that all above #b1 #c1 or at most #d1 are almost universally of digital origin we must admit4 ,exception should properly be made of higher units1 say #ajjj or anything greater1 which could not be expected to conform to any law of derivation governing the first few units of a system4 ,collecting together and comparing with one another the great mass of terms by which we find any number expressed in different languages1 and1 while admitting the great diversity of method practised by different tribes1 we observe certain resemblances which were not at first supposed to exist4 ,the various meanings of #a1 where they can be traced at all1 cluster into a little group of significations with which at last we come to associate the idea of unity4 ,similarly of #b1 or #e1 or #aj1 or any one of the little band which does picket duty for the advance guard of the great host of number words which are to follow4 ,a careful examination of the first decade warrants the assertion that the probable meaning of any one of the units will be found in the list given below4 ,the words selected are intended merely to serve as indications of the thought underlying the savage's choice1 and not necessarily as the exact term by means of which he describes his number4 ,only the commonest meanings are included in the tabulation here given4 #a existence1 piece1 group1 beginning4 #b repetition1 division1 natural pair4 #c collection1 many1 two-one4 #d two twos4 #e hand1 group1 division1 #f five-one1 two threes1 second one4 #g five-two1 second two1 three from ten4 #h five-three1 second three1 two fours1 two from ten4 #i five-four1 three threes1 one from ten4 #aj one 7group71 two fives 7hands71 half a man1 one man4 #ae ten-five1 one foot1 three fives4 #bj two tens1 one man1 two feet4#afe ,,chapter ,v4 ,,miscellaneous ,,number ,,bases4 ,in the development and extension of any series of numbers into a systematic arrangement to which the term system may be applied1 the first and most indispensable step is the selection of some number which is to serve as a base4 ,when the savage begins the process of counting he invents1 one after another1 names with which to designate the successive steps of his numerical journey4 ,at first there is no attempt at definiteness in the description he gives of any considerable number4 ,if he cannot show what he means by the use of his fingers1 or perhaps by the fingers of a single hand1 he unhesitatingly passes it by1 calling it many1 heap1 innumerable1 as many as the leaves on the trees1 or something else equally expressive and equally indefinite4 ,but the time comes at last when a greater degree of exactness is required4 ,perhaps the number #aa is to be indicated1 and indicated precisely4 ,a fresh mental effort is required of the ignorant child of nature2 and the result is all the fingers and one more1 both hands and one more1 one on another count1 or some equivalent circumlocution4 ,if he has an independent word for #aj1 the result will be simply ten-one4 ,when this step has been taken1 the base is established4 ,the savage has1 with entire unconsciousness1 made all his subsequent progress dependent on the number #aj1 or1 in other words1 he has established #aj as the base of his number system4 ,the process just indicated may be gone through with at #e1 or at #bj1 thus giving us a quinary or a vigesimal1 or1 more probably1 a mixed system2 and1 in rare instances1 some other number may serve as the point of departure from simple into compound numeral terms4 ,but the general idea is always the same1 and only the details of formation are found to differ4 ,without the establishment of some base any system of numbers is impossible4 ,the savage has no means of keeping track of his count unless he can at each step refer himself to some well-defined milestone in his course4 ,if1 as has been pointed out in the foregoing chapters1 confusion results whenever an attempt is made to count any number which carries him above #aj1 it must at once appear that progress beyond that point would be rendered many times more difficult if it were not for the fact that1 at each new step1 he has only to indicate the distance he has progressed beyond his base1 and not the distance from his original starting-point4 ,some idea may1 perhaps1 be gained of the nature of this difficulty by imagining the numbers of our ordinary scale to be represented1 each one by a single symbol different from that used to denote any other number4 ,how long would it take the average intellect to master the first #ej even1 so that each number could without hesitation be indicated by its appropriate symbol8 ,after the first #ej were once mastered1 what of the next #ej8 and the next8 and the next8 and so on4 ,the acquisition of a scale for which we had no other means of expression than that just described would be a matter of the extremest difficulty1 and could never1 save in the most exceptional circumstances1 progress beyond the attainment of a limit of a few hundred4 ,if the various numbers in question were designated by words instead of by symbols1 the difficulty of the task would be still further increased4 ,hence1 the establishment of some number as a base is not only a matter of the very highest convenience1 but of absolute necessity1 if any save the first few numbers are ever to be used4 ,in the selection of a base1--of a number from which he makes a fresh start1 and to which he refers the next steps in his count1--the savage simply follows nature when he chooses #aj1 or perhaps #e or #bj4 ,but it is a matter of the greatest interest to find that other numbers have1 in exceptional cases1 been used for this purpose4 ,two centuries ago the distinguished philosopher and mathematician1 ,leibnitz1 proposed a binary system of numeration4 ,the only symbols needed in such a system would be #j and #a4 ,the number which is now symbolized by the figure #b would be represented by #aj2 while #c1 #d1 #e1 #f1 #g1 #h1 etc41 would appear in the binary notation as #aa1 #ajj1 #aja1 #aaj1 #aaa1 #ajjj1 etc4 ,the difficulty with such a system is that it rapidly grows cumbersome1 requiring the use of so many figures for indicating any number4 ,but ,leibnitz found in the representation of all numbers by means of the two digits #j and #a a fitting symbolization of the creation out of chaos1 or nothing1 of the entire universe by the power of the ,deity4 ,in commemoration of this invention a medal was struck bearing on the obverse the words ,numero ,deus impari gaudet1 and on the reverse1 ,omnibus ex nihilo ducendis sufficit ,unum4#aff ,this curious system seems to have been regarded with the greatest affection by its inventor1 who used every endeavour in his power to bring it to the notice of scholars and to urge its claims4 ,but it appears to have been received with entire indifference1 and to have been regarded merely as a mathematical curiosity4 ,unknown to ,leibnitz1 however1 a binary method of counting actually existed during that age2 and it is only at the present time that it is becoming extinct4 ,in ,australia1 the continent that is unique in its flora1 its fauna1 and its general topography1 we find also this anomaly among methods of counting4 ,the natives1 who are to be classed among the lowest and the least intelligent of the aboriginal races of the world1 have number systems of the most rudimentary nature1 and evince a decided tendency to count by twos4 ,this peculiarity1 which was to some extent shared by the ,tasmanians1 the island tribes of the ,torres ,straits1 and other aboriginal races of that region1 has by some writers been regarded as peculiar to their part of the world2 as though a binary number system were not to be found elsewhere4 ,this attempt to make out of the rude and unusual method of counting which obtained among the ,australians a racial characteristic is hardly justified by fuller investigation4 ,binary number systems1 which are given in full on another page1 are found in ,south ,america4 ,some of the ,dravidian scales are binary2#afg and the marked preference1 not infrequently observed among savage races1 for counting by pairs1 is in itself a sufficient refutation of this theory4 ,still it is an unquestionable fact that this binary tendency is more pronounced among the ,australians than among any other extensive number of kindred races4 ,they seldom count in words above #d1 and almost never as high as #g4 ,one of the most careful observers among them expresses his doubt as to a native's ability to discover the loss of two pins1 if he were first shown seven pins in a row1 and then two were removed without his knowledge4#afh ,but he believes that if a single pin were removed from the seven1 the ,blackfellow would become conscious of its loss4 ,this is due to his habit of counting by pairs1 which enables him to discover whether any number within reasonable limit is odd or even4 ,some of the negro tribes of ,africa1 and of the ,indian tribes of ,america1 have the same habit4 ,progression by pairs may seem to some tribes as natural as progression by single units4 ,it certainly is not at all rare2 and in ,australia its influence on spoken number systems is most apparent4 ,any number system which passes the limit #aj is reasonably sure to have either a quinary1 a decimal1 or a vigesimal structure4 ,a binary scale could1 as it is developed in primitive languages1 hardly extend to #bj1 or even to #aj1 without becoming exceedingly cumbersome4 ,a binary scale inevitably suggests a wretchedly low degree of mental development1 which stands in the way of the formation of any number scale worthy to be dignified by the name of system4 ,take1 for example1 one of the dialects found among the western tribes of the ,torres ,straits1 where1 in general1 but two numerals are found to exist4 ,in this dialect the method of counting 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 ,anything above #f they call ras1 a lot4 ,for the sake of uniformity we may speak of this as a system4 ,but in so doing1 we give to the legitimate meaning of the word a severe strain4 ,the customs and modes of life of these people are not such as to require the use of any save the scanty list of numbers given above2 and their mental poverty prompts them to call #c1 the first number above a single pair1 #b-a4 ,in the same way1 #d and #f are respectively #b pairs and #c pairs1 while #e is #a more than #b pairs4 ,five objects1 however1 they sometimes denote by urapuni-getal1 #a hand4 ,a precisely similar condition is found to prevail respecting the arithmetic of all the ,australian tribes4 ,in some cases only two numerals are found1 and in others three4 ,but in a very great number of the native languages of that continent the count proceeds by pairs1 if indeed it proceeds at all4 ,hence we at once reject the theory that ,australian arithmetic1 or ,australian counting1 is essentially peculiar4 ,it is simply a legitimate result1 such as might be looked for in any part of the world1 of the barbarism in which the races of that quarter of the world were sunk1 and in which they were content to live4 ,the following examples of ,australian and ,tasmanian number systems show how scanty was the numerical ability possessed by these tribes1 and illustrate fully their tendency to count by twos or pairs4 ,,murray ,,river4#agj #a4 enea4 #b4 petcheval4 #c4 petchevalenea #b-a4 #d4 petcheval peteheval #b-b4 ,,maroura4 #a4 nukee4 #b4 barkolo4 #c4 barkolo nuke #b-a4 #d4 barkolo barkolo #b-b4 ,,lake ,,kopperamana4 #a4 ngerna4 #b4 mondroo4 #c4 barkooloo4 #d4 mondroo mondroo #b-b4 ,,mort ,,noular4 #a4 gamboden4 #b4 bengeroo4 #c4 bengeroganmel #b-a4 #d4 bengeroovor bengeroo #b #b4 ,,wimmera4 #a4 keyap4 #b4 pollit4 #c4 pollit keyap #b-a4 #d4 pollit pollit #b-b4 ,,popham ,,bay4 #a4 motu4 #b4 lawitbari4 #c4 lawitbari-motu #b-a4 ,,kamilaroi4#aga #a4 mal4 #b4 bularr4 #c4 guliba4 #d4 bularrbularr #b-b4 #e4 bulaguliba #b-c4 #f4 gulibaguliba #c-c4 ,,port ,,essington4#agb #a4 erad4 #b4 nargarik4 #c4 nargarikelerad #b-a4 #d4 nargariknargarik #b-b4 ,,warrego4 #a4 tarlina4 #b4 barkalo4 #c4 tarlina barkalo #a-b4 ,,crocker ,,island4 #a4 roka4 #b4 orialk4 #c4 orialkeraroka #b-a4 ,,warrior ,,island4#agc #a4 woorapoo4 #b4 ocasara4 #c4 ocasara woorapoo #b-a4 #d4 ocasara ocasara #b-b4 ,,dippil4#agd #a4 kalim4 #b4 buller4 #c4 boppa4 #d4 buller gira buller #b #b4 #e4 buller gira buller kalim #b #b #a4 ,,frazer',s ,,island4#age #a4 kalim4 #b4 bulla4 #c4 goorbunda4 #d4 bulla-bulla #b-b4 ,,moreton',s ,,bay4#agf #a4 kunner4 #b4 budela4 #c4 muddan4 #d4 budela berdelu #b-b4 ,,encounter ,,bay4#agg #a4 yamalaitye4 #b4 ningenk4 #c4 nepaldar4 #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 marnkutye4 #d4 yera-bula pair #b4 #e4 yera-bula kuma pair #b-a4 #f4 yera-bula purlaitye pair #b4b4 ,,wiraduroi4#agi #a4 numbai4 #b4 bula4 #c4 bula-numbai #b-a4 #d4 bungu many4 #e4 bungu-galan very many4 ,,wirri-,,wirri4#ahj #a4 mooray4 #b4 boollar4 #c4 belar mooray #b-a4 #d4 boollar boollar #b-b4 #e4 mongoonballa4 #f4 mongun mongun4 ,,cooper',s ,,creek4#aha #a4 goona4 #b4 barkoola4 #c4 barkoola goona #b-a4 #d4 barkoola barkoola #b-b4 ,,bourke1 ,,darling ,,river4#ahb #a4 neecha4 #b4 boolla4 #d4 boolla neecha #b-a4 #c4 boolla boolla #b-b4 ,,murray ,,river1 ,n4,w4 ,,bend4#ahc #a4 mata4 #b4 rankool4 #c4 rankool mata #b-a4 #d4 rankool rankool #b-b4 ,,yit-,,tha4#ahd #a4 mo4 #b4 thral4 #c4 thral mo #b-a4 #d4 thral thral #b-b4 ,,port ,,darwin4#ahe #a4 kulagook4 #b4 kalletillick4 #c4 kalletillick kulagook #b-a4 #d4 kalletillick kalletillick #b-b4 ,,champion ,,bay4#ahf #a4 kootea4 #b4 woothera4 #c4 woothera kootea #b-a4 #d4 woothera woothera #b-b4 ,,belyando ,,river4#ahg #a4 wogin4 #b4 booleroo4 #c4 booleroo wogin #b-a4 #d4 booleroo booleroo #b-b4 ,,warrego ,,river4 #a4 onkera4 #b4 paulludy4 #c4 paulludy onkera #b-a4 #d4 paulludy paulludy #b-b4 ,,richmond ,,river4 #a4 yabra4 #b4 booroora4 #c4 booroora yabra #b-a4 #d4 booroora booroora #b-b4 ,,port ,,macquarie4 #a4 warcol4 #b4 blarvo4 #c4 blarvo warcol #b-a4 #d4 blarvo blarvo #b-b4 ,,hill ,,end4 #a4 miko4 #b4 bullagut4 #c4 bullagut miko #b-a4 #d4 bullagut bullagut #b-b4 ,,moneroo #a4 boor4 #b4 wajala1 blala4 #c4 blala boor #b-a4 #d4 wajala wajala4 ,,gonn ,,station4 #a4 karp4 #b4 pellige4 #c4 pellige karp #b-a4 #d4 pellige pellige #b-b4 ,,upper ,,yarra4 #a4 kaambo4 #b4 benjero4 #c4 benjero kaambo #b-b4 #d4 benjero on benjero #b-b4 ,,omeo4 #a4 bore4 #b4 warkolala4 #c4 warkolala bore #b-a4 #d4 warkolala warkolala #b-b4 ,,snowy ,,river4 #a4 kootook4 #b4 boolong4 #c4 booloom catha kootook #b #a4 #d4 booloom catha booloom #b #b4 ,,ngarrimowro4 #a4 warrangen4 #b4 platir4 #c4 platir warrangen #b-a4 #d4 platir platir #b-b4 ,this ,australian list might be greatly extended1 but the scales selected may be taken as representative examples of ,australian binary scales4 ,nearly all of them show a structure too clearly marked to require comment4 ,in a few cases1 however1 the systems are to be regarded rather as showing a trace of binary structure1 than as perfect examples of counting by twos4 ,examples of this nature are especially numerous in ,curr's extensive list--the most complete collection of ,australian vocabularies ever made4 ,a few binary scales have been found in ,south ,america1 but they show no important variation on the ,australian systems cited above4 ,the only ones ,i have been able to collect are the following3 ,,bakairi4#ahh #a4 tokalole4 #b4 asage4 #c4 asage tokalo #b-a4 #d4 asage asage #b-b4 ,,zapara4#ahi #a4 nuquaqui4 #b4 namisciniqui4 #c4 haimuckumarachi4 #d4 namisciniqui ckara maitacka #b #b4 #e4 namisciniqui ckara maitacka nuquaqui #b pairs #a4 #f4 haimuckumaracki ckaramsitacka #c pairs4 ,,apinages4#aij #a4 pouchi4 #b4 at croudou4 #c4 at croudi-pshi #b-a4 #d4 agontad-acroudo #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 uninitegui4 #b4 iniguata4 #c4 iniguata dugani #b over4 #d4 iniguata driniguata #b-b4 #e4 oguidi many4 ,,tama4#aic #a4 teyo4 #b4 cayapa4 #c4 cho-teyo #b #a4 #d4 cayapa-ria #b again4 #e4 cia-jente hand4 ,,curetu4#aid #a4 tchudyu4 #b4 ap-adyu4 #c4 arayu4 #d4 apaedyi #b #b4 #e4 tchumupa4 ,if the existence of number systems like the above are to be accounted for simply on the ground of low civilization1 one might reasonably expect to find ternary and and quaternary scales1 as well as binary4 ,such scales actually exist1 though not in such numbers as the binary4 ,an example of the former is the ,betoya scale1#aie which runs thus3 #a4 edoyoyoi4 #b4 edoi another4 #c4 ibutu beyond4 #d4 ibutu-edoyoyoi beyond #a1 or #c-a4 #e4 ru-mocoso hand4 ,the ,kamilaroi scale1 given as an example of binary formation1 is partly ternary2 and its word for #f1 guliba guliba1 #c-c1 is purely ternary4 ,an occasional ternary trace is also found in number systems otherwise decimal or quinary vigesimal2 as the dlkunoutl1 second #c1 of the ,haida ,indians of ,british ,columbia4 ,the ,karens of ,india#aif in a system otherwise strictly decimal1 exhibit the following binary-ternary-quaternary vagary3 #f4 then tho #c #b4 #g4 then tho ta #c #b-a4 #h4 lwie tho #d #b4 #i4 lwie tho ta #d #b-a4 ,in the ,wokka dialect1#aig found on the ,burnett ,river1 ,australia1 a single ternary numeral is found1 thus3 #a4 karboon4 #b4 wombura4 #c4 chrommunda4 #d4 chrommuda karboon #c-a4 ,instances of quaternary numeration are less rare than are those of ternary1 and there is reason to believe that this method of counting has been practised more extensively than any other1 except the binary and the three natural methods1 the quinary1 the decimal1 and the vigesimal4 ,the number of fingers on one hand is1 excluding the thumb1 four4 ,possibly there have been tribes among which counting by fours arose as a legitimate1 though unusual1 result of finger counting2 just as there are1 now and then1 individuals who count on their fingers with the forefinger as a starting-point4 ,but no such practice has ever been observed among savages1 and such theorizing is the merest guess-work4 ,still a definite tendency to count by fours is sometimes met with1 whatever be its origin4 ,quaternary traces are repeatedly to be found among the ,indian languages of ,british ,columbia4 ,in describing the ,columbians1 ,bancroft says3 ,systems of numeration are simple1 proceeding by fours1 fives1 or tens1 according to the different languages4444#aih ,the same preference for four is said to have existed in primitive times in the languages of ,central ,asia1 and that this form of numeration1 resulting in scores of #af and #fd1 was a development of finger counting4#aii ,in the ,hawaiian and a few other languages of the islands of the central ,pacific1 where in general the number systems employed are decimal1 we find a most interesting case of the development1 within number scales already well established1 of both binary and quaternary systems4 ,their origin seems to have been perfectly natural1 but the systems themselves must have been perfected very slowly4 ,in ,tahitian1 ,rarotongan1 ,mangarevan1 and other dialects found in the neighbouring islands of those southern latitudes1 certain of the higher units1 tekau1 rau1 mano1 which originally signified #aj1 #ajj1 #ajjj1 have become doubled in value1 and now stand for #bj1 #bjj1 #bjjj4 ,in ,hawaiian and other dialects they have again been doubled1 and there they stand for #dj1 #djj1 #djjj4bjj ,in the ,marquesas group both forms are found1 the former in the southern1 the latter in the northern1 part of the archipelago2 and it seems probable that one or both of these methods of numeration are scattered somewhat widely throughout that region4 ,the origin of these methods is probably to be found in the fact that1 after the migration from the west toward the east1 nearly all the objects the natives would ever count in any great numbers were small1--as yams1 cocoanuts1 fish1 etc41--and would be most conveniently counted by pairs4 ,hence the native1 as he counted one pair1 two pairs1 etc41 might readily say one1 two1 and so on1 omitting the word pair altogether4 ,having much more frequent occasion to employ this secondary than the primary meaning of his numerals1 the native would easily allow the original significations to fall into disuse1 and in the lapse of time to be entirely forgotten4 ,with a subsequent migration to the northward a second duplication might take place1 and so produce the singular effect of giving to the same numeral word three different meanings in different parts of ,oceania4 ,to illustrate the former or binary method of numeration1 the ,tahuatan1 one of the southern dialects of the ,marquesas group1 may be employed4#bja ,here the ordinary numerals are3 #a4 tahi1 #aj4 onohuu4 #bj4 takau4 #bjj4 au4 #b1jjj4 mano4 #bj1jjj4 tini4 #bj1jjj4 tufa4 #b1jjj1jjj4 pohi4 ,in counting fish1 and all kinds of fruit1 except breadfruit1 the scale begins with tauna1 pair1 and then1 omitting onohuu1 they employ the same words again1 but in a modified sense4 ,takau becomes #aj1 au #ajj1 etc42 but as the word pair is understood in each case1 the value is the same as before4 ,the table formed on this basis would be3 #b 7units7 #a tauna #b4 #aj tauna #a takau #bj4 #aj takau #a au #bjj4 #aj au #a mano #bjjj4 #aj mano #a tini #bj1jjj4 #aj tini #a tufa #bjj1jjj4 #aj tufa #a pohi #b1jjj1jjj4 ,for counting breadfruit they use pona1 knot1 as their unit1 breadfruit usually being tied up in knots of four4 ,takau now takes its third signification1 #dj1 and becomes the base of their breadfruit system1 so to speak4 ,for some unknown reason the next unit1 #djj1 is expressed by tauau1 while au1 which is the term that would regularly stand for that number1 has1 by a second duplication1 come to signify #hjj4 ,the next unit1 mano1 has in a similar manner been twisted out of its original sense1 and in counting breadfruit is made to serve for #hjjj4 ,in the northern1 or ,nukuhivan ,islands1 the decimal-quaternary system is more regular4 ,it is in the counting of 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 tini #dj1jjj4 #aj tini #a tufa #djj1jjj4 #aj tufa #a pohi #d1jjj1jjj4 ,in the ,hawaiian dialect this scale is1 with slight modification1 the universal scale1 used not only in counting breadfruit1 but any other objects as well4 ,the result is a complete decimal-quaternary system1 such as is found nowhere else in the world except in this and a few of the neighbouring dialects of the ,pacific4 ,this scale1 which is almost identical with the ,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 tini #dj1jjj4 #aj tini #a lehu #djj1jjj4 ,the quaternary element thus introduced has modified the entire structure of the ,hawaiian number system4 ,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 and #hfd1hie is #b #djj1jjj #dj1jjj #f #djjj #b #djj #b #dj #aj #e4bjd ,such examples show that this secondary influence1 entering and incorporating itself as a part of a well-developed decimal system1 has radically changed it by the establishment of #d as the primary number base4 ,the role which #aj now plays is peculiar4 ,in the natural formation of a quaternary scale new units would be introduced at #af1 #fd1 #bef1 etc42 that is1 at the square1 the cube1 and each successive power of the base4 ,but1 instead of this1 the new units are introduced at #aj #d1 #ajj #d1 #ajjj #d1 etc42 that is1 at the products of #d by each successive power of the old base4 ,this leaves the scale a decimal scale still1 even while it may justly be called quaternary2 and produces one of the most singular and interesting instances of number-system formation that has ever been observed4 ,in this connection it is worth noting that these ,pacific island number scales have been developed to very high limits--in some cases into the millions4 ,the numerals for these large numbers do not seem in any way indefinite1 but rather to convey to the mind of the native an idea as clear as can well be conveyed by numbers of such magnitude4 ,beyond the limits given1 the islanders have indefinite expressions1 but as far as can be ascertained these are only used when the limits given above have actually been passed4 ,to quote one more example1 the ,hervey ,islanders1 who have a binary-decimal scale1 count as follows3 #e kaviri 7bunches of cocoanuts7 #a takau #bj4 #aj takau #a rau #bjj4 #aj rau #a mano #bjjj4 #aj mano #a kiu #bj1jjj4 #aj kiu #a tini #bjj1jjj4 ,anything above this they speak of in an uncertain way1 as mano mano or tini tini1 which may1 perhaps1 be paralleled by our ,english phrases myriads upon myriads1 and millions of millions4#bje ,it is most remarkable that the same quarter of the globe should present us with the stunted number sense of the ,australians1 and1 side by side with it1 so extended and intelligent an appreciation of numerical values as that possessed by many of the lesser tribes of ,polynesia4 ,the ,luli of ,paraguay#bjf show a decided preference for the base #d4 ,this preference gives way only when they reach the number #aj1 which is an ordinary digit numeral4 ,all numbers above that point belong rather to decimal than to quaternary numeration4 ,their numerals are3 #a4 alapea4 #b4 tamop4 #c4 tamlip4 #d4 lokep4 #e4 lokep moile alapea #d with #a1 or is-alapea hand #a4 #f4 lokep moile tamop #d with #b4 #g4 lokep moile tamlip #d with #c4 #h4 lokep moile lokep #d with #d4 #i4 lokep moile lokep alapea #d with #d-a4 #aj4 is yaoum all the fingers of hand4 #aa4 is yaoum moile alapea all the fingers of hand with #a4 #bj4 is elu yaoum all the fingers of hand and foot4 #cj4 is elu yaoum moile is-yaoum all the fingers of hand and foot with all the fingers of hand4 ,still another instance of quaternary counting1 this time carrying with it a suggestion of binary influence1 is furnished by the ,mocobi#bjg of the ,parana region4 ,their scale is exceedingly rude1 and they use the fingers and toes almost exclusively in counting2 only using their spoken numerals when1 for any reason1 they wish to dispense with the aid of their hands and feet4 ,their first eight numerals are3 #a4 iniateda4 #b4 inabaca4 #c4 inabacao caini #b above4 #d4 inabacao cainiba #b above #b2 or natolatata4 #e4 inibacao cainiba iniateda #b above #b-a2 or natolatata iniateda #d-a4 #f4 natolatatata inibaca #d-b4 #g4 natolata inibacao-caini #d-b above4 #h4 natolata-natolata #d-d4 ,there is probably no recorded instance of a number system formed on #f1 #g1 #h1 or #i as a base4 ,no natural reason exists for the choice of any of these numbers for such a purpose2 and it is hardly conceivable that any race should proceed beyond the unintelligent binary or quaternary stage1 and then begin the formation of a scale for counting with any other base than one of the three natural bases to which allusion has already been made4 ,now and then some anomalous fragment is found imbedded in an otherwise regular system1 which carries us back to the time when the savage was groping his way onward in his attempt to give expression to some number greater than any he had ever used before2 and now and then one of these fragments is such as to lead us to the border land of the might-have-been1 and to cause us to speculate on the possibility of so great a numerical curiosity as a senary or a septenary scale4 ,the ,bretons call #ah triouec'h1 #c-f1 but otherwise their language contains no hint of counting by sixes2 and we are left at perfect liberty to theorize at will on the existence of so unusual a number word4 ,pott remarks#bjh that the ,bolans1 of western ,africa1 appear to make some use of #f as their number base1 but their system1 taken as a whole1 is really a quinary-decimal4 ,the language of the ,sundas1#bji or mountaineers of ,java1 contains traces of senary counting4 ,the ,akra words for #g and #h1 paggu and paniu1 appear to mean #f-a and #g-a1 respectively2 and the same is true of the corresponding ,tambi words pagu and panjo4#baj ,the ,watji tribe#baa call #f andee1 and #g anderee1 which probably means #f-a4 ,these words are to be regarded as accidental variations on the ordinary laws of formation1 and are no more significant of a desire to count by sixes than is the ,wallachian term deu-maw1 which expresses #ah as #b-i1 indicates the existence of a scale of which #i is the base4 ,one remarkably interesting number system is that exhibited by the ,mosquito tribe#bab of ,central ,america1 who possess an extensive quinary-vigesimal scale containing one binary and three senary compounds4 ,the first ten words of this singular scale1 which has already been quoted1 are3 #a4 kumi4 #b4 wal4 #c4 niupa4 #d4 wal-wal #b-b4 #e4 mata-sip fingers of one hand4 #f4 matlalkabe4 #g4 matlalkabe pura kumi #f #a4 #h4 matlalkabe pura wal #f #b4 #i4 matlalkabe pura niupa #f #c4 #aj4 mata-wal-sip fingers of the second hand4 ,in passing from #f to #g1 this tribe1 also1 has varied the almost universal law of progression1 and has called #g #f-a4 ,their #h and #i are formed in a similar manner2 but at #aj the ordinary method is resumed1 and is continued from that point onward4 ,few number systems contain as many as three numerals which are associated with #f as their base4 ,in nearly all instances we find such numerals singly1 or at most in pairs2 and in the structure of any system as a whole1 they are of no importance whatever4 ,for example1 in the ,pawnee1 a pure decimal scale1 we find the following odd sequence3#bac #f4 shekshabish4 #g4 petkoshekshabish #b-f1 i4e4 #b;d #f4 #h4 touwetshabish #c-f1 i4e4 #c;d #f4 #i4 loksherewa #aj - #a4 ,in the ,uainuma scale the expressions for #g and #h are obviously referred to #f1 though the meaning of #g is not given1 and it is impossible to guess what it really does signify4 ,the numerals in question are3#bad #f4 aira-ettagapi4 #g4 aira-ettagapi-hairiwigani-apecapecapsi4 #h4 aira-ettagapi-matschahma #f #b4 ,in the dialect of the ,mille tribe a single trace of senary counting appears1 as the numerals given below show3#bae #f4 dildjidji4 #g4 dildjidji me djuun #f #a4 ,finally1 in the numerals used by the natives of the ,marshall ,islands1 the following curiously irregular sequence also contains a single senary numeral3#baf #f4 thil thino #c #c4 #g4 thilthilim-thuon #f #a4 #h4 rua-li-dok #aj - #b4 #i4 ruathim-thuon #aj - #b #a4 ,many years ago a statement appeared which at once attracted attention and awakened curiosity4 ,it was to the effect that the ,maoris1 the aboriginal inhabitants of ,new ,zealand1 used as the basis of their numeral system the number #aa2 and that the system was quite extensively developed1 having simple words for #aba and #acca1 i4e4 for the square and cube of #aa4 ,no apparent reason existed for this anomaly1 and the ,maori scale was for a long time looked upon as something quite exceptional and outside all ordinary rules of number-system formation4 ,but a closer and more accurate knowledge of the ,maori language and customs served to correct the mistake1 and to show that this system was a simple decimal system1 and that the error arose from the following habit4 ,sometimes when counting a number of objects the ,maoris would put aside #a to represent each #aj1 and then those so set aside would afterward be counted to ascertain the number of tens in the heap4 ,early observers among this people1 seeing them count #aj and then set aside #a1 at the same time pronouncing the word tekau1 imagined that this word meant #aa1 and that the ignorant savage was making use of this number as his base4 ,this misconception found its way into the early ,new ,zealand dictionary1 but was corrected in later editions4 ,it is here mentioned only because of the wide diffusion of the error1 and the interest it has always excited4#bag ,aside from our common decimal scale1 there exist in the ,english language other methods of counting1 some of them formal enough to be dignified by the term system--as the sexagesimal method of measuring time and angular magnitude2 and the duodecimal system of reckoning1 so extensively used in buying and selling4 ,of these systems1 other than decimal1 two are noticed by ,tylor1#bah and commented on at some length1 as follows3 ,one is the well-known dicing set1 ace1 deuce1 tray1 cater1 cinque1 size2 thus size-ace is #f-a1 cinques or sinks1 double #e4 ,these came to us from ,france1 and correspond with the common ,french numerals1 except ace1 which is ,latin as1 a word of great philological interest1 meaning 'one4' ,the other borrowed set is to be found in the ,slang ,dictionary4 ,it appears that the ,english street-folk have adopted as a means of secret communication a set of ,italian numerals from the organ-grinders and image-sellers1 or by other ways through which ,italian or ,lingua ,franca is brought into the low neighbourhoods of ,london4 ,in so doing they have performed a philological operation not only curious but instructive4 ,by copying such expressions as due soldi1 tre soldi1 as equivalent to 'twopence1' 'threepence1' the word saltee became a recognized slang term for 'penny'2 and pence are reckoned as follows3 oney saltee #a;d4 uno soldo4 dooe saltee #b;d4 due soldi4 tray saltee #c;d4 tre soldi4 quarterer saltee #d;d4 quattro soldi4 chinker saltee #e;d4 cinque soldi4 say saltee #f;d4 sei soldi4 say oney saltee1 or setter saltee #g;d4 sette soldi4 say dooe saltee1 or otter saltee #h;d4 otto soldi4 say tray saltee1 or nobba saltee #i;d4 nove soldi4 say quarterer saltee1 or dacha saltee #aj;d4 dieci soldi4 say chinker saltee or dacha oney saltee #aa;d4 undici soldi4 oney beong #as4 a beong say saltee #as4 #f;d4 dooe beong say saltee1 or madza caroon #bs4 #f;d4 7half-crown1 mezza corona74 ,one of these series simply adopts ,italian numerals decimally4 ,but the other1 when it has reached #f1 having had enough of novelty1 makes #g by #f-a1 and so forth4 ,it is for no abstract reason that #f is thus made the turning-point1 but simply because the costermonger is adding pence up to the silver sixpence1 and then adding pence again up to the shilling4 ,thus our duodecimal coinage has led to the practice of counting by sixes1 and produced a philological curiosity1 a real senary notation4 ,in addition to the two methods of counting here alluded to1 another may be mentioned1 which is equally instructive as showing how readily any special method of reckoning may be developed out of the needs arising in connection with any special line of work4 ,as is well known1 it is the custom in ocean1 lake1 and river navigation to measure soundings by the fathom4 ,on the ,mississippi ,river1 where constant vigilance is needed because of the rapid shifting of sand-bars1 a special sounding nomenclature has come into vogue1#bai which the following terms will illustrate3 #e ft4 five feet4 #f ft4 six feet4 #i ft4 nine feet4 #aj-a_/b ft4 a quarter less twain2 i4e4 a quarter of a fathom less than #b4 #ab ft4 mark twain4 #ac-a_/b ft4 a quarter twain4 #af-a_/b ft4 a quarter less three4 #ah ft4 mark three4 #ai-a_/b ft4 a quarter three4 #bd ft4 deep four4 ,as the soundings are taken1 the readings are called off in the manner indicated in the table2 #aj-a_/b feet being a quarter less twain1 #ab feet mark twain1 etc4 ,any sounding above deep four is reported as no bottom4 ,in the ,atlantic and ,gulf waters on the coast of this country the same system prevails1 only it is extended to meet the requirements of the deeper soundings there found1 and instead of six feet1 mark twain1 etc41 we find the fuller expressions1 by the mark one1 by the mark two1 and so on1 as far as the depth requires4 ,this example also suggests the older and far more widely diffused method of reckoning time at sea by bells2 a system in which one bell1 two bells1 three bells1 etc41 mark the passage of time for the sailor as distinctly as the hands of the clock could do it4 ,other examples of a similar nature will readily suggest themselves to the mind4 ,two possible number systems that have1 for purely theoretical reasons1 attracted much attention1 are the octonary and the duodecimal systems4 ,in favour of the octonary system it is urged that #h is an exact power of #b2 or in other words1 a large number of repeated halves can be taken with #h as a starting-point1 without producing a fractional result4 ,with #h as a base we should obtain by successive halvings1 #d1 #b1 #a4 ,a similar process in our decimal scale gives #e1 #b-a_/b1 #a-a_/d4 ,all this is undeniably true1 but1 granting the argument up to this point1 one is then tempted to ask ,what of it8 ,a certain degree of simplicity would thereby be introduced into the ,theory of ,numbers2 but the only persons sufficiently interested in this branch of mathematics to appreciate the benefit thus obtained are already trained mathematicians1 who are concerned rather with the pure science involved1 than with reckoning on any special base4 ,a slightly increased simplicity would appear in the work of stockbrokers1 and others who reckon extensively by quarters1 eighths1 and sixteenths4 ,but such men experience no difficulty whatever in performing their mental computations in the decimal system2 and they acquire through constant practice such quickness and accuracy of calculation1 that it is difficult to see how octonary reckoning would materially assist them4 ,altogether1 the reasons that have in the past been adduced in favour of this form of arithmetic seem trivial4 ,there is no record of any tribe that ever counted by eights1 nor is there the slightest likelihood that such a system could ever meet with any general favour4 ,it is said that the ancient ,saxons used the octonary system1#bbj but how1 or for what purposes1 is not stated4 ,it is not to be supposed that this was the common system of counting1 for it is well known that the decimal scale was in use as far back as the evidence of language will take us4 ,but the field of speculation into which one is led by the octonary scale has proved most attractive to some1 and the conclusion has been soberly reached1 that in the history of the ,aryan race the octonary was to be regarded as the predecessor of the decimal scale4 ,in support of this theory no direct evidence is brought forward1 but certain verbal resemblances4 ,those ignes fatuii of the philologist are made to perform the duty of supporting an hypothesis which would never have existed but for their own treacherous suggestions4 ,here is one of the most attractive of them3 ,between the ,latin words novus1 new1 and novem1 nine1 there exists a resemblance so close that it may well be more than accidental4 ,nine is1 then1 the new number2 that is1 the first number on a new count1 of which #h must originally have been the base4 ,pursuing this thought by investigation into different languages1 the same resemblance is found there4 ,hence the theory is strengthened by corroborative evidence4 ,in language after language the same resemblance is found1 until it seems impossible to doubt1 that in prehistoric times1 #i was the new number--the beginning of a second tale4 ,the following table will show how widely spread is this coincidence3 ,sanskrit1 navan #i4 nava new4 ,persian1 nuh #i4 nau new4 ,greek1 ,greek3 ennea #i4 ,greek3 neos new4 ,latin1 novem #i4 novus new4 ,german1 neun #i4 neu new4 ,swedish1 nio #i4 ny new4 ,dutch1 negen #i4 nieuw new4 ,danish1 ni #i4 ny new4 ,icelandic1 nyr #i4 niu new4 ,english1 nine #i4 new new4 ,french1 neuf #i4 nouveau new4 ,spanish1 nueve #i4 neuvo new4 ,italian1 nove #i4 nuovo new4 ,portuguese1 nove #i4 novo new4 ,irish1 naoi #i4 nus new4 ,welsh1 naw #i4 newydd new4 ,breton1 nevez #i4 nuhue new4#bba ,this table might be extended still further1 but the above examples show how widely diffused throughout the ,aryan languages is this resemblance4 ,the list certainly is an impressive one1 and the student is at first thought tempted to ask whether all these resemblances can possibly have been accidental4 ,but a single consideration sweeps away the entire argument as though it were a cobweb4 ,all the languages through which this verbal likeness runs are derived directly or indirectly from one common stock2 and the common every-day words1 nine and new1 have been transmitted from that primitive tongue into all these linguistic offspring with but little change4 ,not only are the two words in question akin in each individual language1 but they are akin in all the languages4 ,hence all these resemblances reduce to a single resemblance1 or perhaps identity1 that between the ,aryan words for nine and new4 ,this was probably an accidental resemblance1 no more significant than any one of the scores of other similar cases occurring in every language4 ,if there were any further evidence of the former existence of an ,aryan octonary scale1 the coincidence would possess a certain degree of significance2 but not a shred has ever been produced which is worthy of consideration4 ,if our remote ancestors ever counted by eights1 we are entirely ignorant of the fact1 and must remain so until much more is known of their language than scholars now have at their command4 ,the word resemblances noted above are hardly more significant than those occurring in two ,polynesian languages1 the ,fatuhivan and the ,nakuhivan1#bbb where new is associated with the number #g4 ,in the former case #g is fitu1 and new is fou2 in the latter #g is hitu1 and new is hou4 ,but no one has1 because of this likeness1 ever suggested that these tribes ever counted by the senary method4 ,another equally trivial resemblance occurs in the ,tawgy and the ,kamassin languages1#bbc thus3 ,,tawgy4 ,,kamassin4 #h4 siti-data #b #d4 #h4 sin-the'de #b #d4 #i4 nameaitjuma another4 #i4 amithun another4 ,but it would be childish to argue1 from this fact alone1 that either #d or #h was the number base used4 ,in a recent antiquarian work of considerable interest1 the author examines into the question of a former octonary system of counting among the various races of the world1 particularly those of ,asia1 and brings to light much curious and entertaining material respecting the use of this number4 ,its use and importance in ,china1 ,india1 and central ,asia1 as well as among some of the islands of the ,pacific1 and in ,central ,america1 leads him to the conclusion that there was a time1 long before the beginning of recorded history1 when #h was the common number base of the world4 ,but his conclusion has no basis in his own material even4 ,the argument cannot be examined here1 but any one who cares to investigate it can find there an excellent illustration of the fact that a pet theory may take complete possession of its originator1 and reduce him finally to a state of infantile subjugation4#bbd ,of all numbers upon which a system could be based1 #ab seems to combine in itself the greatest number of advantages4 ,it is capable of division by #b1 #c1 #d1 and #f1 and hence admits of the taking of halves1 thirds1 quarters1 and sixths of itself without the introduction of fractions in the result4 ,from a commercial stand-point this advantage is very great2 so great that many have seriously advocated the entire abolition of the decimal scale1 and the substitution of the duodecimal in its stead4 ,it is said that ,charles ,,xii4 of ,sweden was actually contemplating such a change in his dominions at the time of his death4 ,in pursuance of this idea1 some writers have gone so far as to suggest symbols for #aj and #aa1 and to recast our entire numeral nomenclature to conform to the duodecimal base4#bbe ,were such a change made1 we should express the first nine numbers as at present1 #aj and #aa by new1 single symbols1 and #ab by #aj4 ,from this point the progression would be regular1 as in the decimal scale--only the same combination of figures in the different scales would mean very different things4 ,thus1 #ag in the decimal scale would become #ae in the duodecimal2 #add in the decimal would become #ajj in the duodecimal2 and #agbh1 the cube of the new base1 would of course be represented by the figures #ajjj4 ,it is impossible that any such change can ever meet with general or even partial favour1 so firmly has the decimal scale become intrenched in its position4 ,but it is more than probable that a large part of the world of trade and commerce will continue to buy and sell by the dozen1 the gross1 or some multiple or fraction of the one or the other1 as long as buying and selling shall continue4 ,such has been its custom for centuries1 and such will doubtless be its custom for centuries to come4 ,the duodecimal is not a natural scale in the same sense as are the quinary1 the decimal1 and the vigesimal2 but it is a system which is called into being long after the complete development of one of the natural systems1 solely because of the simple and familiar fractions into which its base is divided4 ,it is the scale of civilization1 just as the three common scales are the scales of nature4 ,but an example of its use was long sought for in vain among the primitive races of the world4 ,humboldt1 in commenting on the number systems of the various peoples he had visited during his travels1 remarked that no race had ever used exclusively that best of bases1 #ab4 ,but it has recently been announced#bbf that the discovery of such a tribe had actually been made1 and that the ,aphos of ,benu1 an ,african tribe1 count to #ab by simple words1 and then for #ac say #ab-a1 for #ad1 #ab-b1 etc4 ,this report has yet to be verified1 but if true it will constitute a most interesting addition to anthropological knowledge4 ,,chapter ,,vi4 ,,the ,,quinary ,,system4 ,the origin of the quinary mode of counting has been discussed with some fulness in a preceding chapter1 and upon that question but little more need be said4 ,it is the first of the natural systems4 ,when the savage has finished his count of the fingers of a single hand1 he has reached this natural number base4 ,at this point he ceases to use simple numbers1 and begins the process of compounding4 ,by some one of the numerous methods illustrated in earlier chapters1 he passes from #e to #aj1 using here the fingers of his second hand4 ,he now has two fives2 and1 just as we say twenty1 i4e4 two tens1 he says two hands1 the second hand finished1 all the fingers1 the fingers of both hands1 all the fingers come to an end1 or1 much more rarely1 one man4 ,that is1 he is1 in one of the many ways at his command1 saying two fives4 ,at #ae he has three hands or one foot2 and at #bj he pauses with four hands1 hands and feet1 both feet1 all the fingers of hands and feet1 hands and feet finished1 or1 more probably1 one man4 ,all these modes of expression are strictly natural1 and all have been found in the number scales which were1 and in many cases still are1 in daily use among the uncivilized races of mankind4 ,in its structure the quinary is the simplest1 the most primitive1 of the natural systems4 ,its base is almost always expressed by a word meaning hand1 or by some equivalent circumlocution1 and its digital origin is usually traced without difficulty4 ,a consistent formation would require the expression of #aj by some phrase meaning two fives1 #ae by three fives1 etc4 ,such a scale is the one obtained from the ,betoya language1 already mentioned in ,chapter ,,iii41 where the formation of the numerals is purely quinary1 as the following indicate3#bbg #e4 teente #a hand4 #aj4 cayaente1 or caya huena #b hands4 #ae4 toazumba-ente #c hands4 #bj4 caesa-ente #d hands4 ,the same formation appears1 with greater or less distinctness1 in many of the quinary scales already quoted1 and in many more of which mention might be made4 ,collecting the significant numerals from a few such scales1 and tabulating them for the sake of convenience of comparison1 we see this point clearly illustrated by the following3 ,,tamanac4 #e4 amnaitone #a hand4 #aj4 amna atse ponare #b hands4 ,,arawak1 ,,guiana4 #e4 abba tekkabe #a hand4 #aj4 biamantekkabe #b hands4 ,,jiviro4 #e4 alactegladu #a hand4 #aj4 catgladu #b hands4 ,,niam ,,niam #e4 biswe #aj4 bauwe #b;d #e4 ,,nengones #e4 se dono the end 7of the fingers of #a hand74 #aj4 rewe tubenine #b series 7of fingers74 ,,sesake4#bbh #e4 lima hand4 #aj4 dua lima #b hands4 ,,ambrym4#bbi #e4 lim hand4 #aj4 ra-lim #b hands4 ,,pama4#bbi #e4 e-lime hand4 #aj4 ha-lua-lim the #b hands4 ,,dinka4#bcj #e4 wdyets4 #aj4 wtyer1 or wtyar #e #b4 ,,bari #e4 kanat #aj4 puk #e #e8 ,,kanuri #e4 ugu4 #aj4 megu #b #e4 ,,rio ,,norte ,,and ,,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 ,,tlingit1 ,,british ,,columbia4#bcc #e4 kedjin 7from djin hand74 #aj4 djinkat both hands8 ,thus far the quinary formation is simple and regular2 and in view of the evidence with which these and similar illustrations furnish us1 it is most surprising to find an eminent authority making the unequivocal statement that the number #aj is nowhere expressed by #b fives#bcd--that all tribes which begin their count on a quinary base express #aj by a simple word4 ,it is a fact1 as will be fully illustrated in the following pages1 that quinary number systems1 when extended1 usually merge into either the decimal or the vigesimal4 ,the result is1 of course1 a compound of two1 and sometimes of three1 systems in one scale4 ,a pure quinary or vigesimal number system is exceedingly rare2 but quinary scales certainly do exist in which1 as far as we possess the numerals1 no trace of any other influence appears4 ,it is also to be noticed that some tribes1 like the ,eskimos of ,point ,barrow1 though their systems may properly be classed as mixed systems1 exhibit a decided preference for #e as a base1 and in counting objects1 divided into groups of #e1 obtaining the sum in this way4#bce ,but the savage1 after counting up to #aj1 often finds himself unconsciously impelled to depart from his strict reckoning by fives1 and to assume a new basis of reference4 ,take1 for example1 the ,zui system1 in which the first #b fives are3 #e4 pte the notched off4 #aj4 astem'thla all the fingers4 ,it will be noticed that the ,zui does not say two hands1 or the fingers of both hands1 but simply all the fingers4 ,the #e is no longer prominent1 but instead the mere notion of one entire count of the fingers has taken its place4 ,the division of the fingers into two sets of five each is still in his mind1 but it is no longer the leading idea4 ,as the count proceeds further1 the quinary base may be retained1 or it may be supplanted by a decimal or a vigesimal base4 ,how readily the one or the other may predominate is seen by a glance at the following numerals3 ,,galibi4#bcf #e4 atoneigne oietona #a hand4 #aj4 oia batoue the other hand4 #bj4 poupoupatoret oupoume feet and hands4 #dj4 opoupoume twice the feet and hands4 ,,guarani4#bcg #e4 ace popetei #a hand4 #aj4 ace pomocoi #b hands4 #bj4 acepo acepiabe hands and feet4 ,,fate4#bch #e4 lima hand4 #aj4 relima #b hands4 #bj4 relima rua 7#b #e7 #b4 ,,kiriri #e4 mibika misa #a hand4 #aj4 mikriba misa sai both hands4 #bj4 mikriba nusa ideko ibi sai both hands together with the feet4 ,,zamuco #e4 tsuena yimana-ite ended #a hand4 #aj4 tsuena yimana-die ended both hands4 #bj4 tsuena yiri-die ended both feet4 ,,pikumbul #e4 mulanbu4 #aj4 bularin murra belonging to the two hands4 #ae4 mulanba dinna #e toes added on 7to the #aj fingers74 #bj4 bularin dinna belonging to the #b feet4 ,,yaruros4#bci #e4 kani-iktsi-mo #a hand alone4 #aj4 yowa-iktsi-bo all the hands4 #ae4 kani-tao-mo #a foot alone4 #bj4 kani-pume #a man4 ,by the time #bj is reached the savage has probably allowed his conception of any aggregate to be so far modified that this number does not present itself to his mind as #d fives4 ,it may find expression in some phraseology such as the ,kiriris employ--both hands together with the feet--or in the shorter ended both feet of the ,zamucos1 in which case we may presume that he is conscious that his count has been completed by means of the four sets of fives which are furnished by his hands and feet4 ,but it is at least equally probable that he instinctively divides his total into #b tens1 and thus passes unconsciously from the quinary into the decimal scale4 ,again1 the summing up of the #aj fingers and #aj toes often results in the concept of a single whole1 a lump sum1 so to speak1 and the savage then says one man1 or something that gives utterance to this thought of a new unit4 ,this leads the quinary into the vigesimal scale1 and produces the combination so often found in certain parts of the world4 ,thus the inevitable tendency of any number system of quinary origin is toward the establishment of another and larger base1 and the formation of a number system in which both are used4 ,wherever this is done1 the greater of the two bases is always to be regarded as the principal number base of the language1 and the #e as entirely subordinate to it4 ,it is hardly correct to say that1 as a number system is extended1 the quinary element disappears and gives place to the decimal or vigesimal1 but rather that it becomes a factor of quite secondary importance in the development of the scale4 ,if1 for example1 #h is expressed by #e-c in a quinary decimal system1 #ih will be #i #aj #e-c4 ,the quinary element does not disappear1 but merely sinks into a relatively unimportant position4 ,one of the purest examples of quinary numeration is that furnished by the ,betoya scale1 already given in full in ,chapter ,,iii41 and briefly mentioned at the beginning of this chapter4 ,in the simplicity and regularity of its construction it is so noteworthy that it is worth repeating1 as the first of the long list of quinary systems given in the following pages4 ,no further comment is needed on it than that already made in connection with its digital significance4 ,as far as given by ,dr4 ,brinton the scale is3 #a4 tey4 #b4 cayapa4 #c4 toazumba4 #d4 cajezea #b with plural termination4 #e4 teente hand4 #f4 teyente tey hand #a4 #g4 teyente cayapa hand #b4 #h4 teyente toazumba hand #c4 #i4 teyente caesea hand #d4 #aj4 caya ente1 or caya huena #b hands4 #aa4 caya ente-tey #b hands #a4 #ae4 toazumba-ente #c hands4 #af4 toazumba-ente-tey #c hands #a4 #bj4 caesea ente #d hands4 ,a far more common method of progression is furnished by languages which interrupt the quinary formation at #aj1 and express that number by a single word4 ,any scale in which this takes place can1 from this point onward1 be quinary only in the subordinate sense to which allusion has just been made4 ,examples of this are furnished in a more or less perfect manner by nearly all so-called quinary-vigesimal and quinary-decimal scales4 ,as fairly representing this phase of number-system structure1 ,i have selected the first #bj numerals from the following languages3 ,,welsh4#bdj #a4 un4 #b4 dau4 #c4 tri4 #d4 pedwar4 #e4 pump4 #f4 chwech4 #g4 saith4 #h4 wyth4 #i4 naw4 #aj4 deg4 #aa4 un ar ddeg #a #aj4 #ab4 deuddeg #b #aj4 #ac4 tri ar ddeg #c #aj4 #ad4 pedwar ar ddeg #d #aj4 #ae4 pymtheg #e #aj4 #af4 un ar bymtheg #a #e #aj4 #ag4 dau ar bymtheg #b #e #aj4 #ah4 tri ar bymtheg #c #e #aj4 #ai4 pedwar ar bymtheg #d #e #aj4 #bj4 ugain4 ,,nahuatl4#bda #a4 ce4 #b4 ome4 #c4 yei4 #d4 naui4 #e4 macuilli4 #f4 chiquacen #e #a4 #g4 chicome #e #b4 #h4 chicuey #e #c4 #i4 chiucnaui #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 account4 ,,canaque#bdb ,,new ,,caledonia4 #a4 chaguin4 #b4 carou4 #c4 careri4 #d4 caboue #e4 cani4 #f4 cani-mon-chaguin #e #a4 #g4 cani-mon-carou #e #b4 #h4 cani-mon-careri #e #c4 #i4 cani-mon-caboue #e #d4 #aj4 panrere4 #aa4 panrere-mon-chaguin #aj #a4 #ab4 panrere-mon-carou #aj #b4 #ac4 panrere-mon-careri #aj #c4 #ad4 panrere-mon-caboue #aj #d4 #ae4 panrere-mon-cani #aj #e4 #af4 panrere-mon-cani-mon-chaguin #aj #e #a4 #ag4 panrere-mon-cani-mon-carou #aj #e #b4 #ah4 panrere-mon-cani-mon-careri #aj #e #c4 #ai4 panrere-mon-cani-mon-caboue #aj #e #d4 #bj4 jaquemo #a person4 ,,guato4#bdc #a4 cenai4 #b4 dououni4 #c4 coum4 #d4 dekai4 #e4 quinoui4 #f4 cenai-caicaira #a on the other8 #g4 dououni-caicaira #b on the other8 #h4 coum-caicaira #c on the other8 #i4 dekai-caicaira #d on the other8 #aj4 quinoi-da #e #b4 #aa4 cenai-ai-caibo #a 7the7 hands4 #ab4 dououni-ai-caibo #b #aj4 #ac4 coum-ai-caibo #c #aj4 #ad4 dekai-ai-caibo #d #aj4 #ae4 quin-oibo #e #c4 #af4 cenai-ai-quacoibo #a #ae4 #ag4 dououni-ai-quacoibo #b #ae4 #ah4 coum-ai-quacoibo #c #ae4 #ai4 dekai-ai-quacoibo #d #ae4 #bj4 quinoui-ai-quacoibo #e #ae4 ,the meanings assigned to the numerals #f to #i are entirely conjectural4 ,they obviously mean #a1 #b1 #c1 #d1 taken a second time1 and as the meanings ,i have given are often found in primitive systems1 they have1 at a venture1 been given here4 ,,lifu1 ,,loyalty ,,islands4#bdd #a4 ca4 #b4 lue4 #c4 koeni4 #d4 eke4 #e4 tji pi4 #f4 ca ngemen #a above4 #g4 lue ngemen #b above4 #h4 koeni ngemen #c above4 #i4 eke ngemen #d above4 #aj4 lue pi #b #e4 #aa4 ca ko4 #ab4 lue ko4 #ac4 koeni ko4 #ad4 eke ko4 #ae4 koeni pi #c #e4 #af4 ca huai ano4 #ag4 lua huai ano4 #ah4 koeni 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 do mui okpo kotu #aj #e more1 to #e1 #a more4 #ag4 ki dokpo mui do mui okpo ngorr #aj #e more1 to #e1 #b more4 #ah4 ki dokpo mui do mui okpo motta #aj #e more1 to #e1 #c more4 #ai4 ki dokpo mui do mui okpo nehea #aj #e more1 to #e1 #d more4 #bj4 mbaba kotu4 ,above #bj1 the ,lufu and the ,bongo systems are vigesimal1 so that they are1 as a whole1 mixed systems4 ,the ,welsh scale begins as though it were to present a pure decimal structure1 and no hint of the quinary element appears until it has passed #ae4 ,the ,nahuatl1 on the other hand1 counts from #e to #aj by the ordinary quinary method1 and then appears to pass into the decimal form4 ,but when #af is reached1 we find the quinary influence still persistent2 and from this point to #bj1 the numeral words in both scales are such as to show that the notion of counting by fives is quite as prominent as the notion of referring to #aj as a base4 ,above #bj the systems become vigesimal1 with a quinary or decimal structure appearing in all numerals except multiples of #bj4 ,thus1 in ,welsh1 #cf is unarbymtheg ar ugain1 #a #e #aj #bj2 and in ,nahuatl the same number is cempualli caxtolli oce1 #bj #ae #a4 ,hence these and similar number systems1 though commonly alluded to as vigesimal1 are really mixed scales1 with #bj as their primary base4 ,the ,canaque scale differs from the ,nahuatl only in forming a compound word for #ae1 instead of introducing a new and simple term4 ,in the examples which follow1 it is not thought best to extend the lists of numerals beyond #aj1 except in special instances where the illustration of some particular point may demand it4 ,the usual quinary scale will be found1 with a few exceptions like those just instanced1 to have the following structure or one similar to it in all essential 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 ,from these forms the entire system can readily be constructed as soon as it is known whether its principal base is to be #aj or #bj4 ,turning first to the native ,african languages1 ,i have selected the following quinary scales from the abundant material that has been collected by the various explorers of the ,dark ,continent4 ,in some cases the numerals of certain tribes1 as given by one writer1 are found to differ widely from the same numerals as reported by another4 ,no attempt has been made at comparison of these varying forms of orthography1 which are usually to be ascribed to difference of nationality on the part of the collectors4 ,,feloops4#bdf #a4 enory4 #b4 sickaba1 or cookaba4 #c4 sisajee4 #d4 sibakeer4 #e4 footuck4 #f4 footuck-enory #e-a4 #g4 footuck-cookaba #e-b4 #h4 footuck-sisajee #e-c4 #i4 footuck-sibakeer #e-d4 #aj4 sibankonyen4 ,,kissi4#bdg #a4 pili4 #b4 miu4 #c4 nga4 #d4 iol4 #e4 nguenu4 #f4 ngom-pum #e-a4 #g4 ngom-miu #e-b4 #h4 ngommag #e-c4 #i4 nguenu-iol #e-d4 #aj4 to4 ,,ashantee4#bdh #a4 tah4 #b4 noo4 #c4 sah4 #d4 nah4 #e4 taw4 #f4 torata #e #a4 #g4 toorifeenoo #e #b4 #h4 toorifeessa #e #c4 #i4 toorifeena #e #d4 #aj4 nopnoo4 ,,basa4#bdi #a4 do4 #b4 so4 #c4 ta4 #d4 hinye4 #e4 hum4 #f4 hum-le-do #e #a4 #g4 hum-le-so #e #b4 #h4 hum-le-ta #e #c4 #i4 hum-le-hinyo #e #d4 #aj4 bla-bue4 ,,jallonkas4#bej #a4 kidding4 #b4 fidding4 #c4 sarra4 #d4 nani4 #e4 soolo4 #f4 seni4 #g4 soolo ma fidding #e #b4 #h4 soolo ma sarra #e #c4 #i4 soolo ma nani #e #d4 #aj4 nuff4 ,,kru4 #a4 da-do4 #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 ,,jaloffs4#bea #a4 wean4 #b4 yar4 #c4 yat4 #d4 yanet4 #e4 judom4 #f4 judom-wean #e-a4 #g4 judom-yar #e-b4 #h4 judom-yat #e-c4 #i4 judom yanet #e-d4 #aj4 fook4 ,,golo4#beb #a4 mbali4 #b4 bisi4 #c4 bitta4 #d4 banda4 #e4 zonno4 #f4 tsimmi tongbali #e #a4 #g4 tsimmi tobisi #e #b4 #h4 tsimmi tobitta #e #c4 #i4 tsimmi to banda #e #d4 #aj4 nifo4 ,,foulah4#bec #a4 go4 #b4 deeddee4 #c4 tettee4 #d4 nee4 #e4 jouee4 #f4 jego #e-a4 #g4 jedeeddee #e-b4 #h4 je-tettee #e-c4 #i4 je-nee #e-d4 #aj4 sappo4 ,,soussou4#bed #a4 keren4 #b4 firing4 #c4 sarkan4 #d4 nani4 #e4 souli4 #f4 seni4 #g4 solo-fere #e-b4 #h4 solo-mazarkan #e #c4 #i4 solo-manani #e #d4 #aj4 fu4 ,,bullom4#bee #a4 bul4 #b4 tin4 #c4 ra4 #d4 hyul4 #e4 men4 #f4 men-bul #e-a4 #g4 men-tin #e-b4 #h4 men-ra #e-c4 #i4 men-hyul #e-d4 #aj4 won4 ,,vei4#bef #a4 dondo4 #b4 fera4 #c4 sagba4 #d4 nani4 #e4 soru4 #f4 sun-dondo #e-a4 #g4 sum-fera #e-b4 #h4 sun-sagba #e-c4 #i4 sun-nani #e-d4 #aj4 tan4 ,,dinka4#beg #a4 tok4 #b4 rou4 #c4 dyak4 #d4 nuan4 #e4 wdyets4 #f4 wdetem #e-a4 #g4 wderou #e-b4 #h4 bet1 bed #e-c4 #i4 wdenuan #e-d4 #aj4 wtyer #e #b4 ,,temne4 #a4 in4 #b4 ran4 #c4 sas4 #d4 anle4 #e4 tr-amat4 #f4 tr-amat rok-in #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-ofatr4 ,,abaker4#beh #a4 kili4 #b4 bore4 #c4 dotla4 #d4 ashe4 #e4 ini4 #f4 im kili #e-a4 #g4 im-bone #e-b4 #h4 ini-dotta #e-c4 #i4 tin ashe #e-d4 #aj4 chica4 ,,bagrimma4#bei #a4 kede4 #b4 sab4 #c4 muta4 #d4 so4 #e4 mi4 #f4 mi-ga #e #a4 #g4 tsidi4 #h4 marta #e #b4 #i4 do-so #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 atjeenne #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 nini4 #b4 gu-ba4 #c4 gu-ta4 #d4 gu-ni4 #e4 gu-tsun4 #f4 gu-sua-yin #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 ttin4 #f4 itjekee #e #a4 #g4 ittiaba #e #b4 #h4 itteiata #e #c4 #i4 huschukiet4 #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 legar4 #aj4 megu #b #e4 ,,binin4#bfe #a4 bo4 #b4 be4 #c4 la4 #d4 nin4 #e4 tang4 #f4 tahu #e #a8 #g4 tabi #e #b4 #h4 tara #e #c4 #i4 ianin 7tanin87 #e #d8 #aj4 te4 ,,kredy4#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 ,,herero4#bfg #a4 mue4 #b4 vari4 #c4 tatu4 #d4 ne4 #e4 tano4 #f4 hambou-mue #e #a4 #g4 hambou-vari #e #b4 #h4 hambou-tatu #e #c4 #i4 hambou-ne #e #d4 #aj4 ,,ki-,,yau4#bfh #a4 jumo4 #b4 wawiri4 #c4 watatu4 #d4 mcheche4 #e4 msano4 #f4 musano na jumo #e #a4 #g4 musano na wiri #e #b4 #h4 musano na watatu #e #c4 #i4 musano na mcheche #e #d4 #aj4 ikumi4 ,,fernando ,,po4#bfi #a4 muli4 #b4 mempa4 #c4 meta4 #d4 miene4 #e4 mimito4 #f4 mimito na muli #e #a4 #g4 mimito na mempa #e #b4 #h4 mimito na meta #e #c4 #i4 mimito na miene #e #d4 #aj4 miemieu #e-e8 ,,ki-,,nyassa #a4 kimodzi4 #b4 vi-wiri4 #c4 vi-tatu4 #d4 vinye4 #e4 visano4 #f4 visano na kimodzi #e #a4 #g4 visano na vi-wiri #e #b4 #h4 visano na vitatu #e #c4 #i4 visano na vinye #e #d4 #aj4 chikumi4 ,,balengue4#bgj #a4 guevoho4 #b4 ibare4 #c4 raro4 #d4 ina4 #e4 itano4 #f4 itano na guevoho #e #a4 #g4 itano na ibare #e #b4 #h4 itano na raro #e #c4 #i4 itano na ina #e #d4 #aj4 ndioum1 or nai-hina4 ,,kunama4#bga #a4 ella4 #b4 bare4 #c4 sadde4 #d4 salle4 #e4 kussume4 #f4 kon-t'-ella hand #a4 #g4 kon-te-bare hand #b4 #h4 kon-te-sadde hand #c4 #i4 kon-te-salle hand #d4 #aj4 kol-lakada4 ,,gola4#bgb #a4 ngoumou4 #b4 ntie4 #c4 nta4 #d4 tina4 #e4 nonon4 #f4 diegoum #e #a4 #g4 dientie #e #b4 #h4 dietai #e #c4 #i4 dectina #e #d4 #aj4 esia4 ,,barea4#bgc #a4 doko #b4 arega4 #c4 sane4 #d4 sone4 #e4 oita4 #f4 data4 #g4 dz-ariga #e #b4 #h4 dis-sena #e #c4 #i4 lefete-mada without #aj4 #aj4 lefek4 ,,matibani4#bgd #a4 mosa4 #b4 pili4 #c4 taru4 #d4 teje4 #e4 taru4 #f4 tana mosa #e-a4 #g4 tana pili #e-b4 #h4 tana taru #e-c4 #i4 loco4 #aj4 loco nakege4 ,,bonz4#bge #a4 tan4 #b4 vele4 #c4 daba4 #d4 nani4 #e4 lolou4 #f4 mada #e #a4 #g4 mafile #e #b4 #h4 mashaba #e #c4 #i4 manan #e #d4 #aj4 bou4 ,,mpovi #a4 moueta4 #b4 bevali4 #c4 betata4 #d4 bena4 #e4 betani4 #f4 betani moueta #e-a4 #g4 betani bevali #e-b4 #h4 betani betata #e-c4 #i4 betani benai #e-d4 #aj4 nchinia4 ,,triton',s ,,bay1 ,,new ,,quinea4#bgf #a4 samosi4 #b4 roueti4 #c4 tourou4 #d4 faat4 #e4 rimi4 #f4 rim-samosi #e-a4 #g4 rim-roueti #e-b4 #h4 rim-tourou #e-c4 #i4 rim-faat #e-d4 #aj4 outsia4 ,,ende1 ,,or ,,flores4#bgg #a4 sa4 #b4 zua4 #c4 telu4 #d4 wutu4 #e4 lima hand4 #f4 lima-sa #e-a1 or hand #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 senearn4 ,,ebon1 ,,marshall ,,islands4#bgi #a4 iuwun4 #b4 drud4 #c4 chilu4 #d4 emer4 #e4 lailem4 #f4 chilchinu #e #a4 #g4 chilchime #e #b4 #h4 twalithuk #aj - #b4 #i4 twahmejuwou #aj - #a4 #aj4 iungou4 ,,uea1 ,,loyalty ,,island4#bhj #a4 tahi4 #b4 lua4 #c4 tolu4 #d4 fa4 #e4 lima4 #f4 tahi4 #g4 lua4 #h4 tolu4 #i4 fa4 #aj4 lima4 ,,uea4#bhj--;another dialect4 #a4 hacha4 #b4 lo4 #c4 kuun4 #d4 thack4 #e4 thabumb4 #f4 lo-acha #b;d #a4 #g4 lo-alo #b;d #b4 #h4 lo-kuun #b;d #c4 #i4 lo-thack #b;d #d4 #aj4 lebenetee4 ,,isle ,,of ,,pines4#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 ,,ureparapara1 ,,banks ,,islands4#bhb #a4 vo towa4 #b4 vo ro4 #c4 vo tol4 #d4 vo vet4 #e4 teveliem #a hand4 #f4 leve jea other #a4 #g4 leve ro other #b4 #h4 leve tol other #c4 #i4 leve vet other #d4 #aj4 sanowul #b sets4 ,,mota1 ,,banks ,,islands4#bhb #a4 tuwale4 #b4 nirua4 #c4 nitol4 #d4 nivat4 #e4 tavelima #a hand4 #f4 laveatea other #a4 #g4 lavearua other #b4 #h4 laveatol other #c4 #i4 laveavat other #d4 #aj4 sanavul #b sets4 ,,new ,,caledonia4#bhc #a4 parai4 #b4 paroo4 #c4 parghen4 #d4 parbai4 #e4 panim4 #f4 panim-gha #e-a4 #g4 panim-roo #e-b4 #h4 panim-ghen #e-c4 #i4 panim-bai #e-d4 #aj4 parooneek4 ,,yengen1 ,,new ,,cal4#bhd #a4 hets4 #b4 heluk4 #c4 heyen4 #d4 pobits4 #e4 nim hand4 #f4 nim-wet #e-a4 #g4 nim-weluk #e-b4 #h4 nim-weyen #e-c4 #i4 nim-pobit #e-d4 #aj4 pain-duk4 ,,aneiteum4#bhe #a4 ethi4 #b4 ero4 #c4 eseik4 #d4 manohwan4 #e4 nikman4 #f4 nikman cled et ethi #e #a4 #g4 nikman cled et oro #e #b4 #h4 nikman cled et eseik #e #c4 #i4 nikman cled et manohwan #e #d4 #aj4 nikman lep ikman #e #e4 ,,tanna #a4 riti4 #b4 karu4 #c4 kahar4 #d4 kefa4 #e4 krirum4 #f4 krirum riti #e-a4 #g4 krirum karu #e-b4 #h4 krirum kahar8 #e-c4 #i4 krirum kefa8 #e-d4 #aj4 ---- ,,eromanga #a4 sai4 #b4 duru4 #c4 disil4 #d4 divat4 #e4 siklim #a hand4 #f4 misikai other #a8 #g4 siklim naru #e-b4 #h4 siklim disil #e-c4 #i4 siklim mindivat #e #d4 #aj4 narolim #b hands4 ,,fate1 ,,new ,,heb4#bhf #a4 iskei4 #b4 rua4 #c4 tolu4 #d4 bate4 #e4 lima hand4 #f4 la tesa other #a4 #g4 la rua other #b4 #h4 la tolu other #c4 #i4 la fiti other #d4 #aj4 relima #b hands4 ,,api1 ,,new ,,heb4 #a4 tai4 #b4 lua4 #c4 tolu4 #d4 vari4 #e4 lima hand4 #f4 o rai other #a4 #g4 o lua other #b4 #h4 o tolo other #c4 #i4 o vari other #d4 #aj4 lua lima #b hands4 ,,sesake1 ,,new ,,heb4 #a4 sikai4 #b4 dua4 #c4 dolu4 #d4 pati4 #e4 lima hand4 #f4 la tesa other #a4 #g4 la dua other #b4 #h4 la dolu other #c4 #i4 lo veti other #d4 #aj4 dua lima #b hands4 ,,pama1 ,,new ,,heb4 #a4 tai4 #b4 e lua4 #c4 e tolu4 #d4 e hati4 #e4 e lime hand4 #f4 a hitai other #a4 #g4 o lu other #b4 #h4 o tolu other #c4 #i4 o hati other #d4 #aj4 ha lua lim #b hands ,,aurora1 ,,new ,,heb4 #a4 tewa4 #b4 i rua4 #c4 i tol4 #d4 i vat4 #e4 tavalima #a hand4 #f4 lava tea other #a4 #g4 lava rua other #b4 #h4 lava tol other #c4 #i4 la vat other #d4 #aj4 sanwulu two sets4 ,,tobi4#bhg #a4 yat4 #b4 glu4 #c4 ya4 #d4 uan4 #e4 yanim #a hand4 #f4 yawor other #a4 #g4 yavic other #b4 #h4 yawa other #c4 #i4 yatu other #d4 #aj4 yasec4 ,,palm ,,island4#bhh #a4 yonkol4 #b4 yakka4 #c4 tetjora4 #d4 tarko4 #e4 yonkol mala #a hand4 ,,jajowerong1 ,,victoria4#bhh #a4 kiarp4 #b4 bulaits4 #c4 bulaits kiarp #b-a4 #d4 bulaits bulaits #b-b4 #e4 kiarp munnar #a hand4 #f4 bulaits bulaits bulaits #b-b-b4 #aj4 bulaits munnar #b hands4 ,the last two scales deserve special notice4 ,they are ,australian scales1 and the former is strongly binary1 as are so many others of that continent4 ,but both show an incipient quinary tendency in their names for #e and #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 ,,tschukschi4#bij #a4 inen4 #b4 nirach4 #c4 n'roch4 #d4 n'rach4 #e4 miligen hand4 #f4 inen miligen #a-e4 #g4 nirach miligen #b-e4 #h4 anwrotkin4 #i4 chona tsinki4 #aj4 migitken both hands4 ,,kottisch#bia #a4 hutsa4 #b4 ina4 #c4 tona4 #d4 sega4 #e4 chega4 #f4 chelutsa #e #a4 #g4 chelina #e #b4 #h4 chaltona #e #c4 #i4 tsumnaga #aj - #a4 #aj4 haga4 ,,eskimo ,,of ,n4-,w4 ,,alaska4#bib #a4 a towshek4 #b4 hipah1 or malho4 #c4 pingishute4 #d4 sesaimat4 #e4 talema4 #f4 okvinile1 or ahchegaret another #a8 #g4 talema-malronik #e-two of them4 #h4 pingishu-okvingile #b;d #c8 #i4 kolingotalia #aj - #a8 #aj4 koleet4 ,,kamtschatka1 ,,south4#bic #a4 dischak4 #b4 kascha4 #c4 tschook4 #d4 tschaaka4 #e4 kumnaka4 #f4 ky'lkoka4 #g4 itatyk #b #e4 #h4 tschookotuk #c #e4 #i4 tschuaktuk #d #e4 #aj4 kumechtuk #e #e4 ,,aleuts#bid #a4 ataqan4 #b4 aljak4 #c4 qankun4 #d4 sitsin4 #e4 tsan my hand4 #f4 atun #a #e4 #g4 ulun #b #e4 #h4 qamtsin #c #e4 #i4 sitsin #d #e4 #aj4 hatsiq4 ,,tchiglit1 ,,mackenzie ,r4#bie #a4 ataotirkr4 #b4 aypak1 or malloerok4 #c4 illaak1 or piatcut4 #d4 titamat4 #e4 tallemat4 #f4 arveneloerit4 #g4 arveneloerit-aypak #e #b4 #h4 arveneloerit-illaak #e #c4 #i4 arveneloerit-titamat #e #d4 #aj4 krolit4 ,,sahaptin 7,,nez ,,perces74#bif #a4 naks4 #b4 lapit4 #c4 mitat4 #d4 pi-lapt #b #b4 #e4 pachat4 #f4 oi-laks #e #a4 #g4 oi-napt #e #b4 #h4 oi-matat #e #c4 #i4 koits4 #aj4 putimpt4 ,,greenland4#big #a4 atauseq4 #b4 machdluq4 #c4 pinasut4 #d4 sisamat #e4 tadlimat4 #f4 achfineq-atauseq other hand #a4 #g4 achfineq-machdluq other hand #b4 #h4 achfineq-pinasut other hand #c4 #i4 achfineq-sisamat other hand #d4 #aj4 qulit4 #aa4 achqaneq-atauseq first foot #a4 #ab4 achqaneq-machdluq first foot #b4 #ac4 achqaneq-pinasut first foot #c4 #ad4 achqaneq-sisamat first foot #d4 #ae4 achfechsaneq8 #af4 achfechsaneq-atauseq other foot #a4 #ag4 achfechsaneq-machdlup other foot #b4 #ah4 achfechsaneq-pinasut other foot #c4 #ai4 achfechsaneq-sisamat other foot #d4 #bj4 inuk navdlucho a man ended4 ,up to this point the ,greenlander's scale is almost purely quinary4 ,like those of which mention was made at the beginning of this chapter1 it persists in progressing by fives until it reaches #bj1 when it announces a new base1 which shows that the system will from now on be vigesimal4 ,this scale is one of the most interesting of which we have any record1 and will be noticed again in the next chapter4 ,in many respects it is like the scale of the ,point ,barrow ,eskimo1 which was given early in ,chapter ,,iii4 ,the ,eskimo languages are characteristically quinary-vigesimal in their number systems1 but few of them present such perfect examples of that method of counting as do the two just mentioned4 ,,chippeway4#bih #a4 bejig4 #b4 nij4 #c4 nisswi4 #d4 niwin4 #e4 nanun4 #f4 ningotwasswi #a again8 #g4 nijwasswi #b again8 #h4 nishwasswi #c again8 #i4 jangasswi #d again8 #aj4 midasswi #e again4 ,,massachusetts4#bii #a4 nequt4 #b4 neese4 #c4 nish4 #d4 yaw4 #e4 napanna on one side1 i4e4 #a hand4 #f4 nequttatash #a added4 #g4 nesausuk #b again8 #h4 shawosuk #c again8 #i4 pashoogun it comes near1 i4e4 to #aj4 #aj4 puik4 ,,ojibwa ,,of ,,chegoimegon4#cjj #a4 bashik4 #b4 neensh4 #c4 niswe4 #d4 newin4 #e4 nanun4 #f4 ningodwaswe #a again8 #g4 nishwaswe #b again8 #h4 shouswe #c again8 #i4 shangaswe #d again8 #aj4 medaswe #e again8 ,,ottawa4 #a4 ningotchau4 #b4 ninjwa4 #c4 niswa4 #d4 niwin4 #e4 nanau4 #f4 ningotwaswi #a again8 #g4 ninjwaswi #b again8 #h4 nichwaswi #c again8 #i4 shang4 #aj4 kwetch4 ,,delaware4 #a4 n'gutti4 #b4 niskha4 #c4 nakha4 #d4 newa4 #e4 nalan akin to palenach1 hand4 #f4 guttash #a on the other side4 #g4 nishash #b on the other side4 #h4 khaash #c on the other side4 #i4 peshgonk coming near4 #aj4 tellen no more4 ,,shawnoe4 #a4 negote4 #b4 neshwa4 #c4 nithuie4 #d4 newe4 #e4 nialinwe gone4 #f4 negotewathwe #a further4 #g4 neshwathwe #b further4 #h4 sashekswa #c further8 #i4 chakatswe akin to chagisse1 used up4 #aj4 metathwe no further4 ,,micmac4#cja #a4 naiookt4 #b4 tahboo4 #c4 seest4 #d4 naioo4 #e4 nahn4 #f4 usoo-cum4 #g4 eloo-igunuk4 #h4 oo-gumoolchin4 #i4 pescoonaduk4 #aj4 mtlin4 ,one peculiarity of the ,micmac numerals is most noteworthy4 ,the numerals are real verbs1 instead of adjectives1 or1 as is sometimes the case1 nouns4 ,they are conjugated through all the variations of mood1 tense1 person1 and number4 ,the forms given above are not those that would be used in counting1 but are for specific use1 being varied according to the thought it was intended to express4 ,for example1 naiooktaich there is #a1 is present tense2 naiooktaichcus1 there was #a1 is imperfect2 and encoodaichdedou1 there will be #a1 is future4 ,the variation in person is shown by the following inflection3 ,,present ,,tense4 #ast pers4 tahboosee-ek there are #b of us4 #b;d pers4 tahboosee-yok there are #b of you4 #c;d pers4 tahboo-sijik there are #b of them4 ,,imperfect ,,tense4 #ast pers4 tahboosee-egup there were #b of us4 #b;d pers4 tahboosee-yogup there were #b of you4 #c;d pers4 tahboosee-sibunik there were #b of them4 ,,future ,,tense4 #c;d pers4 tahboosee-dak there will be #b of them1 etc4 ,the negative form is also comprehended in the list of possible variations4 ,thus1 tahboo-seekw1 there are not #b of them2 mah tahboo-seekw1 there will not be #b of them2 and so on1 through all the changes which the conjugation of the verb permits4 ,,old ,,algonquin4 #a4 peygik4 #b4 ninsh4 #c4 nisswey4 #d4 neyoo4 #e4 nahran gone4 #f4 ningootwassoo #a on the other side4 #g4 ninshwassoo #b on the other side4 #h4 nisswasso #c on the other side4 #i4 shangassoo akin to chagisse1 used up4 #aj4 mitassoo no further4 ,,omaha4 #a4 meeachchee4 #b4 nomba4 #c4 rabeenee4 #d4 tooba4 #e4 satta hand1 i4e4 all the fingers turned down4 #f4 shappai #a more4 #g4 painumba fingers #b4 #h4 pairabeenee fingers #c4 #i4 shonka only #a finger 7remains74 #aj4 kraibaira unbent4#cjb ,,choctaw4 #a4 achofee4 #b4 tuklo4 #c4 tuchina4 #d4 ushta4 #e4 tahlape the first hand ends4 #f4 hanali4 #g4 untuklo again #b4 #h4 untuchina again #c4 #i4 chokali soon the end2 i4e4 next the last4 #aj4 pokoli4 ,,caddoe4 #a4 kouanigh4 #b4 behit4 #c4 daho4 #d4 hehweh4 #e4 dihsehkon4 #f4 dunkeh4 #g4 bisekah #e #b4 #h4 dousehka #e #c4 #i4 hehwehsehka #d hand4 #aj4 behnehaugh4 ,,chippeway4 #a4 payshik4 #b4 neesh4 #c4 neeswoy4 #d4 neon4 #e4 naman gone4 #f4 nequtwosswoy #a on the other side4 #g4 neeshswosswoy #b on the other side4 #h4 swoswoy #c on the other side8 #i4 shangosswoy akin to chagissi1 used up4 #aj4 metosswoy no further4 ,,adaize4 #a4 nancas4 #b4 nass4 #c4 colle4 #d4 tacache4 #e4 seppacan4 #f4 pacanancus #e #a4 #g4 pacaness #e #b4 #h4 pacalcon #e #c4 #i4 sickinish hands minus8 #aj4 neusne4 ,,pawnee4 #a4 askoo4 #b4 peetkoo4 #c4 touweet4 #d4 shkeetiksh4 #e4 sheeooksh hands half4 #f4 sheekshabish #e #a4 #g4 peetkoosheeshabish #b #e4 #h4 touweetshabish #c #e4 #i4 looksheereewa #aj - #a4 #aj4 looksheeree #b;d #e8 ,,minsi4 #a4 gutti4 #b4 niskha4 #c4 nakba4 #d4 newa4 #e4 nulan gone8 #f4 guttash #a added4 #g4 nishoash #b added4 #h4 khaash #c added4 #i4 noweli4 #aj4 wimbat4 ,,konlischen4 #a4 tlek4 #b4 tech4 #c4 nezk4 #d4 taakun4 #e4 kejetschin4 #f4 klet uschu #e #a4 #g4 tachate uschu #e #b4 #h4 nesket uschu #e #c4 #i4 kuschok #aj - #a8 #aj4 tschinkat4 ,,tlingit4#cjc #a4 tlek4 #b4 deq4 #c4 natsk4 #d4 dak'on #b;d #b4 #e4 kedjin hand4 #f4 tle durcu other #a4 #g4 daqa durcu other #b4 #h4 natska durcu other #c4 #i4 gocuk4 #aj4 djinkat both hands4 ,,rapid1 ,,or ,,fall1 ,,indians4 #a4 karci4 #b4 neece4 #c4 narce4 #d4 nean4 #e4 yautune4 #f4 neteartuce #a over8 #g4 nesartuce #b over8 #h4 narswartuce #c over8 #i4 anharbetwartuce #d over8 #aj4 mettartuce no further8 ,,heiltsuk4#cjd #a4 men4 #b4 matl4 #c4 yutq4 #d4 mu4 #e4 sky'a4 #f4 katla4 #g4 matlaaus other #b8 #h4 yutquaus other #c8 #i4 mamene #aj - #a4 #aj4 aiky'as4 ,,nootka4#cje #a4 nup4 #b4 atla4 #c4 katstsa4 #d4 mo4 #e4 sutca4 #f4 nopo other #a8 #g4 atlpo other #b8 #h4 atlakutl #aj - #b4 #i4 ts'owakutl #aj - #a4 #aj4 haiu4 ,,tsimshian4#cjf #a4 gyak4 #b4 tepqat4 #c4 guant4 #d4 tqalpq4 #e4 kctonc 7from anon1 hand74 #f4 kalt #b;d #a4 #g4 t'epqalt #b;d #b4 #h4 guandalt #b;d #c8 #i4 kctemac4 #aj4 gy'ap4 ,,bilqula4#cjf #a4 7s7maotl4 #b4 tlnos4 #c4 asmost4 #d4 mos4 #e4 tsech4 #f4 tqotl #b;d #a8 #g4 nustlnos #b;d #b8 #h4 k'etlnos #b #d4 #i4 k'esman4 #aj4 tskchlakcht4 ,,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 laginstshiatkus4 #aj4 nawitspu4 ,,waiilatpu4#cjh #a4 na4 #b4 leplin4 #c4 matnin4 #d4 piping4 #e4 tawit4 #f4 noina #e #a4 #g4 noilip #e #b4 #h4 noimat #e #c4 #i4 tanauiaishimshim4 #aj4 ningitelp4 ,,lutuami4#cjg #a4 natshik4 #b4 lapit4 #c4 ntani4 #d4 wonip4 #e4 tonapni4 #f4 nakskishuptane #a #e4 #g4 tapkishuptane #b #e4 #h4 ndanekishuptane #c #e4 #i4 natskaiakish #aj - #a4 #aj4 taunip4 ,,saste 7,,shasta74#cji #a4 tshiamu4 #b4 hoka4 #c4 hatski4 #d4 irahaia4 #e4 etsha4 #f4 tahaia4 #g4 hokaikinis #b #e4 #h4 hatsikikiri #c #e4 #i4 kirihariki-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 marua4 #f4 mareka #e #a #g4 pikitsa #e #b #h4 pikinahu #e #c #i4 peke-tsaketa #e #d #aj4 tuma4 ,,otomi#cab #a4 nara4 #b4 yocho4 #c4 chiu4 #d4 gocho4 #e4 kuto4 #f4 rato #a #e4 #g4 yoto #b #e4 #h4 chiato #c #e4 #i4 guto #d #e4 #aj4 reta4 ,,tarasco4#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 temben4 ,,matlaltzincan4#cad #a4 indawi4 #b4 inawi4 #c4 inyuhu4 #d4 inkunowi4 #e4 inkutaa4 #f4 inda-towi #a #e4 #g4 ine-towi #b #e4 #h4 ine-ukunowi #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 7akin to moamati1 hand74 ,,aymara4#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 ,,caribs ,,of ,,essequibo1 ,,guiana4#cag #a4 oween4 #b4 oko4 #c4 oroowa4 #d4 oko-baimema4 #e4 wineetanee #a hand4 #f4 owee-puimapo #a again8 #g4 oko-puimapo #b again8 #h4 oroowa-puimapo #c again8 #i4 oko-baimema-puimapo #d again8 #aj4 oween-abatoro4 ,,carib4#cah 7,,roucouyenne87 #a4 aban1 amoin4 #b4 biama4 #c4 eleoua4 #d4 biam-bouri #b again8 #e4 ouacabo-apourcou-aban-tibateli4 #f4 aban laoyagone-ouacabo-apourcou4 #g4 biama laoyagone-ouacabo-apourcou4 #h4 eleoua laoyagone-ouacabo-apourcou4 #i4 ---- #aj4 chon noucabo4 ,it is unfortunate that the meanings of these remarkable numerals cannot be given4 ,the counting is evidently quinary1 but the terms used must have been purely descriptive expressions1 having their origin undoubtedly in certain gestures or finger motions4 ,the numerals obtained from this region1 and from the tribes to the south and east of the ,carib country1 are especially rich in digital terms1 and an analysis of the above numerals would probably show clearly the mental steps through which this people passed in constructing the rude scale which served for the expression of their ideas of number4 ,,kiriri4#cai #a4 biche4 #b4 watsani4 #c4 watsani dikie4 #d4 sumara oroba4 #e4 mi biche misa #a hand4 #f4 mirepri bu-biche misa sai4 #g4 mirepri watsani misa sai4 #h4 mirepri watsandikie misa sai4 #i4 mirepri sumara oraba sai4 #aj4 mikriba misa sai both hands4 ,,cayubaba#cbj #a4 pebi4 #b4 mbeta4 #c4 kimisa4 #d4 pusi4 #e4 pisika4 #f4 sukuta4 #g4 pa-kaluku #b again8 #h4 kimisa-kaluku #c again8 #i4 pusu-kaluku #d again8 #aj4 tunka4 ,,sapibocona#cbj #a4 karata4 #b4 mitia4 #c4 kurapa4 #d4 tsada4 #e4 maidara 7from arue1 hand74 #f4 karata-rirobo #a hand with4 #g4 mitia-rirobo #b hand with4 #h4 kurapa-rirobo #c hand with4 #i4 tsada-rirobo #d hand with4 #aj4 bururutse hand hand4 ,,ticuna4#cba #a4 hueih4 #b4 tarepueh4 #c4 tomepueh4 #d4 aguemoujih #e4 hueamepueh4 #f4 namehueapueh #e #a4 #g4 namehueatareh #e #b4 #h4 namehueatameapueh #e #c4 #i4 gomeapueh #aj - #a4 #aj4 gomeh4 ,,yanua4#cbb #a4 tckini4 #b4 nanojui4 #c4 munua4 #d4 narojuino #b;d #b4 #e4 tenaja4 #f4 teki-natea #a again8 #g4 nanojui-natea #b again8 #h4 munua-natea #c again8 #i4 narojuino-natea #d again8 #aj4 huijejuino #b #e8 ,the foregoing examples will show with considerable fulness the wide dispersion of the quinary scale4 ,every part of the world contributes its share except ,europe1 where the only exceptions to the universal use of the decimal system are the half-dozen languages1 which still linger on its confines1 whose number base is the vigesimal4 ,not only is there no living ,european tongue possessing a quinary number system1 but no trace of this method of counting is found in any of the numerals of the earlier forms of speech1 which have now become obsolete4 ,the only possible exceptions of which ,i can think are the ,greek ,greek3 pempazein1 to count by fives1 and a few kindred words which certainly do hint at a remote antiquity in which the ancestors of the ,greeks counted on their fingers1 and so grouped their units into fives4 ,the ,roman notation1 the familiar ,i41 ,,ii41 ,,iii41 ,,iv4 7originally ,,iiii471 ,v41 ,,vi41 etc41 with equal certainty suggests quinary counting1 but the ,latin language contains no vestige of anything of the kind1 and the whole range of ,latin literature is silent on this point1 though it contains numerous references to finger counting4 ,it is quite within the bounds of possibility that the prehistoric nations of ,europe possessed and used a quinary numeration4 ,but of these races the modern world knows nothing save the few scanty facts that can be gathered from the stone implements which have now and then been brought to light4 ,their languages have perished as utterly as have the races themselves1 and speculation concerning them is useless4 ,whatever their form of numeration may have been1 it has left no perceptible trace on the languages by which they were succeeded4 ,even the languages of northern and central ,europe which were contemporary with the ,greek and ,latin of classical times have1 with the exception of the ,celtic tongues of the extreme ,north-west1 left behind them but meagre traces for the modern student to work on4 ,we presume that the ancient ,gauls and ,goths1 ,huns and ,scythians1 and other barbarian tribes had the same method of numeration that their descendants now have2 and it is a matter of certainty that the decimal scale was1 at that time1 not used with the universality which now obtains2 but wherever the decimal was not used1 the universal method was vigesimal2 and that the quinary ever had anything of a foothold in ,europe is only to be guessed from its presence to-day in almost all of the other corners of the world4 ,from the fact that the quinary is that one of the three natural scales with the smallest base1 it has been conjectured that all tribes possess1 at some time in their history1 a quinary numeration1 which at a later period merges into either the decimal or the vigesimal1 and thus disappears or forms with one of the latter a mixed system4#cbc ,in support of this theory it is urged that extensive regions which now show nothing but decimal counting were1 beyond all reasonable doubt1 quinary4 ,it is well known1 for example1 that the decimal system of the ,malays has spread over almost the entire ,polynesian region1 displacing whatever native scales it encountered4 ,the same phenomenon has been observed in ,africa1 where the ,arab traders have disseminated their own numeral system very widely1 the native tribes adopting it or modifying their own scales in such a manner that the ,arab influence is detected without difficulty4 ,in view of these facts1 and of the extreme readiness with which a tribe would through its finger counting fall into the use of the quinary method1 it does not at first seem improbable that the quinary was the original system4 ,but an extended study of the methods of counting in vogue among the uncivilized races of all parts of the world has shown that this theory is entirely untenable4 ,the decimal scale is no less simple in its structure than the quinary2 and the savage1 as he extends the limit of his scale from #e to #f1 may call his new number #e-a1 or1 with equal probability1 give it an entirely new name1 independent in all respects of any that have preceded it4 ,with the use of this new name there may be associated the conception of #e and #a more2 but in such multitudes of instances the words employed show no trace of any such meaning1 that it is impossible for any one to draw1 with any degree of safety1 the inference that the signification was originally there1 but that the changes of time had wrought changes in verbal form so great as to bury it past the power of recovery4 ,a full discussion of this question need not be entered upon here4 ,but it will be of interest to notice two or three numeral scales in which the quinary influence is so faint as to be hardly discernible4 ,they are found in considerable numbers among the ,north ,american ,indian languages1 as may be seen by consulting the vocabularies that have been prepared and published during the last half century4#cbd ,from these ,i have selected the following1 which are sufficient to illustrate the point in question3 ,,quappa4 #a4 milchtih4 #b4 nonnepah4 #c4 dahghenih4 #d4 tuah4 #e4 sattou4 #f4 schappeh4 #g4 pennapah4 #h4 pehdaghenih4 #i4 schunkkah4 #aj4 gedeh bonah4 ,,terraba4#cbe #a4 krara4 #b4 krow4 #c4 krom miah4 #d4 krob king4 #e4 krasch kingde4 #f4 terdeh4 #g4 kogodeh4 #h4 kwongdeh4 #i4 schkawdeh4 #aj4 dwowdeh4 ,,mohican #a4 ngwitloh4 #b4 neesoh4 #c4 noghhoh4 #d4 nauwoh4 #e4 nunon4 #f4 ngwittus4 #g4 tupouwus4 #h4 ghusooh4 #i4 nauneeweh4 #aj4 mtannit4 ,in the ,quappa scale #g and #h appear to be derived from #b and #c1 while #f and #i show no visible trace of kinship with #a and #d4 ,in ,mohican1 on the other hand1 #f and #i seem to be derived from #a and #d1 while #g and #h have little or no claim to relationship with #b and #c4 ,in some scales a single word only is found in the second quinate to indicate that #e was originally the base on which the system rested4 ,it is hardly to be doubted1 even1 that change might affect each and every one of the numerals from #e to #aj or #f to #i1 so that a dependence which might once have been easily detected is now unrecognizable4 ,but if this is so1 the natural and inevitable question follows--might not this have been the history of all numeral scales now purely decimal8 ,may not the changes of time have altered the compounds which were once a clear indication of quinary counting1 until no trace remains by which they can be followed back to their true origin8 ,perhaps so4 ,it is not in the least degree probable1 but its possibility may1 of course1 be admitted4 ,but even then the universality of quinary counting for primitive peoples is by no means established4 ,in ,chapter ,,ii1 examples were given of races which had no number base4 ,later on it was observed that in ,australia and ,south ,america many tribes used #b as their number base2 in some cases counting on past #e without showing any tendency to use that as a new unit4 ,again1 through the habit of counting upon the finger joints1 instead of the fingers themselves1 the use of #c as a base is brought into prominence1 and #f and #i become #b threes and #c threes1 respectively1 instead of #e #a and #e #d4 ,the same may be noticed of #d4 ,counting by means of his fingers1 without including the thumbs1 the savage begins by dividing into fours instead of fives4 ,traces of this form of counting are somewhat numerous1 especially among the ,north ,american aboriginal tribes4 ,hence the quinary form of counting1 however widespread its use may be shown to be1 can in no way be claimed as the universal method of any stage of development in the history of mankind4 ,in the vast majority of cases1 the passage from the base to the next succeeding number in any scale1 is clearly defined4 ,but among races whose intelligence is of a low order1 or--if it be permissible to express it in this way--among races whose number sense is feeble1 progression from one number to the next is not always in accordance with any well-defined law4 ,after one or two distinct numerals the count may1 as in the case of the ,veddas and the ,andamans1 proceed by finger pantomime and by the repetition of the same word4 ,occasionally the same word is used for two successive numbers1 some gesture undoubtedly serving to distinguish the one from the other in the savage's mind4 ,examples of this are not infrequent among the forest tribes of ,south ,america4 ,in the ,tariana dialect #i and #aj are expressed by the same word1 paihipawalianuda2 in ,cobeu1 #h and #i by pepelicoloblicouilini2 in ,barre1 #d1 #e1 and #i by ualibucubi4#cbf ,in other languages the change from one numeral to the next is so slight that one instinctively concludes that the savage is forming in his own mind another1 to him new1 numeral immediately from the last4 ,in such cases the entire number system is scanty1 and the creeping hesitancy with which progress is made is visible in the forms which the numerals are made to take4 ,a single illustration or two of this must suffice2 but the ones chosen are not isolated cases4 ,the scale of the ,macunis1#cbg one of the numerous tribes of ,brazil1 is #a4 pocchaenang4 #b4 haihg4 #c4 haigunhgnill4 #d4 haihgtschating4 #e4 haihgtschihating another #d8 #f4 hathig-stchihathing #b-d8 #g4 hathink-tschihathing #b-e8 #h4 hathink-tschihating #b #d8 ,the complete absence of--one is tempted to say--any rhyme or reason from this scale is more than enough to refute any argument which might tend to show that the quinary1 or any other scale1 was ever the sole number scale of primitive man4 ,irregular as this is1 the system of the ,montagnais fully matches it1 as the subjoined numerals show3#cbh #a4 inl'are4 #b4 nak'e4 #c4 t'are4 #d4 dinri4 #e4 se-sunlare4 #f4 elkke-t'are #b #c4 #g4 t'a-ye-oyertan #aj - #c1 or inl'as dinri #d #c8 #h4 elkke-dinri #b #d4 #i4 inl'a-ye-oyertan #aj - #a4 #aj4 onernan4 ,,chapter ,,vii4 ,,the ,,vigesimal ,,system4 ,in its ordinary development the quinary system is almost sure to merge into either the decimal or the vigesimal system1 and to form1 with one or the other or both of these1 a mixed system of counting4 ,in ,africa1 ,oceanica1 and parts of ,north ,america1 the union is almost always with the decimal scale2 while in other parts of the world the quinary and the vigesimal systems have shown a decided affinity for each other4 ,it is not to be understood that any geographical law of distribution has ever been observed which governs this1 but merely that certain families of races have shown a preference for the one or the other method of counting4 ,these families1 disseminating their characteristics through their various branches1 have produced certain groups of races which exhibit a well-marked tendency1 here toward the decimal1 and there toward the vigesimal form of numeration4 ,as far as can be ascertained1 the choice of the one or the other scale is determined by no external circumstances1 but depends solely on the mental characteristics of the tribes themselves4 ,environment does not exert any appreciable influence either4 ,both decimal and vigesimal numeration are found indifferently in warm and in cold countries2 in fruitful and in barren lands2 in maritime and in inland regions2 and among highly civilized or deeply degraded peoples4 ,whether or not the principal number base of any tribe is to be #bj seems to depend entirely upon a single consideration2 are the fingers alone used as an aid to counting1 or are both fingers and toes used8 ,if only the fingers are employed1 the resulting scale must become decimal if sufficiently extended4 ,if use is made of the toes in addition to the fingers1 the outcome must inevitably be a vigesimal system4 ,subordinate to either one of these the quinary may and often does appear4 ,it is never the principal base in any extended system4 ,to the statement just made respecting the origin of vigesimal counting1 exception may1 of course1 be taken4 ,in the case of numeral scales like the ,welsh1 the ,nahuatl1 and many others where the exact meanings of the numerals cannot be ascertained1 no proof exists that the ancestors of these peoples ever used either finger or toe counting2 and the sweeping statement that any vigesimal scale is the outgrowth of the use of these natural counters is not susceptible of proof4 ,but so many examples are met with in which the origin is clearly of this nature1 that no hesitation is felt in putting the above forward as a general explanation for the existence of this kind of counting4 ,any other origin is difficult to reconcile with observed facts1 and still more difficult to reconcile with any rational theory of number system development4 ,dismissing from consideration the quinary scale1 let us briefly examine once more the natural process of evolution through which the decimal and the vigesimal scales come into being4 ,after the completion of one count of the fingers the savage announces his result in some form which definitely states to his mind the fact that the end of a well-marked series has been reached4 ,beginning again1 he now repeats his count of #aj1 either on his own fingers or on the fingers of another4 ,with the completion of the second #aj the result is announced1 not in a new unit1 but by means of a duplication of the term already used4 ,it is scarcely credible that the unit unconsciously adopted at the termination of the first count should now be dropped1 and a new one substituted in its place4 ,when the method here described is employed1 #bj is not a natural unit to which higher numbers may be referred4 ,it is wholly artificial2 and it would be most surprising if it were adopted4 ,but if the count of the second #aj is made on the toes in place of the fingers1 the element of repetition which entered into the previous method is now wanting4 ,instead of referring each new number to the #aj already completed1 the savage is still feeling his way along1 designating his new terms by such phrases as #a on the foot1 #b on the other foot1 etc4 ,and now1 when #bj is reached1 a single series is finished instead of a double series as before2 and the result is expressed in one of the many methods already noticed--one man1 hands and feet1 the feet finished1 all the fingers of hands and feet1 or some equivalent formula4 ,ten is no longer the natural base4 ,the number from which the new start is made is #bj1 and the resulting scale is inevitably vigesimal4 ,if pebbles or sticks are used instead of fingers1 the system will probably be decimal4 ,but back of the stick and pebble counting the #aj natural counters always exist1 and to them we must always look for the origin of this scale4 ,in any collection of the principal vigesimal number systems of the world1 one would naturally begin with those possessed by the ,celtic races of ,europe4 ,these races1 the earliest ,european peoples of whom we have any exact knowledge1 show a preference for counting by twenties1 which is almost as decided as that manifested by ,teutonic races for counting by tens4 ,it has been conjectured by some writers that the explanation for this was to be found in the ancient commercial intercourse which existed between the ,britons and the ,carthaginians and ,phoenicians1 whose number systems showed traces of a vigesimal tendency4 ,considering the fact that the use of vigesimal counting was universal among ,celtic races1 this explanation is quite gratuitous4 ,the reason why the ,celts used this method is entirely unknown1 and need not concern investigators in the least4 ,but the fact that they did use it is important1 and commands attention4 ,the five ,celtic languages1 ,breton1 ,irish1 ,welsh1 ,manx1 and ,gaelic1 contain the following well-defined vigesimal scales4 ,only the principal or characteristic numerals are given1 those being sufficient to enable the reader to follow intelligently the growth of the systems4 ,each contains the decimal element also1 and is1 therefore1 to be regarded as a mixed decimal-vigesimal system4 ,,irish4#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 deich4 #bj4 fichead4 #cj4 deich ar fichead #aj #bj4 #dj4 da fhichead #b-bj4 #ej4 da fhichead is deich #dj #aj4 #fj4 tri fichead #c-bj4 #gj4 tri fichead is deich #fj #aj4 #hj4 ceithir fichead #d-bj4 #ij4 ceithir fichead is deich #hj #aj4 #ajj4 ceud4 #ajjj4 mile4 ,,welsh4#cca #aj4 deg4 #bj4 ugain4 #cj4 deg ar hugain #aj #bj4 #dj4 deugain #b-bj4 #ej4 deg a deugain #aj #dj4 #fj4 trigain #c-bj4 #gj4 deg a thrigain #aj #fj4 #hj4 pedwar ugain #d-bj4 #ij4 deg a pedwar ugain #hj #aj4 #ajj4 cant4 ,,manx4#ccb #aj4 jeih4 #bj4 feed4 #cj4 yn jeih as feed #aj #bj4 #dj4 daeed #b-bj4 #ej4 jeih as daeed #aj #dj4 #fj4 three-feed #c-bj4 #gj4 three-feed as jeih #fj #aj4 #hj4 kiare-feed #d-bj4 #ajj4 keead4 #ajjj4 thousane1 or jeih cheead4 ,,breton4#ccc #aj4 dec4 #bj4 ueguend4 #cj4 tregond #c-aj4 #dj4 deu ueguend #b-bj4 #ej4 hanter hand half hundred4 #fj4 tri ueguend #c-bj4 #gj4 dec ha tri ueguend #aj #fj4 #hj4 piar ueguend #d-bj4 #ij4 dec ha piar ueguend #aj #hj4 #ajj4 cand4 #abj4 hueh ueguend #f-bj4 #adj4 seih ueguend #g-bj4 #afj4 eih ueguend #h-bj4 #ahj4 nau ueguend #i-bj4 #bjj4 deu gand #b-ajj4 #bdj4 deuzec ueguend #ab-bj4 #bhj4 piarzec ueguend #ad-bj4 #cjj4 tri hand1 or pembzec ueguend4 #djj4 piar hand #d-ajj4 #ajjj4 mil4 ,these lists show that the native development of the ,celtic number systems1 originally showing a strong preference for the vigesimal method of progression1 has been greatly modified by intercourse with ,teutonic and ,latin races4 ,the higher numerals in all these languages1 and in ,irish many of the lower also1 are seen at a glance to be decimal4 ,among the scales here given the ,breton1 the legitimate descendant of the ancient ,gallic1 is especially interesting2 but here1 just as in the other ,celtic tongues1 when we reach #ajjj1 the familiar ,latin term for that number appears in the various corruptions of mille1 #ajjj1 which was carried into the ,celtic countries by missionary and military influences4 ,in connection with the ,celtic language1 mention must be made of the persistent vigesimal element which has held its place in ,french4 ,the ancient ,gauls1 while adopting the language of their conquerors1 so far modified the decimal system of ,latin as to replace the natural septante1 #gj1 octante1 #hj1 nonante1 #ij1 by soixante-dix1 #fj-aj1 quatre-vingt1 #d-bj1 and quatrevingt-dix1 #d-bj-aj4 ,from #fa to #ii the ,french method of counting is wholly vigesimal1 except for the presence of the one word soixante4 ,in old ,french this element was still more pronounced4 ,soixante had not yet appeared2 and #fj and #gj were treis vinz1 #c-bj1 and treis vinz et dis1 #c-bj and #aj respectively4 ,also1 #abj was six vinz1 #f-bj1 #adj was sept-vinz1 etc4#ccd ,how far this method ever extended in the ,french language proper1 it is1 perhaps1 impossible to say2 but from the name of an almshouse1 les quinze-vingts1#cce which formerly existed in ,paris1 and was designed as a home for #cjj blind persons1 and from the pembzek-ueguent1 #ae-bj1 of the ,breton1 which still survives1 we may infer that it was far enough to make it the current system of common life4 ,europe yields one other example of vigesimal counting1 in the number system of the ,basques4 ,like most of the ,celtic scales1 the ,basque seems to become decimal above #ajj4 ,it does not appear to be related to any other ,european system1 but to be quite isolated philologically4 ,the higher units1 as mila1 #ajjj1 are probably borrowed1 and not native4 ,the tens in the ,basque scale are3#ccf #aj4 hamar4 #bj4 hogei4 #cj4 hogei eta hamar #bj #aj4 #dj4 berrogei #b-bj4 #ej4 berrogei eta hamar #b-bj #aj4 #fj4 hirurogei #c-bj4 #gj4 hirurogei eta hamar #c-bj #aj4 #hj4 laurogei #d-bj4 #ij4 laurogei eta hamar #d-bj #aj4 #ajj4 ehun4 #ajjj4 milla4 ,besides these we find two or three numeral scales in ,europe which contain distinct traces of vigesimal counting1 though the scales are1 as a whole1 decidedly decimal4 ,the ,danish1 one of the essentially ,germanic languages1 contains the following numerals3 #cj4 tredive #c-aj4 #dj4 fyrretyve #d-aj4 #ej4 halvtredsindstyve half 7of #bj7 from #c-bj4 #fj4 tresindstyve #c-bj4 #gj4 halvfierdsindstyve half from #d-bj4 #hj4 fiirsindstyve #d-bj4 #ij4 halvfemsindstyve half from #e-bj4 #ajj4 hundrede4 ,germanic number systems are1 as a rule1 pure decimal systems2 and the ,danish exception is quite remarkable4 ,we have1 to be sure1 such expressions in ,english as three score1 four score1 etc41 and the ,swedish1 ,icelandic1 and other languages of this group have similar terms4 ,still1 these are not pure numerals1 but auxiliary words rather1 which belong to the same category as pair1 dozen1 dizaine1 etc41 while the ,danish words just given are the ordinary numerals which form a part of the every-day vocabulary of that language4 ,the method by which this scale expresses #ej1 #gj1 and #ij is especially noticeable4 ,it will be met with again1 and further examples of its occurrence given4 ,in ,albania there exists one single fragment of vigesimal numeration1 which is probably an accidental compound rather than the remnant of a former vigesimal number system4 ,with this single exception the ,albanian scale is of regular decimal formation4 ,a few of the numerals are given for the sake of comparison3#ccg #cj4 tridgiete #c-aj4 #dj4 dizet #b-bj4 #ej4 pesedgiete #e-aj4 #fj4 giastedgiete #f-aj1 etc4 ,among the almost countless dialects of ,africa we find a comparatively small number of vigesimal number systems4 ,the powers of the negro tribes are not strongly developed in counting1 and wherever their numeral scales have been taken down by explorers they have almost always been found to be decimal or quinary-decimal4 ,the small number ,i have been able to collect are here given4 ,they are somewhat fragmentary1 but are as complete as it was possible to make them4 ,,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 7borrowed from the ,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 bande a person finished4 #cj4 mo bande ako tan #bj #aj4 #dj4 mo fera bande #b #bj4 #ajj4 mo soru bande #e persons finished4 ,,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 ,the ,yoruba scale1 to which reference has already been made1 p4 #gj1 again shows its peculiar structure1 by continuing its vigesimal formation past #ajj with no interruption in its method of numeral building4 ,it will be remembered that none of the ,european scales showed this persistency1 but passed at that point into decimal numeration4 ,this will often be found to be the case2 but now and then a scale will come to our notice whose vigesimal structure is continued1 without any break1 on into the hundreds and sometimes into the thousands4 ,,bongo4#cdc #aj4 kih4 #bj4 mbaba kotu #bj #a4 #dj4 mbaba gnorr #bj #b4 #ajj4 mbaba mui #bj #e4 ,,mende4#cdd #aj4 pu4 #bj4 nu yela gboyongo mai a man finished4 #cj4 nu yela gboyongo mahu pu #bj #aj4 #dj4 nu fele gboyongo #b men finished4 #ajj4 nu lolu gboyongo #e men finished4 ,,nupe4#cde #aj4 gu-wo4 #bj4 esin4 #cj4 gbonwo4 #dj4 si-ba #b #bj4 #ej4 arota4 #fj4 sita #c #bj4 #gj4 adoni4 #hj4 sini #d #bj4 #ij4 sini be-guwo #hj #aj4 #ajj4 sisun #e #bj4 ,,logone4#cdf #aj4 chkan4 #bj4 tkam4 #cj4 tkam ka chkan #bj #aj4 #dj4 tkam ksde #bj #b4 #ej4 tkam ksde ka chkan #dj #aj4 #fj4 tkam gachkir #bj #c4 #ajj4 mia 7from ,arabic74 #ajjj4 debu4 ,,mundo4#cdg #aj4 nujorquoi4 #bj4 tiki bere4 #cj4 tiki bire nujorquoi #bj #aj4 #dj4 tiki borsa #bj #b4 #ej4 tike borsa nujorquoi #dj #aj4 ,,mandingo4#cdh #aj4 tang4 #bj4 mulu4 #cj4 mulu nintang #bj #aj4 #dj4 mulu foola #bj #b4 #ej4 mulu foola nintang #dj #aj4 #fj4 mulu sabba #bj #c4 #gj4 mulu sabba nintang #fj #aj4 #hj4 mulu nani #bj #d4 #ij4 mulu nani nintang #hj #aj4 #ajj4 kemi4 ,this completes the scanty list of ,african vigesimal number systems that a patient and somewhat extended search has yielded4 ,it is remarkable that the number is no greater4 ,quinary counting is not uncommon in the ,dark ,continent1 and there is no apparent reason why vigesimal reckoning should be any less common than quinary4 ,any one investigating ,african modes of counting with the material at present accessible1 will find himself hampered by the fact that few explorers have collected any except the first ten numerals4 ,this leaves the formation of higher terms entirely unknown1 and shows nothing beyond the quinary or non-quinary character of the system4 ,still1 among those which ,stanley1 ,schweinfurth1 ,salt1 and others have collected1 by far the greatest number are decimal4 ,as our knowledge of ,african languages is extended1 new examples of the vigesimal method may be brought to light4 ,but our present information leads us to believe that they will be few in number4 ,in ,asia the vigesimal system is to be found with greater frequency than in ,europe or ,africa1 but it is still the exception4 ,as ,asiatic languages are much better known than ,african1 it is probable that the future will add but little to our stock of knowledge on this point4 ,new instances of counting by twenties may still be found in northern ,siberia1 where much ethnological work yet remains to be done1 and where a tendency toward this form of numeration has been observed to exist4 ,but the total number of ,asiatic vigesimal scales must always remain small--quite insignificant in comparison with those of decimal formation4 ,in the ,caucasus region a group of languages is found1 in which all but three or four contain vigesimal systems4 ,these systems are as follows3 ,,abkhasia4#cdi #aj4 zpha-ba4 #bj4 gphozpha #b #aj4 #cj4 gphozphei zphaba #bj #aj4 #dj4 gphin-gphozpha #b #bj4 #fj4 chin-gphozpha #c #bj4 #hj4 phsin-gphozpha #d #bj4 #ajj4 sphki4 ,,avari #aj4 antsh-go4 #bj4 qo-go4 #cj4 lebergo4 #dj4 khi-qogo #b #bj4 #ej4 khiqojalda antshgo #dj #aj4 #fj4 lab-qogo #c #bj4 #gj4 labqojalda antshgo #fj #aj4 #hj4 un-qogo #d #bj4 #ajj4 nusgo4 ,,kuri #aj4 tshud4 #bj4 chad4 #cj4 channi tshud #bj #aj4 #dj4 jachtshur4 #ej4 jachtshurni tshud #dj #aj4 #fj4 put chad #c #bj4 #gj4 putchanni tshud #fj #aj4 #hj4 kud-chad #d #bj4 #ij4 kudchanni tshud #hj #aj4 #ajj4 wis4 ,,udi #aj4 witsh4 #bj4 qa4 #cj4 sa-qo-witsh #bj #aj4 #dj4 pha-qo #b #bj4 #ej4 pha-qo-witsh #dj #aj4 #fj4 chib-qo #c #bj4 #gj4 chib-qo-witsh #fj #aj4 #hj4 bip-qo #d #bj4 #ij4 bip-qo-witsh #hj #aj4 #ajj4 bats4 #ajjj4 hazar 7,persian74 ,,tchetchnia #aj4 ith4 #bj4 tqa4 #cj4 tqe ith #bj #aj4 #dj4 sauz-tqa #b #bj4 #ej4 sauz-tqe ith #dj #aj4 #fj4 chuz-tqa #c #bj4 #gj4 chuz-tqe ith #fj #aj4 #hj4 w-iez-tqa #d #bj4 #ij4 w-iez-tqe ith #hj #aj4 #ajj4 b'e4 #ajjj4 ezir 7akin to ,persian74 ,,thusch #aj4 itt4 #bj4 tqa4 #cj4 tqa-itt #bj #aj4 #dj4 sauz-tq #b #bj4 #ej4 sauz-tqa-itt #dj #aj4 #fj4 chouz-tq #c #bj4 #gj4 chouz-tqa-itt #fj #aj4 #hj4 dhewuz-tq #d #bj4 #ij4 dhewuz-tqa-itt #hj #aj4 #ajj4 phchauz-tq #e #bj4 #bjj4 itsha-tq #aj #bj4 #cjj4 phehiitsha-tq #ae #bj4 #ajjj4 satsh tqauz-tqa itshatqa #b #bj #bj #bjj4 ,,georgia #aj4 athi4 #bj4 otsi4 #cj4 ots da athi #bj #aj4 #dj4 or-m-otsi #b #bj4 #ej4 ormots da athi #dj #aj4 #fj4 sam-otsi #c #bj4 #gj4 samots da athi #fj #aj4 #hj4 othch-m-otsi #d #bj4 #ij4 othmots da athi #hj #aj4 #ajj4 asi4 #ajjj4 ath-asi #aj #ajj4 ,,lazi #aj4 wit4 #bj4 ts4 #cj4 ts do wit #bj #aj4 #dj4 dzur en ts #b #bj4 #ej4 dzur en ts do wit #dj #aj4 #fj4 dzum en ts #c #bj4 #gj4 dzum en ts do wit #fj #aj4 #hj4 otch-an-ts #d #bj4 #ajj4 os4 #ajjj4 silia 7akin to ,greek74 ,,chunsag4#cej #aj4 ants-go4 #bj4 chogo4 #cj4 chogela antsgo #bj #aj4 #dj4 kichogo #b #bj4 #ej4 kichelda antsgo #dj #aj4 #fj4 taw chago #c #bj4 #gj4 taw chogelda antsgo #fj #aj4 #hj4 uch' chogo #d #bj4 #ij4 uch' chogelda antsgo4 #ajj4 nusgo4 #ajjj4 asargo 7akin to ,persian74 ,,dido4#cea #aj4 zino4 #bj4 ku4 #cj4 kunozino4 #dj4 kaeno ku #b #bj4 #ej4 kaeno kuno zino #dj #aj4 #fj4 sonno ku #c #bj4 #gj4 sonno kuno zino #fj #aj4 #hj4 uino ku #d #bj4 #ij4 uino huno zino #hj #aj4 #ajj4 bischon4 #djj4 kaeno kuno zino #dj #aj4 ,,akari #aj4 entzelgu4 #bj4 kobbeggu4 #cj4 lowergu4 #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 askergu 7from ,persian74 ,,circassia #aj4 psche4 #bj4 to-tsch4 #cj4 totsch-era-pschirre #bj #aj4 #dj4 ptl'i-sch #d #aj4 #ej4 ptl'isch-era-pschirre #dj #aj4 #fj4 chi-tsch #f #aj4 #gj4 chitsch-era-pschirre #fj #aj4 #hj4 toshitl #bj #d8 #ij4 toshitl-era-pschirre #hj #aj4 #ajj4 scheh4 #ajjj4 min 7,tartar7 or schi-psche #ajj #aj4 ,the last of these scales is an unusual combination of decimal and vigesimal4 ,in the even tens it is quite regularly decimal1 unless #hj is of the structure suggested above4 ,on the other hand1 the odd tens are formed in the ordinary vigesimal manner4 ,the reason for this anomaly is not obvious4 ,i know of no other number system that presents the same peculiarity1 and cannot give any hypothesis which will satisfactorily account for its presence here4 ,in nearly all the examples given the decimal becomes the leading element in the formation of all units above #ajj1 just as was the case in the ,celtic scales already noticed4 ,among the northern tribes of ,siberia the numeral scales appear to be ruder and less simple than those just examined1 and the counting to be more consistently vigesimal than in any scale we have thus far met with4 ,the two following examples are exceedingly interesting1 as being among the best illustrations of counting by twenties that are to be found anywhere in the ,old ,world4 ,,tschukschi4#ceb #aj4 migitken both hands4 #bj4 chlik-kin a whole man4 #cj4 chlikkin mingitkin parol #bj #aj4 #dj4 nirach chlikkin #b #bj4 #ajj4 milin chlikkin #e #bj4 #bjj4 mingit chlikkin #aj #bj1 i4e4 #aj men4 #ajjj4 miligen chlin-chlikkin #e #bjj1 i4e4 five 7times7 #aj men4 ,,aino4#cec #aj4 wambi4 #bj4 choz4 #cj4 wambi i-doehoz #aj from #dj4 #dj4 tochoz #b #bj4 #ej4 wambi i-richoz #aj from #fj4 #fj4 rechoz #c #bj4 #gj4 wambi i8 inichoz #aj from #hj4 #hj4 inichoz #d #bj4 #ij4 wambi aschikinichoz #aj from #ajj4 #ajj4 aschikinichoz #e #bj4 #aaj4 wambi juwanochoz #aj from #abj4 #abj4 juwano choz #f #bj4 #acj4 wambi aruwanochoz #aj from #adj4 #adj4 aruwano choz #g #bj4 #aej4 wambi tubischano choz #aj from #afj4 #afj4 tubischano choz #h #bj4 #agj4 wambi schnebischano choz #aj from #ahj4 #ahj4 schnebischano choz #i #bj4 #aij4 wambi schnewano choz #aj from #bjj4 #bjj4 schnewano choz #aj #bj4 #cjj4 aschikinichoz i gaschima chnewano choz #e #bj #aj #bj4 #djj4 toschnewano choz #b 7#aj #bj74 #ejj4 aschikinichoz i gaschima toschnewano choz #ajj #djj4 #fjj4 reschiniwano choz #c #bjj4 #gjj4 aschikinichoz i gaschima reschiniwano choz #ajj #fjj4 #hjj4 inischiniwano choz #d #bjj4 #ijj4 aschikinichoz i gaschima inischiniwano choz #ajj #hjj4 #ajjj4 aschikini schinewano choz #e #bjj4 #bjjj4 wanu schinewano choz #aj 7#aj #bj74 ,this scale is in one sense wholly vigesimal1 and in another way it is not to be regarded as pure1 but as mixed4 ,below #bj it is quinary1 and1 however far it might be extended1 this quinary element would remain1 making the scale quinary-vigesimal4 ,but in another sense1 also1 the ,aino system is not pure4 ,in any unmixed vigesimal scale the word for #djj must be a simple word1 and that number must be taken as the vigesimal unit corresponding to #ajj in the decimal scale4 ,but the ,ainos have no simple numeral word for any number above #bj1 forming all higher numbers by combinations through one or more of the processes of addition1 subtraction1 and multiplication4 ,the only number above #bj which is used as a unit is #bjj1 which is expressed merely as #aj twenties4 ,any even number of hundreds1 or any number of thousands1 is then indicated as being so many times #aj twenties2 and the odd hundreds are so many times #aj twenties1 plus #e twenties more4 ,this scale is an excellent example of the cumbersome methods used by uncivilized races in extending their number systems beyond the ordinary needs of daily life4 ,in ,central ,asia a single vigesimal scale comes to light in the following fragment of the ,leptscha scale1 of the ,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 ,further to the south1 among the ,dravidian races1 the vigesimal element is also found4 ,the following will suffice to illustrate the number systems of these dialects1 which1 as far as the material at hand shows1 are different from each other only in minor particulars3 ,,mundari4#cee #aj4 gelea4 #bj4 mi hisi4 #cj4 mi hisi gelea #bj #aj4 #dj4 bar hisi #b #bj4 #fj4 api hisi #c #bj4 #hj4 upun hisi #d #bj4 #ajj4 mone hisi #e #bj4 ,in the ,nicobar ,islands of the ,indian ,ocean a well-developed example of vigesimal numeration is found4 ,the inhabitants of these islands are so low in the scale of civilization that a definite numeral system of any kind is a source of some surprise4 ,their neighbours1 the ,andaman ,islanders1 it will be remembered1 have but two numerals at their command2 their intelligence does not seem in any way inferior to that of the ,nicobar tribes1 and one is at a loss to account for the superior development of the number sense in the case of the latter4 ,the intercourse of the coast tribes with traders might furnish an explanation of the difficulty were it not for the fact that the numeration of the inland tribes is quite as well developed as that of the coast tribes2 and as the former never come in contact with traders and never engage in barter of any kind except in the most limited way1 the conclusion seems inevitable that this is merely one of the phenomena of mental development among savage races for which we have at present no adequate explanation4 ,the principal numerals of the inland and of the coast tribes are3#cef ,,inland ,,tribes ,,coast ,,tribes #aj4 teya4 #aj4 sham4 #bj4 heng-inai4 #bj4 heang-inai4 #cj4 heng-inai-tain #cj4 heang-inai-tanai #bj #e 7couples74 #bj #e 7couples74 #dj4 au-inai #b #bj4 #dj4 an-inai #b #bj4 #ajj4 tain-inai #e #bj4 #ajj4 tanai-inai #e #bj4 #bjj4 teya-inai #aj #bj4 #bjj4 sham-inai #aj #bj4 #cjj4 teya-tain-inai #cjj4 heang-tanai-inai 7#aj #e7 #bj4 7#aj #e7 #bj4 #djj4 heng-teo4 #djj4 heang-momchiama4 ,in no other part of the world is vigesimal counting found so perfectly developed1 and1 among native races1 so generally preferred1 as in ,north and ,south ,america4 ,in the eastern portions of ,north ,america and in the extreme western portions of ,south ,america the decimal or the quinary decimal scale is in general use4 ,but in the northern regions of ,north ,america1 in western ,canada and northwestern ,united ,states1 in ,mexico and ,central ,america1 and in the northern and western parts of ,south ,america1 the unit of counting among the great majority of the native races was #bj4 ,the ethnological affinities of these races are not yet definitely ascertained2 and it is no part of the scope of this work to enter into any discussion of that involved question4 ,but either through contact or affinity1 this form of numeration spread in prehistoric times over half or more than half of the western hemisphere4 ,it was the method employed by the rude ,eskimos of the north and their equally rude kinsmen of ,paraguay and eastern ,brazil2 by the forest ,indians of ,oregon and ,british ,columbia1 and by their more southern kinsmen1 the wild tribes of the ,rio ,grande and of the ,orinoco4 ,and1 most striking and interesting of all1 it was the method upon which were based the numeral systems of the highly civilized races of ,mexico1 ,yucatan1 and ,new ,granada4 ,some of the systems obtained from the languages of these peoples are perfect1 extended examples of vigesimal counting1 not to be duplicated in any other quarter of the globe4 ,the ordinary unit was1 as would be expected1 one man1 and in numerous languages the words for #bj and man are identical4 ,but in other cases the original meaning of that numeral word has been lost2 and in others still it has a signification quite remote from that given above4 ,these meanings will be noticed in connection with the scales themselves1 which are given1 roughly speaking1 in their geographical order1 beginning with the ,eskimo of the far north4 ,the systems of some of the tribes are as follows3 ,,alaskan ,,eskimos4#ceg #aj4 koleet4 #bj4 enuenok4 #cj4 enuenok kolinik #bj #aj4 #dj4 malho kepe ak #b #bj4 #ej4 malho-kepe ak-kolmik che pah ak to #b #bj #aj4 #fj4 pingi shu-kepe ak #c #bj4 #ajj4 tale ma-kepe ak #e #bj4 #djj4 enue nok ke pe ak #bj #bj4 ,,tchiglit4#ceh #aj4 krolit4 #bj4 kroleti1 or innun man4 #cj4 innok krolinik-tchikpalik man #b hands4 #dj4 innum mallerok #b men4 #ej4 adjigaynarmitoat as many times #aj as the fingers of the hand4 #fj4 innumipit #c men4 #gj4 innunmalloeronik arveneloerit #g men8 #hj4 innun pinatunik arveneloerit #h men8 #ij4 innun tcitamanik arveneloerit #i men8 #ajj4 itchangnerkr4 #ajjj4 itchangner-park great #ajj4 ,the meanings for #gj1 #hj1 #ij1 are not given by ,father ,petitot1 but are of such a form that the significations seem to be what are given above4 ,only a full acquaintance with the ,tchiglit language would justify one in giving definite meanings to these words1 or in asserting that an error had been made in the numerals4 ,but it is so remarkable and anomalous to find the decimal and vigesimal scales mingled in this manner that one involuntarily suspects either incompleteness of form1 or an actual mistake4 ,,tlingit4#cei #aj4 djinkat both hands8 #bj4 tle ka #a man4 #cj4 natsk djinkat #c #aj4 #dj4 dak'on djinkat #d #aj4 #ej4 kedjin djinkat #e #aj4 #fj4 tle durcu djinkat #f #aj4 #gj4 daqa durcu djinkat #g #aj4 #hj4 natska durcu djinkat #h #aj4 #ij4 gocuk durcu djinkat #i #aj4 #ajj4 kedjin ka #e men1 or #e #bj4 #bjj4 djinkat ka #aj #bj4 #cjj4 natsk djinkat ka #cj men4 #djj4 dak'on djinkat ka #dj men4 ,this scale contains a strange commingling of decimal and vigesimal counting4 ,the words for #bj1 #ajj1 and #bjj are clear evidence of vigesimal1 while #cj to #ij1 and the remaining hundreds1 are equally unmistakable proof of decimal1 numeration4 ,the word ka1 man1 seems to mean either #aj or #bj2 a most unusual occurrence4 ,the fact that a number system is partly decimal and partly vigesimal is found to be of such frequent occurrence that this point in the ,tlingit scale need excite no special wonder4 ,but it is remarkable that the same word should enter into numeral composition under such different meanings4 ,,nootka4#cfj #aj4 haiu4 #bj4 tsakeits4 #cj4 tsakeits ic haiu #bj #aj4 #dj4 atlek #b #bj4 #fj4 katstsek #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 ,this scale is quinary-vigesimal1 with no apparent decimal element in its composition4 ,but the derivation of some of the terms used is detected with difficulty4 ,in the following scale the vigesimal structure is still more obscure4 ,,tsimshian4#cfa #aj4 gy'ap4 #bj4 kyedeel #a man4 #cj4 gulewulgy'ap4 #dj4 t'epqadalgyitk1 or tqalpqwulgyap4 #ej4 kctoncwulgyap4 #ajj4 kcenecal4 #bjj4 k'pal4 #cjj4 k'pal te kcenecal #bjj #ajj4 #djj4 kyedal4 #ejj4 kyedal te kcenecal #djj #ajj4 #fjj4 gulalegyitk4 #gjj4 gulalegyitk te kcenecal #fjj #ajj4 #hjj4 tqalpqtalegyitk4 #ijj4 tqalpqtalegyitk te kcenecal #hjj #ajj4 #ajjj4 k'pal4 ,to the unobservant eye this scale would certainly appear to contain no more than a trace of the vigesimal in its structure4 ,but ,dr4 ,boas1 who is one of the most careful and accurate of investigators1 says in his comment on this system3 ,it will be seen at once that this system is quinary-vigesimal4444 ,in #bj we find the word gyat1 man4 ,the hundreds are identical with the numerals used in counting men 7see p4 #hg71 and then the quinary-vigesimal system is most evident4 ,,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 ,,caribs ,,of ,,essiquibo1 ,,guiana #aj4 oween-abatoro4 #bj4 owee-carena #a person4 #dj4 oko-carena #b persons4 #fj4 oroowa-carena #c persons4 ,,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 nanthebe #a #ajj4 ,,maya1 ,,yucatan4#cfc #a4 hun4 #aj4 lahun it is finished4 #bj4 hunkal a measure1 or more correctly1 a fastening together4 #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 tying around4 #ejj4 hotubak4 #fjj4 lahutubak #hjj4 calbak #b #djj4 #ijj4 hotu yoxbak4 #ajjj4 lahuyoxbak4 #abjj4 oxbak #c #djj4 #bjjj4 capic 7modern74 #hjjj4 hunpic #a sack4 #af1jjj4 ca pic 7ancient74 #afj1jjj4 calab a filling full #c1bjj1jjj4 kinchil4 #fd1jjj1jjj4 hunalau4 ,in the ,maya scale we have one of the best and most extended examples of vigesimal numeration ever developed by any race4 ,to show in a more striking and forcible manner the perfect regularity of the system1 the following tabulation is made of the various ,maya units1 which will correspond to the #aj units make one ten1 #aj tens make one hundred1 #aj hundreds make one thousand1 etc41 which old-fashioned arithmetic compelled us to learn in childhood4 ,the scale is just as regular by twenties in ,maya as by tens in ,english4 ,it 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 kinchil #c1bjj1jjj4 tzotzceh #bj kinchil #a alau #fd1jjj1jjj4 ,the original meaning of pic1 given in the scale as a sack1 was rather a short petticoat1 somtimes used as a sack4 ,the word tzotzceh signified deerskin4 ,no reason can be given for the choice of this word as a numeral1 though the appropriateness of the others is sufficiently manifest4 ,no evidence of digital numeration appears in the first #aj units1 but1 judging from the almost universal practice of the ,indian tribes of both ,north and ,south ,america1 such may readily have been the origin of ,maya counting4 ,whatever its origin1 it certainly expanded and grew into a system whose perfection challenges our admiration4 ,it was worthy of the splendid civilization of this unfortunate race1 and1 through its simplicity and regularity1 bears ample testimony to the intellectual capacity which originated it4 ,the only example of vigesimal reckoning which is comparable with that of the ,mayas is the system employed by their northern neighbours1 the ,nahuatl1 or1 as they are more commonly designated1 the ,aztecs of ,mexico4 ,this system is quite as pure and quite as simple as the ,maya1 but differs from it in some important particulars4 ,in its first #bj numerals it is quinary 7see p4 #ada71 and as a system must be regarded as quinary-vigesimal4 ,the ,maya scale is decimal through its first #bj numerals1 and1 if it is to be regarded as a mixed scale1 must be characterized as decimal-vigesimal4 ,but in both these instances the vigesimal element preponderates so strongly that these1 in common with their kindred number systems of ,mexico1 ,yucatan1 and ,central ,america1 are always thought of and alluded to as vigesimal scales4 ,on account of its importance1 the ,nahuatl system#cfe is given in fuller detail than most of the other systems ,i have made use of4 #aj4 matlactli #b hands4 #bj4 cempoalli #a counting4 #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 chiquacempoalli #f #bj4 #adj4 chicompoalli #g #bj4 #afj4 chicuepoalli #h #bj4 #ahj4 chiconauhpoalli #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 centzontli #a bunch of grass1 or #a tuft of hair4 #hjj4 ometzontli #b #djj4 #abjj4 eitzontli #c #djj4 #gfjj4 caxtolli onnauhtzontli #ai #djj4 #hjjj4 cenxiquipilli1 or cexiquipilli4 #afj1jjj4 cempoalxiquipilli #bj #hjjj4 #c1bjj1jjj4 centzonxiquipilli #djj #hjjj4 #fd1jjj1jjj4 cempoaltzonxiquipilli #bj #djj #hjjj4 ,up to #afj1jjj the ,nahuatl system is as simple and regular in its construction as the ,english4 ,but at this point it fails in the formation of a new unit1 or rather in the expression of its new unit by a simple word2 and in the expression of all higher numbers it is forced to resort in some measure to compound terms1 just as the ,english might have done had it not been able to borrow from the ,italian4 ,the higher numeral terms1 under such conditions1 rapidly become complex and cumbersome1 as the following analysis of the number #a1bgi1iii1iii shows4#cff ,the analysis will be readily understood when it is remembered that 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 show the compounding which takes place in the higher numerals1 the analysis may be made more literally1 thus3 7#ae #d7 #djj #hjj 7#ae #d7 #bj #hjjj 7#ae #d7 #hjjj 7#ae #d7 #djj 7#ae #d7 #bj #ae #d4 ,of course this resolution suffers from the fact that it is given in digits arranged in accordance with decimal notation1 while the ,nahuatl numerals express values by a base twice as great4 ,this gives the effect of a complexity and awkwardness greater than really existed in the actual use of the scale4 ,except for the presence of the quinary element the number just given is really expressed with just as great simplicity as it could be in ,english words if our words million and billion were replaced by thousand thousand and thousand thousand thousand4 ,if ,mexico had remained undisturbed by ,europeans1 and science and commerce had been left to their natural growth and development1 uncompounded words would undoubtedly have been found for the higher units1 #afj1jjj1 #c1bjj1jjj1 etc41 and the system thus rendered as simple as it is possible for a quinary-vigesimal system to be4 ,other number scales of this region are given as follows3 ,,huasteca4#cfg #aj4 laluh4 #bj4 hum-inic #a man4 #cj4 hum-inic-lahu #a man #aj4 #dj4 tzab-inic #b men4 #ej4 tzab-inic-lahu #b men #aj4 #fj4 ox-inic #c men4 #gj4 ox-inic-lahu #c men #aj4 #hj4 tze-tnic #d men4 #ij4 tze-ynic-kal-laluh #d men and #aj4 #ajj4 bo-inic #e men4 #bjj4 tzab-bo-inic #b #e men4 #cjj4 ox-bo-inic #c #e men4 #djj4 tsa-bo-inic #d #e men4 #fjj4 acac-bo-inic #f #e men4 #hjj4 huaxic-bo-inic #h #e men4 #ajjj4 xi4 #hjjj4 huaxic-xi #h-ajjj4 ,the essentially vigesimal character of this system changes in the formation of some of the higher numerals1 and a suspicion of the decimal enters4 ,one hundred is boinic1 #e men2 but #bjj1 instead of being simply lahuh-inic1 #aj men1 is tsa-bo-inic1 #b #ajj1 or more strictly1 #b times #e men4 ,similarly1 #cjj is #c #ajj1 #djj is #d #ajj1 etc4 ,the word for #ajjj is simple instead of compound1 and the thousands appear to be formed wholly on the decimal base4 ,a comparison of this scale with that of the ,nahuatl shows how much inferior it is to the latter1 both in simplicity and consistency4 ,,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 ,the essential character of the vigesimal element is shown by the last two numerals4 ,tontamen1 the square of #bj1 is a simple word1 and #ajjj is1 as it should be1 #b times #djj1 plus #bjj4 ,it is most unfortunate that the numeral for #hjjj1 the cube of #bj1 is not given4 ,,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 allied with the ,maya numerals and method of counting are those of the ,quiches of ,guatemala4 ,the resemblance is so obvious that no detail in the ,quiche scale calls for special mention4 ,,quiche4#cgj #aj4 lahuh4 #bj4 hu-uinac #a man4 #cj4 hu-uinac-lahuh #bj #aj4 #dj4 ca-uinac #b men4 #ej4 lahu-r-ox-kal -#aj #c #bj4 #fj4 ox-kal #c #bj4 #gj4 lahu-u-humuch -#aj #hj4 #hj4 humuch4 #ij4 lahu-r-ho-kal -#aj #ajj4 #ajj4 hokal4 #ajjj4 o-tuc-rox-o-kal4 ,among ,south ,american vigesimal systems1 the best known is that of the ,chibchas or ,muyscas of the ,bogota region1 which was obtained at an early date by the missionaries who laboured among them4 ,this system is much less extensive than that of some of the more northern races2 but it is as extensive as almost any other ,south ,american system with the exception of the ,peruvian1 which was1 however1 a pure decimal system4 ,as has already been stated1 the native races of ,south ,america were1 as a rule1 exceedingly deficient in regard to the number sense4 ,their scales are rude1 and show great poverty1 both in formation of numeral words and in the actual extent to which counting was carried4 ,if extended as far as #bj1 these scales are likely to become vigesimal1 but many stop far short of that limit1 and no inconsiderable number of them fail to reach even #e4 ,in this respect we are reminded of the ,australian scales1 which were so rudimentary as really to preclude any proper use of the word system in connection with them4 ,counting among the ,south ,american tribes was often equally limited1 and even less regular4 ,following are the significant numerals of the scale in question3 ,,chibcha1 ,,or ,,muysca4#cga #aj4 hubchibica4 #bj4 quihica ubchihica thus says the foot1 #aj #aj-aj1 or gueta house4 #cj4 guetas asaqui ubchihica #bj #aj4 #dj4 gue-bosa #bj #b4 #fj4 gue-mica #bj #c4 #hj4 gue-muyhica #bj #d4 #ajj4 gue-hisca #bj #e4 ,,nagranda4#cgb #aj4 guha4 #bj4 dino4 #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 ,in considering the influence on the manners and customs of any people which could properly be ascribed to the use among them of any other base than #aj1 it must not be forgotten that no races1 save those using that base1 have ever attained any great degree of civilization1 with the exception of the ancient ,aztecs and their immediate neighbours1 north and south4 ,for reasons already pointed out1 no highly civilized race has ever used an exclusively quinary system2 and all that can be said of the influence of this mode of counting is that it gives rise to the habit of collecting objects in groups of five1 rather than of ten1 when any attempt is being made to ascertain their sum4 ,in the case of the subsidiary base #ab1 for which the ,teutonic races have always shown such a fondness1 the dozen and gross of commerce1 the divisions of ,english money1 and of our common weights and measures are probably an outgrowth of this preference2 and the ,babylonian base1 #fj1 has fastened upon the world forever a sexagesimal method of dividing time1 and of measuring the circumference of the circle4 ,the advanced civilization attained by the races of ,mexico and ,central ,america render it possible to see some of the effects of vigesimal counting1 just as a single thought will show how our entire lives are influenced by our habit of counting by tens4 ,among the ,aztecs the universal unit was #bj4 ,a load of cloaks1 of dresses1 or other articles of convenient size1 was #bj4 ,time was divided into periods of #bj days each4 ,the armies were numbered by divisions of #hjjj2cgc and in countless other ways the vigesimal element of numbers entered into their lives1 just as the decimal enters into ours2 and it is to be supposed that they found it as useful and as convenient for all measuring purposes as we find our own system2 as the tradesman of to-day finds the duodecimal system of commerce2 or as the ,babylonians of old found that singularly curious system1 the sexagesimal4 ,habituation1 the laws which the habits and customs of every-day life impose upon us1 are so powerful1 that our instinctive readiness to make use of any concept depends1 not on the intrinsic perfection or imperfection which pertains to it1 but on the familiarity with which previous use has invested it4 ,hence1 while one race may use a decimal1 another a quinary-vigesimal1 and another a sexagesimal scale1 and while one system may actually be inherently superior to another1 no user of one method of reckoning need ever think of any other method as possessing practical inconveniences1 of which those employing it are ever conscious4 ,and1 to cite a single instance which illustrates the unconscious daily use of two modes of reckoning in one scale1 we have only to think of the singular vigesimal fragment which remains to this day imbedded in the numeral scale of the ,french4 ,in counting from #gj to #ajj1 or in using any number which lies between those limits1 no ,frenchman is conscious of employing a method of numeration less simple or less convenient in any particular1 than when he is at work with the strictly decimal portions of his scale4 ,he passes from the one style of counting to the other1 and from the second back to the first again1 entirely unconscious of any break or change2 entirely unconscious1 in fact1 that he is using any particular system1 except that which the daily habit of years has made a part himself4 ,deep regret must be felt by every student of philology1 that the primitive meanings of simple numerals have been so generally lost4 ,but1 just as the pebble on the beach has been worn and rounded by the beating of the waves and by other pebbles1 until no trace of its original form is left1 and until we can say of it now only that it is quartz1 or that it is diorite1 so too the numerals of many languages have suffered from the attrition of the ages1 until all semblance of their origin has been lost1 and we can say of them only that they are numerals4 ,beyond a certain point we can carry the study neither of number nor of number words4 ,at that point both the mathematician and the philologist must pause1 and leave everything beyond to the speculations of those who delight in nothing else so much as in pure theory4 ,,the ,,end4 ,,index ,,of ,,authors4 ,adam1 ,l41 #dd1 #aei1 #aff1 #age4 ,armstrong1 ,r4,a41 #ahj4 ,aymonier1 ,a41 #aef4 ,bachofen1 ,j4,j41 #aca4 ,balbi1 ,a41 #aea4 ,bancroft1 ,h4,h41 #bi1 #dg1 #hi1 #ic1 #aac1 #aii4 ,barlow1 ,h41 #ajh4 ,beauregard1 ,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 ,brinton1 ,d4,g41 #b1 #bb1 #df1 #eb1 #eg1 #fa1 #aaa1 #aab1 #adj1 #aii1 #bjj4 ,burton1 ,r4,f41 #cg1 #ga4 ,chamberlain1 ,a4,f41 #de1 #fe1 #ic4 ,chase1 ,p4,e41 #ii4 ,clarke1 ,h41 #aac4 ,codrington1 ,r4,h41 #af1 #ie1 #if1 #acf1 #ach1 #ade1 #aec1 #aed4 ,crawfurd1 ,j41 #hi1 #ic1 #acj4 ,curr1 ,e4,m41 #bd-bg1 #ajd1 #ajg-aaj1 #aab4 ,cushing1 ,f4,h41 #ac1 #dh4 ,de ,flacourt1 #h1 #i4 ,de ,quincey1 ,t41 #ce4 ,deschamps1 ,m41 #bh4 ,dobrizhoffer1 ,m41 #ga4 ,dorsey1 ,j4,o41 #ei4 ,du ,chaillu1 ,p4,b41 #ff1 #fg1 #aej1 #aea4 ,du ,graty1 ,a4,m41 #ach4 ,ellis1 ,a4,a41 #fd1 #ia4 ,ellis1 ,r41 #cg1 #adb4 ,ellis1 ,w41 #hc1 #aai4 ,erskine1 ,j4,e41 #aec1 #aed4 ,flegel1 ,r41 #acc4 ,gallatin1 ,a41 #acf1 #aei1 #aff1 #aga1 #aii1 #bjd1 #bjf1 #bjh4 ,galton1 ,f41 #d4 ,gatschet1 ,a4,s41 #eh1 #ei1 #fh4 ,gilij1 ,f4,s41 #ed4 ,gill1 ,w4,w41 #ah1 #aah4 ,goedel1 ,m41 #hc1 #adg4 ,grimm1 ,j4,l4,c41 #dh4 ,grber1 ,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 ,hervas1 ,l41 #agj4 ,humboldt1 ,a4 von1 #cb1 #bjg4 ,hyades1 ,m41 #bb4 ,kelly1 ,j4,w41 #aeg1 #aif4 ,kelly1 ,j41 #ahj4 ,kleinschmidt1 ,s41 #eb1 #hj4 ,lang1 ,j4,d41 #ajh4 ,lappenberg1 ,j4,m41 #abg4 ,latham1 ,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 ,mackenzie1 ,a41 #bf4 ,man1 ,e4,h41 #bh1 #aid4 ,mann1 ,a41 #dg4 ,marcoy1 ,p4 7,saint ,cricq71 #bc1 #afh4 ,mariner1 ,a41 #he4 ,martius1 ,c4,f4 von1 #bc1 #gi1 #aaa1 #abb1 #ach1 #adb1 #agd4 ,mason1 #aab4 ,mill1 ,j4,s41 #c4 ,moncelon1 ,m41 #adb4 ,morice1 ,a41 #ae1 #hf4 ,mller1 ,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 ,murdoch1 ,j41 #cj1 #di1acg4 ,nystron1 ,j4,w41 #acb4 ,o',donovan1 ,j41 #ahj4 ,oldfield1 ,a41 #bi1 #gg4 ,olmos1 ,a4 de1 #ada4 ,parisot1 ,j41 #dd4 ,park1 ,m41 #ade-adg4 ,parry1 ,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 ,pruner-,bey1 #aj1 #ajd4 ,pughe1 ,w4,o41 #ada4 ,ralph1 ,j41 #abe4 ,ray1 ,s4,h41 #de1 #gh1 #hj4 ,ridley1 ,w41 #eg4 ,roth1 ,h4,l41 #gi4 ,salt1 ,h41 #ahg4 ,sayce1 ,a4,h41 #ge4 ,schoolcraft1 ,h4,r41 #ff1 #ha1 #hc1 #hd1 #aei1 #afj4 ,schrder1 ,p41 #ij4 ,schweinfurth1 ,g41 #adc1 #adf1 #adi1 #ahf1 #ahg4 ,simeon1 ,r41 #bja4 ,spix1 ,j4,b4 von1 #g4 ,spurrell1 ,w41 #ahj4 ,squier1 ,g4,e41 #hj1 #bjg4 ,stanley1 ,h4,m41 #ch1 #db1 #fd1 #fi1 #gh1 #aej1 #ahg4 ,taplin1 ,g41 #ajf4 ,thiel1 ,b4,a41 #agb4 ,toy1 ,c4,h41 #gj4 ,turner1 ,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 ,whewell1 ,w41 #c4 ,wickersham1 ,j41 #if4 ,wiener1 ,c41 #bb4 ,williams1 ,w4,l41 #abc4 ,,index ,,of ,,subjects4 ,abacus1 #ai4 ,abeokuta1 #cc4 ,abipone1 #ga1 #gb4 ,abkhasia1 #ahh4 ,aboker1 #adh4 ,actuary1 ,life ins41 #ai4 ,adaize1 #afb4 ,addition1 #ai1 #dc1 #df1 #ib4 ,adelaide1 #ajh4 ,admiralty ,islands1 #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 ,aino 7,ainu71 #de1 #aia4 ,akra1 #abj4 ,akari1 #aij4 ,alaska1 #aeg1 #aif4 ,albania1 #ahd4 ,albert ,river1 #bf4 ,aleut1 #aeg4 ,algonkin 7,algonquin71 #de1 #ib1 #afa4 ,amazon1 #bc4 ,ambrym1 #acf4 ,american1 #aj1 #af1 #ai1 #ih1 #aje4 ,andaman1 #h1 #ae1 #bh1 #ca1 #gf1 #agd1 #aic4 ,aneitum1 #aed4 ,animal1 #c1 #f4 ,anthropological1 #ba4 ,apho1 #acc4 ,api1 #hj1 #acf1 #aee4 ,apinage1 #aaa4 ,arab1 #agj4 ,arawak1 #eb-ed1 #ace4 ,arctic1 #bi4 ,arikara1 #df4 ,arithmetic1 #a1 #e1 #cj1 #cc1 #gc1 #ic4 ,aryan1 #gf1 #abh-acj4 ,ashantee1 #ade4 ,asia 7,asiatic71 #bh1 #aac1 #aca1 #ahg4 ,assiniboine1 #ff1 #ib4 ,athapaskan1#ib4 ,atlantic1 #abf4 ,aurora1 #aee4 ,australia 7,australian71 #b1 #f1 #ai1 #bb1 #bd-cj1 #eg1 #eh1 #ga1 #ge1 #gf1 #hd1 #ajc1 #aje1 #ajf1 #aaj1 #aab1 #aah1 #agc1 #bjf4 ,avari1 #ahh4 ,aymara1 #aff4 ,aztec1 #fc1 #gh1 #hc1 #hi1 #ic1 #bja1 #bjg1 #bjh4 ,babusess1 #ch4 ,babylonian1 #bjh4 ,bagrimma1 #adh4 ,bahnars1 #ae4 ,bakairi1 #aaa4 ,balad1 #fg4 ,balenque1 #aej4 ,bambarese1 #ie4 ,banks ,islands1 #af1 #if1 #aec4 ,barea1 #aea4 ,bargaining1 #ah1 #ai1 #cb4 ,bari1 #acf4 ,barre1 #agd4 ,basa1 #adf4 ,basque1 #dj1 #ahb4 ,bellacoola1 see ,bilqula4 ,belyando ,river1 #aji4 ,bengal1 ,bay of1 #bh4 ,benu1 #acc4 ,betoya1 #eg1 #aab1 #ace1 #adj4 ,bilqula1 #df1 #afd4 ,binary1 chap4 v4 ,binin1 #adi4 ,bird-nesting1 #e4 ,bisaye1 #ij4 ,bogota1 #bjf4 ,bolan1 #abj4 ,bolivia1 #b1 #ba4 ,bongo1 #adc1 #ahf4 ,bonz1 #aea4 ,bororo1 #bc4 ,botocudo1 #bb1 #ca1 #dh1 #ga4 ,bourke1 #ajh4 ,boyne ,river1 #bd4 ,brazil1 #b1 #g1 #cj1 #agd1 #aie4 ,bretagne 7,breton71 #abj1 #abi1 #aha1 #ahb4 ,british ,columbia1 #de1 #df1 #fe1 #hf1 #hh1 #hi1 #aab1 #aac1 #aie4 ,bullom1 #adg4 ,bunch1 #fd4 ,burnett ,river1 #aab4 ,bushman1 #bh1 #ca4 ,butong1 #ic4 ,caddoe1 #afb4 ,cahuillo1 #afe4 ,calculating machine1 #ai4 ,campa1 #bb4 ,canada1 #bi1 #ec1 #ed1 #hf1 #aie4 ,canaque1 #adb1 #add4 ,caraja1 #bc4 ,carib1 #aff1 #afg1 #aii4 ,carnarvon1 #ce1 #cf4 ,carrier1 #hf4 ,carthaginian1 #agi4 ,caucasus1 #ahh4 ,cayriri 7see ,kiriri71 #gi4 ,cayubaba 7,cayubabi71 #hd1 #afg4 ,celtic1 #dj1 #afi1 #agi1 #aha1 #aij4 ,cely1 ,mom1 #i4 ,central ,america1 #bi1 #fi1 #gi1 #aba1 #aca1 #aie1 #bja1 #bjh4 ,ceylon1 #bh4 ,chaco1 #bb4 ,champion ,bay1 #aji4 ,charles ,,xii41 #acb4 ,cheyenne1 #fb4 ,chibcha1 #bjf4 ,china 7,chinese71 #dj1 #aca4 ,chippeway1 #fb1 #aei1 #afb4 ,chiquito1 #b1 #f1 #ba1 #dj1 #ga1 #gf4 ,choctaw1 #fe1 #he1 #afb4 ,chunsag1 #ahi4 ,circassia1 #aij4 ,cobeu1 #agd4 ,cochin ,china1 #ae4 ,columbian1 #aac4 ,comanche1 #bi1 #hc4 ,conibo1 #bc4 ,cooper's ,creek1 #ajh4 ,cora1 #aff4 ,cotoxo1 #aaa4 ,cowrie1 #fd1 #gj1 #ga4 ,cree1 #ia4 ,crocker ,island1 #ajg4 ,crow1 #c1 #d1 #ib4 ,crusoe1 ,robinson1 #g4 ,curetu1 #aaa4 ,dahomey1 #ga4 ,dakota1 #ha1 #ia1 #ib4 ,danish1 #cj1 #df1 #abi1 #ahc4 ,darnley ,islands1 #bd4 ,delaware1 #ia1 #afj4 ,demara1 #d1 #f4 ,dn1 #hf4 ,dido1 #ahi4 ,dinka1 #acf1 #adg4 ,dippil1 #ajg4 ,division1 #ai4 ,dravidian1 #ajd1 #aic4 ,dual number1 #ge4 ,duluth1 #cd4 ,duodecimal1 chap4 v4 ,dutch1 #abi4 ,eaw1 #bd4 ,ebon1 #aeb4 ,efik1 #adh1 #ahe4 ,encabellada1 #bb4 ,encounter ,bay1 #ajh4 ,ende1 #fh1 #aeb4 ,english1 #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 ,eyer's ,sand ,patch1 #bf4 ,ewe1 #fd1 #ia4 ,fall1 #afc4 ,fate1 #ach1 #aee4 ,fatuhiva1 #acj4 ,feloop1 #ade4 ,fernando ,po1 #aej4 ,fiji1 #if4 ,finger pantomime1 #aj1 #bc1 #bi1 #fg1 #hb4 ,fingoe1 #cc4 ,fist1 #af1 #ei1 #gb4 ,flinder's ,river1 #bd4 ,flores1 #fh1 #aeb4 ,forefinger1 #ab1 #ae1 #af1 #ed1 #fa1 #ia1 #aac4 ,foulah1 #adg4 ,fourth finger1 #ah4 ,frazer's ,island1 #ajh4 ,french1 #dj1 #da1 #abd1 #abi1 #aha1 #ahb1 #bji4 ,fuegan1 #bb4 ,gaelic1 #ahj4 ,galibi1 #ach4 ,gaul1 #afi1 #ahb4 ,georgia1 #ahi4 ,german1 #ch-dc1 #abi1 #ahc4 ,gesture1 #ah1 #ei4 ,gola1 #aea4 ,golo1 #adf4 ,gonn ,station1 #aaj4 ,goth1 #afi4 ,greek1 #hf1 #abi1 #afh1 #afi4 ,green ,island1 #de4 ,greenland1 #bi1 #eb1 #hj1 #aeh4 ,guachi1 #bc1 #ca4 ,guarani1 #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 ,herero1 #aej4 ,hervey ,islands1 #aah4 ,hidatsa1 #hj1 #ia4 ,hill ,end1 #aji4 ,himalaya1 #aic4 ,hottentot1 #hj1 #ib4 ,huasteca1 #bjd4 ,hudson's ,bay1 #dh1 #fa4 ,hun1 #afi4 ,hunt1 ,leigh1 #cc4 ,ibo1 #ahe4 ,icelandic1 #abi1 #ahc4 ,illinois1 #ia4 ,index finger1 #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 ,irish1 #abi1 #ahj4 ,italian1 #ci1 #hj1 #abd1 #abi1 #bjc4 ,jajowerong1 #aef4 ,jallonkas1 #adf4 ,jaloff1 #adf4 ,japanese1 #dj1 #hf1 #hi1 #ic-ie4 ,java1 #ic1 #abj4 ,jiviro1 #fa1 #acf4 ,joints of fingers1 #g1 #ah1 #agc4 ,juri1 #gi4 ,kamassin1 #acj4 ,kamilaroi1 #bg1 #ajg1 #aab4 ,kamtschatka1 #ge1 #aeg4 ,kanuri1 #acf1 #adi4 ,karankawa1 #fh4 ,karen1 #aab4 ,keppel ,bay1 #bd4 ,ki-,nyassa1 #aej4 ,kiriri1 #ee1 #ach1 #aci1 #afg4 ,kissi1 #ade4 ,ki-,swahili1 #db4 ,ki-,yau1 #aej4 ,klamath1 #eh1 #ei4 ,knot1 #g1 #i1 #ai1 #dj1 #ic1 #aae4 ,kolyma1 #ge4 ,kootenay1 #fe4 ,koriak1 #ge4 ,kredy1 #adi4 ,kru1 #adf4 ,ku-,mbutti1 #gh4 ,kunama1 #aea4 ,kuri1 #ahh4 ,kusaie1 #gh1 #hj4 ,kwakiutl1 #de4 ,labillardire1 #he4 ,labrador1 #bi4 ,lake ,kopperamana1 #ajg4 ,latin1 #dj1 #dd1 #gf1 #ha1 #hf1 #abd1 #abh1 #afh1 #afi1 #aha1 #ahb4 ,lazi1 #ahi4 ,left hand1 #aj-ag1 #ed4 ,leper's ,island1 #af4 ,leptscha1 #aic4 ,lifu1 #adc4 ,little finger1 #aj-ah1 #dh1 #ed1 #fa1 #ia4 ,logone1 #ahf4 ,london1 #abd4 ,lower ,california1 #bi4 ,luli1 #aah4 ,lutuami1 #afd4 ,maba1 #hj4 ,macassar1 #ic4 ,machine1 ,calculating1 #ai1 #bj4 ,mackenzie ,river1 #aeg4 ,macuni1 #agd4 ,madagascar1 #h1 #i4 ,maipures1 #ae1 #ef4 ,mairassis1 #aj4 ,malagasy1 #hc1 #ie4 ,malanta1 #if4 ,malay1 #h1 #de1 #ij1 #ic1 #agj4 ,mallicolo1 #aeb4 ,manadu1 #ic4 ,mandingo1 #ahf4 ,mangareva1 #aad4 ,manx1 #ahj4 ,many1 #b1 #ba-bc1 #be1 #bh1 #ajj4 ,maori1 #fd1 #ic1 #abb4 ,marachowie1 #bf4 ,mar1 #hd4 ,maroura1 #ajf4 ,marquesas1 #ic1 #aad1 #aae4 ,marshall ,islands1 #abb1 #aeb4 ,massachusetts1 #ia1 #aei4 ,mathematician1 #b1 #c1 #ce1 #ajb1 #abg1 #baj4 ,matibani1 #aea4 ,matlaltzinca1 #aff4 ,maya1 #de1 #df1 #aii1 #bje4 ,mbayi1 #aaa4 ,mbocobi1 #bb4 ,mbousha1 #ff4 ,melanesia1 #af1 #bb1 #bh1 #hd1 #ie4 ,mende1 #ahf4 ,mexico1 #bi1 #aie1 #bja1 #bjd1 #bjh4 ,miami1 #ia4 ,micmac1 #ij1 #afj4 ,middle finger1 #ab1 #ae1 #fb4 ,mille1 #abb4 ,minnal ,yungar1 #bf4 ,minsi1 #afb4 ,mississaga1 #dd1 #ib4 ,mississippi1 #abe4 ,mocobi1 #aai4 ,mohegan1 #ia4 ,mohican1 #agb4 ,mokko1 #adi4 ,molele1 #afd4 ,moneroo1 #aji4 ,mongolian1 #h4 ,montagnais1 #ec1 #ed1 #age4 ,moree1 #bd4 ,moreton ,bay1 #ajh4 ,mort ,noular1 #ajg4 ,mosquito1 #fi1 #gj1 #aba4 ,mota1 #ie1 #aec4 ,mpovi1 #aeb4 ,multiplication1 #ai1 #cc1 #dj1 #dc1 #ei4 ,mundari1 #aic4 ,mundo1 #ahf4 ,muralug1 #ag4 ,murray ,river1 #ajf1 #aji4 ,muysca1 #bjf4 ,nagranda1 #bjg4 ,nahuatl1 #ada1 #add1 #agg1 #bja1 #bje4 ,nakuhiva1 #aaf1 #acj4 ,negro1 #h1 #i1 #ae1 #bi1 #ahd4 ,nengone1 #fc1 #acf4 ,new1 #abh-acj4 ,new ,caledonia1 #aed4 ,new ,granada1 #aie4 ,new ,guinea1 #aj1 #aeb4 ,new ,hebrides1 #aee4 ,new ,ireland1 #de4 ,new ,zealand1 #abc4 ,nez ,perces1 #fe1 #aeh4 ,ngarrimowro1 #aaj4 ,niam ,niam1 #fd1 #acf4 ,nicaragua1 #hj4 ,nicobar1 #gh1 #aic4 ,nightingale1 #d4 ,nootka1 #afc1 #aih4 ,norman ,river1 #bd4 ,north ,america1 #bh1 #hb1 #aga1 #agc1 #agf1 #aid1 #bja4 ,notch1 #g1 #i1 #ic4 ,numeral frame1 #ai4 ,nupe1 #adi1 #ahf4 ,nusqually1 #if4 ,oceania1 #aae1 #agf4 ,octonary1 chap4 v4 ,odessa1 #cd4 ,ojibwa1 #hd1 #aei4 ,okanaken1 #hh4 ,omaha1 #afa4 ,omeo1 #aaj4 ,oregon1 #eh1 #aie4 ,orejone1 #bc4 ,orinoco1 #ed1 #ef1 #aie4 ,ostrich1 #ga1 #gb4 ,otomac1 #ae4 ,otomi1 #afe1 #aii4 ,ottawa1 #aei4 ,oyster ,bay1 #gi4 ,pacific1 #bi1 #aac1 #aaf1 #aag1 #aca4 ,palm 7of the hand71 #ab1 #ad1 #ae4 ,palm ,island1 #aef4 ,pama1 #acf1 #aee4 ,pampanaga1 #ff4 ,papaa1 #adh4 ,paraguay1 #ee1 #ga1 #aah1 #aie4 ,parana1 #aai4 ,paris1 #ahb4 ,pawnee1 #ia1 #aba1 #afb4 ,pebble1 #g-i1 #ai1 #dj1 #ic1 #agi4 ,peno1 #b4 ,peru 7,peruvian71 #b1 #bb1 #fa1 #bjf4 ,philippine1 #ff4 ,philology 7,philologist71 #abh1 #bji1 #baj4 ,phoenician1 #ij1 #agi4 ,pigmy1 #fi1 #gj1 #gh4 ,pikumbul1 #eg1 #ach4 ,pines1 ,isle of1 #aec4 ,pinjarra1 #bf4 ,plenty1 #be1 #gg4 ,point ,barrow1 #cj1 #ea1 #fd1 #hc1 #acg1 #aei4 ,polynesia1 #bb1 #bh1 #aah1 #acj1 #agj4 ,pondo1 #cc4 ,popham ,bay1 #ajg4 ,port ,darwin1 #aji4 ,port ,essington1 #bd1 #ajg4 ,port ,mackay1 #bf4 ,port ,macquarie1 #aji4 ,puget ,sound1 #if4 ,puri1 #bb1 #ib4 ,quappa1 #aga1 #agb4 ,quaternary1 chap4 v4 ,queanbeyan1 #bd4 ,quiche1 #bje4 ,quichua1 #fa4 ,rapid1 #afc4 ,rarotonga1 #aad4 ,richmond ,river1 #aji4 ,right hand1 #aj-ah1 #ed4 ,right-handedness1 #ac1 #ad4 ,ring finger1 #ae4 ,rio ,grande1 #aie4 ,rio ,napo1 #bb4 ,rio ,norte1 #acf1 #aii4 ,russia 7,russian71 #cj1 #ce4 ,sahaptin1 #aeh4 ,san ,antonio1 #acf4 ,san ,blas1 #gi1 #hj4 ,sanskrit1 #dj1 #ib1 #ig1 #abh4 ,sapibocone1 #hd1 #afg4 ,saste 7,shasta71 #afe4 ,scratch1 #g4 ,scythian1 #afi4 ,seed1 #ic4 ,semitic1 #hi4 ,senary1 chap4 v4 ,sesake1 #acf1 #aee4 ,several1 #bb4 ,sexagesimal1 #abd1 #bjh4 ,shawnoe1 #afj4 ,shell1 #g1 #ai1 #gj1 #ic4 ,shushwap1 #hh4 ,siberia1 #bi1 #cj1 #ahg1 #aij4 ,sierra ,leone1 #hc4 ,sign language1 #f4 ,sioux1 #hc4 ,slang1 #abd4 ,slavonic1 #dj4 ,snowy ,river1 #aaj4 ,soussou1 #hc1 #adg4 ,south ,africa1 #d1 #ae1 #bh4 ,south ,america1 #b1 #ae1 #bb1 #bc1 #bg-bi1 #ed1 #eg1 #gb1 #gf1 #gh1 #gi1 #ajd1 #aaj1 #agc1 #agd1 #aid1 #bja1 #bjf4 ,spanish1 #b1 #bc1 #db4 ,splint1 #g4 ,stick1 #g1 #agi4 ,stlatlumh1 #hh4 ,streaky ,bay1 #bf4 ,string1 #g1 #i1 #fd1 #ga4 ,strong's ,island1 #gh4 ,subtraction1 #ai1 #dd-dg4 ,sunda1 #abj4 ,sweden 7,swedish71 #abi1 #acb1 #ahc4 ,tacona1 #b4 ,taensa1 #dd4 ,tagala1 #ff4 ,tahiti1 #aad4 ,tahuata1 #aae4 ,tama1 #aaa4 ,tamanac1 #ed1 #ace4 ,tambi1 #abj4 ,tanna1 #aed4 ,tarascan1 #afe4 ,tariana1 #agd4 ,tasmania1 #bd1 #bg1 #gi1 #ajd1 #ajf4 ,tawgy1 #acj4 ,tchetchnia1 #ahh4 ,tchiglit1 #aeg1 #aif4 ,tembu1 #cc4 ,temne1 #adh4 ,ternary1 chap4 v4 ,terraba1 #agb4 ,teutonic1 #dj1 #da1 #dc1 #agi1 #aha1 #bjh4 ,texas1 #fi4 ,thibet1 #if4 ,thumb1 #aj-ah1 #ed1 #ei1 #fa1 #fb1 #aac1 #agc4 ,thusch1 #ahi4 ,ticuna1 #afh4 ,timukua1 #afe4 ,tlingit1 #acf1 #afc1 #aig4 ,tobi1 #aef4 ,tonga1 #cc1 #he4 ,torres1 #ag1 #if1 #ajd1 #aje4 ,totonaco1 #bje4 ,towka1 #gh4 ,triton's ,bay1 #aeb4 ,tschukshi1 #aef1 #aia4 ,tsimshian1 #hf1 #afd1 #aih4 ,tweed ,river1 #bf4 ,uainuma1 #abb4 ,udi1 #ahh4 ,uea1 #fg1 #aec4 ,united ,states1 #bi1 #hc1 #aie4 ,upper ,yarra1 #aaj4 ,ureparapara1 #aec4 ,vaturana1 #if4 ,vedda1 #bh1 #ca1 #gf1 #agd4 ,vei1 #af1 #adg1 #ahe4 ,victoria1 #aef4 ,vilelo1 #fj4 ,waiclatpu1 #afd4 ,wales 7,welsh71 #ce1 #df1 #ada1 #add1 #agg1 #ahj4 ,wallachia1 #aba4 ,warrego1 #ajg1 #aji4 ,warrior ,island1 #ajg4 ,wasp1 #e4 ,watchandie1 #bi1 #gg4 ,watji1 #abj4 ,weedookarry1 #bd4 ,wimmera1 #ajg4 ,winnebago1 #he4 ,wiraduroi1 #bg1 #ajh4 ,wirri-,wirri1 #ajh4 ,wokke1 #aab4 ,worcester1 ,mass41 ,schools of1 #aa4 ,yahua1 #afh4 ,yaruro1 #aci4 ,yengen1 #aed4 ,yit-tha1 #aji4 ,yoruba1 #cc1 #dg1 #fd1 #gj1 #ahe4 ,yucatan1 #aie1 #bja4 ,yuckaburra1 #bf4 ,zamuco1 #ee1 #fj1 #ach1 #aci4 ,zapara1 #aaa4 ,zulu1 #af1 #fb4 ,zui1 #ac1 #ad1 #dh1 #di1 #ec1 #ed1 #fj1 #hc1 #acg4 ,,footnotes3 #a ,brinton1 ,d4,g41 ,essays of an ,americanist1 p4 #djf2 and ,american ,race1 p4 #cei4 #b ,this information ,i received from ,dr4 ,brinton by letter4 #c ,tylor1 ,primitive ,culture1 ,vol4 ,i4 p4 #bdj4 #d ,nature1 ,vol4 ,,xxxiii4 p4 #de4 #e ,spix and ,martius1 ,travels in ,brazil1 ,tr4 from ,german by ,h4,e4 ,lloyd1 ,vol4 ,,ii4 p4 #bee4 #f ,de ,flacourt1 ,histoire de le grande ,isle de ,madagascar1 ch4 xxviii4 ,quoted by ,peacock1 ,encyc4 ,met41 ,vol4 ,i4 p4 #cic4 #g ,bellamy1 ,elizabeth ,w41 ,atlantic ,monthly1 ,march1 #ahic1 p4 #cag4 #h ,grundriss der ,sprachwissenschaft1 ,bd4 ,,iii4 ,abt4 i41 p4 #id4 #i ,pruner-,bey1 ,bulletin de la ,socit d',anthr4 de ,paris1 #ahfa1 p4 #dfb4 #aj ,manual ,concepts1 ,am4 ,anthropologist1 #ahib1 p4 #bib4 #aa ,tylor1 ,primitive ,culture1 ,vol4 ,i4 p4 #bde4 #ab ,op4 cit41 loc4 cit4 #ac ,aboriginal ,inhabitants of ,andaman ,islands1 ,journ4 ,anth4 ,inst41 #ahhb1 p4 #ajj4 #ad ,morice1 ,a41 ,revue d',anthropologie1 #ahgh1 p4 #fcd4 #ae ,macdonald1 ,j41 ,manners1 ,customs1 etc41 of ,south ,african ,tribes1 ,journ4 ,anthr4 ,inst41 #ahhi1 p4 #bij4 ,about a dozen tribes are enumerated by ,mr4 ,macdonald3 ,pondos1 ,tembucs1 ,bacas1 ,tolas1 etc4 #af ,codrington1 ,r4,h41 ,melanesians1 their ,anthropology and ,folk-,lore1 p4 #cec4 #ag ,e4g4 the ,zuis4 ,see ,cushing's paper quoted above4 #ah ,haddon1 ,a4,c41 ,ethnography ,western ,tribes ,torres ,strait1 ,journ4 ,anth4 ,inst41 #ahhi1 p4 #cje4 ,for a similar method1 see ,life in the ,southern ,isles1 by ,w4,w4 ,gill4 #ai ,tylor1 ,primitive ,culture1 ,vol4 ,i4 p4 #bdf4 #bj ,brinton1 ,d4,g41 ,letter of ,sept4 #bc1 #ahic4 #ba ,ibid4 ,the reference for the ,mbocobi1 infra1 is the same4 ,see also ,brinton's ,american ,race1 p4 #cfa4 #bb ,tylor1 ,primitive ,culture1 ,vol4 ,i4 p4 #bdc4 #bc ,op4 cit41 loc4 cit4 #bd ,hyades1 ,bulletin de la ,socit d',anthr4 de ,paris1 #ahhg1 p4 #cdj4 #be ,wiener1 ,c41 ,prou et ,bolivie1 p4 #cfj4 #bf ,marcoy1 ,p41 ,travels in ,south ,america1 ,vol4 ,,ii p4 #dg4 ,according to the same authority1 most of the tribes of the ,upper ,amazon cannot count above #b or #c except by reduplication4 #bg ,op4 cit41 ,vol4 ,,ii4 p4 #bha4 #bh ,glossaria ,linguarum ,brasiliensium4 ,bororos1 p4 #ae2 ,guachi1 p4 #acc2 ,carajas1 p4 #bfe4 #bi ,curr1 ,e4,m41 ,the ,australian ,race1 ,vol4 ,i4 p4 #bhb4 ,the next eight lists are1 in order1 from ,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 ,the ,daily ,life and ,origin of the ,tasmanians1 p4 #add4 #ca ,latham1 ,comparative ,philology1 p4 #ccf4 #cb ,the ,australian ,race1 ,vol4 ,i4 p4 #bje4 #cc ,mackenzie1 ,a41 ,native ,australian ,langs41 ,journ4 ,anthr4 ,inst41 #ahgd1 p4 #bfc4 #cd ,curr1 ,the ,australian ,race1 ,vol4 ,,ii4 p4 #acd4 ,the next four lists are from ,,ii4 p4 #d1 ,i4 p4 #cbb1 ,i4 p4 #cdf1 and ,i4 p4 #cih1 respectively4 #ce ,curr1 op4 cit41 ,vol4 ,,iii4 p4 #ej4 #cf ,op4 cit41 ,vol4 ,,iii4 p4 #bcf4 #cg ,mller1 ,sprachwissenschaft4 ,,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 ,deschamps1 ,l',anthropologie1 #ahia1 p4 #cah4 #db ,man1 ,e4,h4 ,aboriginal ,inhabitants of the ,andaman ,islands1 p4 #cb4 #dc ,mller1 ,sprachwissenschaft1 ,i4 ii4 p4 #bi4 #dd ,oldfield1 ,a41 ,tr4 ,eth4 ,soc4 ,vol4 ,,iii4 p4 #bia4 #de ,bancroft1 ,h4,h41 ,native ,races1 ,vol4 ,i4 p4 #efd4 #df ,notes on ,counting1 etc41 among the ,eskimos of ,point ,barrow4 ,am4 ,anthrop41 #ahij1 p4 #ch4 #dg ,second ,voyage1 p4 #eef4 #dh ,personal ,narrative1 ,vol4 ,i4 p4 #caa4 #di ,burton1 ,b4,f41 ,mem4 ,anthr4 ,soc4 of ,london1 ,vol4 ,i4 p4 #cad4 #ej ,confessions4 ,in collected works1 ,edinburgh1 #ahij1 ,vol4 ,,iii4 p4 #ccg4 #ea ,ellis1 ,robert1 ,on ,numerals as ,signs of ,primeval ,unity4 ,see also ,peruvia ,scythia1 by the same author4 #eb ,stanley1 ,h4,m41 ,in ,darkest ,africa1 ,vol4 ,,ii4 p4 #dic4 #ec ,stanley1 ,h4,m41 ,through the ,dark ,continent1 ,vol4 ,,ii4 p4 #dhf4 #ed ,haumont1 ,parisot1 ,adam1 ,grammaire et ,vocabulaire de la ,langue ,taensa1 p4 #bj4 #ee ,chamberlain1 ,a4,f41 ,lang4 of the ,mississaga ,indians of ,skugog4 ,vocab4 #ef ,boas1 ,fr41 ,sixth ,report on the ,indians of the ,northwest1 p4 #aje4 #eg ,beauregard1 ,o41 ,bulletin de la ,soc4 d',anthr4 de ,paris1 #ahhf1 p4 #ebf4 #eh ,ray1 ,s4,h41 ,journ4 ,anthr4 ,inst41 #ahia1 p4 #h4 #ei ,op4 cit41 p4 #ab4 #fj ,mller1 ,sprachwissenschaft1 ,,iv4 i4 p4 #acf4 #fa ,brinton1 ,the ,maya ,chronicles1 p4 #ej4 #fb ,trumbull1 ,on ,numerals in ,am4 ,ind4 ,lang41 p4 #ce4 #fc ,boas1 ,fr4 ,this information was received directly from ,dr4 ,boas4 ,it has never before been published4 #fd ,bancroft1 ,h4,h41 ,native ,races1 ,vol4 ,,ii4 p4 #gec4 ,see also p4 #aii1 infra4 #fe ,mann1 ,a41 ,notes on the ,numeral ,syst4 of the ,yoruba ,nation1 ,journ4 ,anth4 ,inst41 #ahhf1 p4 #ei1 et seq4 #ff ,mller1 ,sprachwissenschaft1 ,,iv4 i4 p4 #bjb4 #fg ,trumbull1 ,j4,h41 ,on ,numerals in ,am4 ,ind4 ,langs41 p4 #aa4 #fh ,cushing1 ,f4,h41 ,manual ,concepts1 ,am4 ,anthr41 #ahib1 p4 #bhi4 #fi ,grimm1 ,geschichte der deutschen ,sprache1 ,vol4 ,i4 p4 #bci4 #gj ,murdoch1 ,j41 ,american ,anthropologist1 #ahij1 p4 #ci4 #ga ,kleinschmidt1 ,s41 ,grammatik der ,grnlandischen ,sprache1 p4 #cg4 #gb ,brinton1 ,the ,arawak ,lang4 of ,guiana1 p4 #d4 #gc ,petitot1 ,e41 ,dictionnaire de la langue ,dn-,dindjie1 p4 lv4 #gd ,gilij1 ,f4,s41 ,saggio di ,storia ,am41 ,vol4 ,,ii4 p4 #ccc4 #ge ,mller1 ,sprachwissenschaft1 ,,ii4 i4 p4 #chi4 #gf ,op4 cit41 p4 #cie4 #gg ,mller1 ,sprachwissenschaft1 ,,ii4 i4 p4 #dch4 #gh ,peacock1 ,arithmetic1 in ,encyc4 ,metropolitana1 #a1 p4 #dhj4 #gi ,brinton1 ,d4,g41 ,the ,betoya ,dialects1 ,proc4 ,am4 ,philos4 ,soc41 #ahib1 p4 #bgc4 #hj ,ridley1 ,w41 ,report on ,australian ,languages and ,traditions4 ,journ4 ,anth4 ,inst41 #ahgc1 p4 #bfb4 #ha ,gatschet1 ,gram4 ,klamath ,lang4 ,u4,s4 ,geog4 and ,geol4 ,survey1 ,vol4 ,,ii4 part #a1 pp4 #ebd and #ecf4 #hb ,letter of ,nov4 #ag1 #ahic4 #hc ,mller1 ,sprachwissenschaft1 ,,ii4 i4 p4 #dci4 #hd ,hale1 ,indians of ,no4 ,west4 ,am41 ,tr4 ,am4 ,eth4 ,soc41 ,vol4 ,,ii4 p4 #hb4 #he ,brinton1 ,d4,g41 ,studies in ,so4 ,am4 ,native ,languages1 p4 #be4 #hf ,tr4 ,am4 ,philological ,association1 #ahgd1 p4 #da4 #hg ,tylor1 ,primitive ,culture1 ,vol4 ,i4 p4 #bea4 #hh ,mller1 ,sprachwissenschaft1 ,,iv4 i4 p4 #bg4 #hi ,see infra1 ,chapter ,,vii4 #ij ,ellis1 ,a4,b41 ,ewe ,speaking ,peoples1 etc41 p4 #bec4 #ia ,tylor1 ,primitive ,culture1 ,vol4 ,i4 p4 #bef4 #ib ,stanley1 ,in ,darkest ,africa1 ,vol4 ,,ii4 p4 #dic4 #ic ,chamberlain1 ,a4,f41 ,proc4 ,brit4 ,ass4 ,adv4 of ,sci41 #ahib1 p4 #eii4 #id ,boas1 ,fr41 ,sixth ,report on ,northwestern ,tribes of ,canada1 ,proc4 ,brit4 ,ass4 ,adv4 ,sci41 #ahij1 p4 #feg4 #ie ,hale1 ,h41 ,indians of ,northwestern ,am41 ,tr4 ,am4 ,eth4 ,soc41 ,vol4 ,,ii4 p4 #hh4 #if ,op4 cit41 p4 #ie4 #ig ,mller1 ,sprachwissenschaft1 ,,ii4 ii4 p4 #adg4 #ih ,schoolcraft1 ,archives of ,aboriginal ,knowledge1 ,vol4 ,,iv4 p4 #dbi4 #ii ,du ,chaillu1 ,p4,b41 ,tr4 ,eth4 ,soc41 ,london1 ,vol4 ,i4 p4 #cae4 #ajj ,latham1 ,r4,g41 ,essays1 chiefly ,philological and ,ethnographical1 p4 #bdg4 ,the above are so unlike anything else in the world1 that they are not to be accepted without careful verification4 #aja ,pott1 ,zhlmethode1 p4 #de4 #ajb ,gatschet1 ,a4,s41 ,the ,karankawa ,indians1 the ,coast ,people of ,texas4 ,the meanings of #f1 #g1 #h1 and #i are conjectural with me4 #ajc ,stanley1 ,h4,m41 ,in ,darkest ,africa1 ,vol4 ,,ii4 p4 #dib4 #ajd ,mller1 ,sprachwissenschaft1 ,,ii4 i4 p4 #cag4 #aje ,toy1 ,c4,h41 ,trans4 ,am4 ,phil4 ,assn41 #ahgh1 p4 #bi4 #ajf ,burton1 ,r4,f41 ,mem4 ,anthrop4 ,soc4 of ,london4 #a1 p4 #cad4 ,in the illustration which follows1 ,burton gives #fhbj1 instead of #dhbj2 which is obviously a misprint4 #ajg ,dobrizhoffer1 ,history of the ,abipones1 ,vol4 ,,ii4 p4 #afi4 #ajh ,sayce1 ,a4,h41 ,comparative ,philology1 p4 #bed4 #aji ,tr4 ,eth4 ,society of ,london 1 ,vol4 ,,iii4 p4 #bia4 #aaj ,ray1 ,s4,h41 ,journ4 ,anthr4 ,inst41 #ahhi1 p4 #eja4 #aaa ,stanley1 ,in ,darkest ,africa1 ,vol4 ,,ii4 p4 #dib4 #aab ,op4 cit41 loc4 cit4 #aac ,tylor1 ,primitive ,culture1 ,vol4 ,i4 p4 #bdi4 #aad ,mller1 ,sprachwissenschaft1 ,,iv4 i4 p4 #cf4 #aae ,martius1 ,glos4 ,ling4 ,brasil41 p4 #bga4 #aaf ,tylor1 ,primitive ,culture1 ,vol4 ,i4 p4 #bdh4 #aag ,roth1 ,h4 ,ling1 ,aborigines of ,tasmania1 p4 #adf4 #aah ,lull1 ,e4,p41 ,tr4 ,am4 ,phil1 ,soc41 #ahgc1 p4 #ajh4 #aai ,ray1 ,s4,h4 ,sketch of ,api ,gram41 ,journ4 ,anthr4 ,inst41 #ahhh1 p4 #cjj4 #abj ,kleinschmidt1 ,s41 ,grammatik der ,grnlandischen ,spr41 p4 #ci4 #aba ,mller1 ,sprachwissenschaft1 ,i4 ii4 p4 #ahd4 #abb ,op4 cit41 ,i4 ii4 p4 #ah1 and ,,ii4 i4 p4 #bbb4 #abc ,squier1 ,g4,e41 ,nicaragua1 ,vol4 ,,ii4 p4 #cbf4 #abd ,schoolcraft1 ,h4,r41 ,archives of ,aboriginal ,knowledge1 ,vol4 ,,ii4 p4 #bjh4 #abe ,tylor1 ,primitive ,culture1 ,vol4 ,i4 p4 #bfd4 #abf ,goedel1 ,ethnol4 des ,soussous1 ,bull4 de la ,soc4 d',anthr4 de ,paris1 #ahib1 p4 #ahe4 #abg ,ellis1 ,w41 ,history of ,madagascar1 ,vol4 ,i4 p4 #ejg4 #abh ,beauregard1 ,o41 ,bull4 de la ,soc4 d',anthr4 de ,paris1 #ahhf1 p4 #bcf4 #abi ,schoolcraft1 ,h4,r41 ,archives of ,aboriginal ,knowledge1 ,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 ,schoolcraft1 ,h4,r41 ,archives of ,aboriginal ,knowledge1 ,vol4 ,,ii4 p4 #bac4 #ace ,op4 cit41 p4 #baf4 #acf ,op4 cit41 p4 #bjf4 #acg ,mariner1 ,gram4 ,tonga ,lang41 last part of book4 ,not paged4 #ach ,morice1 ,a4,g41 ,the ,dn ,langs1 ,trans4 ,can4 ,inst41 ,march #ahij1 p4 #ahf4 #aci ,boas1 ,fr41 ,fifth ,report on the ,northwestern ,tribes of ,canada1 ,proc4 ,brit4 ,ass4 ,adv4 of ,science1 #ahhi1 p4 #hha4 #adj ,do4 ,sixth ,rep41 #ahij1 pp4 #fhd1 #fhf1 #fhg4 #ada ,op4 cit41 p4 #feh4 #adb ,bancroft1 ,h4,h41 ,native ,races1 ,vol4 ,,ii4 p4 #dii4 #adc ,tr4 ,ethnological ,soc4 of ,london1 ,vol4 ,,iv4 p4 #ib4 #add ,any ,hebrew lexicon4 #ade ,schrder1 ,p41 ,die ,phnizische ,sprache1 p4 #ahd et seq4 #adf ,mller1 ,sprachwissenschaft1 ,,ii4 ii4 p4 #adg4 #adg ,on ,numerals in ,am4 ,indian ,languages4 #adh ,ellis1 ,a4,b41 ,ewe ,speaking ,peoples1 etc41 p4 #bec4 ,the meanings here given are partly conjectural4 #adi ,pott1 ,zhlmethode1 p4 #bi4 #aej ,schoolcraft1 op4 cit41 ,vol4 ,,iv4 p4 #dbi4 #aea ,trumbull1 op4 cit4 #aeb ,chamberlain1 ,a4,f41 ,lang1 of the ,mississaga ,indians1 ,vocab4 #aec ,crawfurd1 ,hist4 ,ind4 ,archipelago1 #a1 p4 #beh4 #aed ,hale1 ,h41 ,eth4 and ,philol41 ,vol4 ,,vii42 ,wilkes1 ,expl4 ,expedition1 ,phil4 #ahdf1 p4 #agb4 #aee ,crawfurd1 op4 cit41 #a1 p4 #beh4 #aef ,op4 cit41 loc4 cit4 #aeg ,bancroft1 ,h4,h41 ,native ,races1 ,vol4 ,,ii4 p4 #dih4 #aeh ,vignoli1 ,t41 ,myth and ,science1 p4 #bjc4 #aei ,codrington1 ,r4,h41 ,the ,melanesian ,languages1 p4 #bdi4 #afj ,op4 cit41 loc4 cit4 #afa ,codrington1 ,r4,h41 ,the ,melanesian ,languages1 p4 #bdi4 #afb ,wickersham1 ,j41 ,japanese ,art on ,puget ,sound1 ,am4 ,antiq41 #ahid1 p4 #gi4 #afc ,codrington1 ,r4,h41 op4 cit41 p4 #bej4 #afd ,tylor1 ,primitive ,culture1 ,vol4 ,i4 p4 #beb4 #afe ,compare a similar table by ,chase1 ,proc4 ,amer4 ,philos4 ,soc41 #ahfe1 p4 #bc4 #aff ,leibnitzii ,opera1 ,,iii4 p4 #cdf4 #afg ,pruner-,bey1 ,bulletin de la ,soc4 d',anthr4 de ,paris1 #ahfj1 p4 #dhf4 #afh ,curr1 ,e4,m41 ,the ,australian ,race1 ,vol4 ,i4 p4 #cb4 #afi ,haddon1 ,a4,c41 ,western ,tribes of the ,torres ,straits1 ,journ4 ,anthr4 ,inst41 #ahhi1 p4 #cjc4 #agj ,taplin1 ,rev4 ,g41 ,notes on a ,table of ,australian ,languages1 ,journ4 ,anthr4 ,inst41 #ahgb1 p4 #hh4 ,the first nine scales are taken from this source4 #aga ,latham1 ,r4,g41 ,comparative ,philology1 p4 #ceb4 #agb ,it will be observed that this list differs slightly from that given in ,chapter ,,ii4 #agc ,curr1 ,e4,m41 ,the ,australian ,race1 ,vol4 ,,iii4 p4 #fhd4 #agd ,bonwick1 ,tasmania1 p4 #adc4 #age ,lang1 ,j4,d41 ,queensland1 p4 #dce4 #agf ,bonwick1 ,tasmania1 p4 #adc4 #agg ,mller1 ,sprachwissenschaft1 ,,ii4 i4 p4 #eh4 #agh ,op4 cit41 ,,ii4 i4 p4 #gj4 #agi ,op4 cit41 ,,ii4 i4 p4 #bc4 #ahj ,barlow1 ,h41 ,aboriginal ,dialects of ,queensland1 ,journ4 ,anth4 ,inst41 #ahgc1 p4 #aga4 #aha ,curr1 ,e4,m41 ,the ,australian ,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 ,the next ten lists are taken from the same volume1 pp4 #bhb1 #bhh1 #cdj1 #cgf1 #dcb1 #ejf1 #ecj1 #eeh1 #efj1 #ehh1 respectively4 #ahh ,brinton1 ,the ,american ,race1 p4 #cea4 #ahi ,martius1 ,glossaria ,ling4 ,brazil41 p4 #cjg4 #aij ,op4 cit41 p4 #adh4 #aia ,mller1 ,sprachwissenschaft1 ,,ii4 i4 p4 #dch4 #aib ,peacock1 ,arithmetic1 ,encyc4 ,metropolitana1 #a1 p4 #dhj4 #aic ,brinton1 ,studies in ,so4 ,am4 ,native ,langs41 p4 #fg4 #aid ,op4 cit41 loc4 cit4 #aie ,brinton1 ,studies in ,so4 ,am4 ,native ,langs41 p4 #fg4 ,the meanings of the numerals are from ,peacock1 ,encyc4 ,metropolitana1 #a1 p4 #dhj4 #aif ,mason1 ,journ4 ,as4 ,soc4 of ,bengal1 ,vol4 ,,xxvi4 p4 #adf4 #aig ,curr1 ,e4,m41 ,the ,australian ,race1 ,vol4 ,,iii4 p4 #ajh4 #aih ,bancroft1 ,h4,h41 ,native ,races1 ,vol4 ,i4 p4 #bgd4 #aii ,clarke1 ,hyde1 ,journ4 ,anthr4 ,inst41 #ahgb1 p4 clvii4 ,in the article from which this is quoted1 no evidence is given to substantiate the assertion made4 ,it is to be received with great caution4 #bjj ,hale1 ,h41 ,wilkes ,exploring ,expedition1 ,vol4 ,,vii4 p4 #agb4 #bja ,op4 cit41 p4 #bdh4 #bjb ,hale1 ,ethnography and ,philology1 p4 #bdg4 #bjc ,loc4 cit4 #bjd ,ellis1 ,polynesian ,researches1 ,vol4 ,,iv4 p4 #cda4 #bje ,gill1 ,w4,w41 ,myths and ,songs of the ,south ,pacific1 p4 #cbe4 #bjf ,peacock1 ,arithmetic1 ,encyc4 ,metropolitana1 #a1 p4 #dgi4 #bjg ,peacock1 ,encyc4 ,metropolitana1 #a1 p4 #dhj4 #bjh ,sprachverschiedenheit1 p4 #cj4 #bji ,crawfurd1 ,history of the ,indian ,archipelago1 ,vol4 ,i4 p4 #bef4 #baj ,pott1 ,zhlmethode1 p4 #ci4 #baa ,op4 cit41 p4 #da4 #bab ,mller1 ,sprachwissenschaft1 ,,ii4 i4 p4 #cag4 ,see also ,chap4 ,,iii41 supra4 #bac ,long1 ,s4,h41 ,expedition1 ,vol4 ,,ii4 p4 lxxviii4 #bad ,martius1 ,glossaria ,ling4 ,brasil41 p4 #bdf4 #bae ,hale1 ,ethnography and ,philology1 p4 #dcd4 #baf ,mller1 ,sprachwissenschaft1 ,,ii4 ii4 p4 #hb4 #bag ,the information upon which the above statements are based was obtained from ,mr4 ,w4,l4 ,williams1 of ,gisborne1 ,n4,z4 #bah ,primitive ,culture1 ,vol4 ,i4 p4 #bfh4 #bai ,ralph1 ,julian1 ,harper's ,monthly1 ,vol4 #hf1 p4 #ahd4 #bbj ,lappenberg1 ,j4,m41 ,history of ,eng4 under the ,anglo-,saxon ,kings1 ,vol4 ,i4 p4 #hb4 #bba ,the compilation of this table was suggested by a comparison found in the ,bulletin ,soc4 ,anth4 de ,paris1 #ahhf1 p4 #ij4 #bbb ,hale1 ,ethnography and ,philology1 p4 #abf4 #bbc ,mller1 ,sprachwissenschaft1 ,,ii4 ii4 p4 #ahc4 #bbd ,bachofen1 ,j4,j41 ,antiquarische ,briefe1 ,vol4 ,i4 pp4 #aja-aae1 and ,vol4 ,,ii4 pp4 #a-ij4 #bbe ,an extended table of this kind may be found in the last part of ,nystrom's ,mechanics4 #bbf ,schubert1 ,h41 quoting ,robert ,flegel1 in ,neumayer's ,anleitung zu ,wissenschaftlichen ,beobachtung auf ,reisen1 ,vol4 ,,ii4 p4 #bij4 #bbg ,these numerals1 and those in all the sets immediately following1 except those for which the authority is given1 are to be found in ,chapter ,,iii4 #bbh ,codrington1 ,the ,melanesian ,languages1 p4 #bbb4 #bbi ,mller1 ,sprachwissenschaft1 ,,ii4 ii4 p4 #hc4 #bcj ,op4 cit41 ,i4 ii4 p4 #ee4 ,the next two are the same1 p4 #hc and p4 #baj4 ,the meaning given for the ,bari puk is wholly conjectural4 #bca ,gallatin1 ,semi-civilized ,nations1 ,tr4 ,am4 ,eth4 ,soc41 ,vol4 ,i4 p4 #aad4 #bcb ,mller1 ,sprachwissenschaft1 ,,ii4 ii4 p4 #hj4 ,erromango1 the same4 #bcc ,boas1 ,fr41 ,proc4 ,brit4 ,ass'n4 ,adv4 ,science1 #ahhi1 p4 #heg4 #bcd ,hankel1 ,h41 ,geschichte der ,mathematik1 p4 #bj4 #bce ,murdoch1 ,j41 ,eskimos of ,point ,barrow1 ,am4 ,anthr41 #ahij1 p4 #dj4 #bcf ,martius1 ,glos4 ,ling4 ,brasil41 p4 #cfj4 #bcg ,du ,graty1 ,a4,m41 ,la ,rpublique du ,paraguay1 p4 #bag4 #bch ,codrington1 ,the ,melanesian ,languages1 p4 #bba4 #bci ,mller1 ,sprachwissenschaft1 ,,ii4 i4 p4 #cfc4 #bdj ,spurrell1 ,w41 ,welsh ,grammar1 p4 #ei4 #bda ,olmos1 ,andr de1 ,grammaire ,nahuatl ou ,mexicaine1 p4 #aia4 #bdb ,moncelon1 ,bull4 ,soc4 d',anthr4 de ,paris1 #ahhe1 p4 #ced4 ,this is a purely digital scale1 but unfortunately ,m4 ,moncelon does not give the meanings of any of the numerals except the last4 #bdc ,ellis1 ,peruvia ,scythia1 p4 #cg4 ,part of these numerals are from ,martius1 ,glos4 ,brasil41 p4 #baj4 #bdd ,codrington1 ,the ,melanesian ,languages1 p4 #bcf4 #bde ,schweinfurth1 ,g41 ,linguistische ,ergebnisse einer ,reise nach ,centralafrika1 p4 #be4 #bdf ,park1 ,m41 ,travels in the ,interior ,districts of ,africa1 p4 #h4 #bdg ,pott1 ,zhlmethode1 p4 #cg4 #bdh ,op4 cit41 p4 #ci4 #bdi ,mller1 ,sprachwissenschaft1 ,,iv4 i4 p4 #aja4 ,the ,kru scale1 kindred with the ,basa1 is from the same page4 #bej ,park1 in ,pinkerton's ,voyages and ,travels1 ,vol4 ,,xvi4 p4 #ijb4 #bea ,park1 ,travels1 ,vol4 ,i4 p4 #af4 #beb ,schweinfurth1 ,g41 ,linguistische ,ergebnisse einer ,reise nach ,centralafrika1 p4 #gh4 #bec ,park1 ,travels1 ,vol4 ,i4 p4 #eh4 #bed ,goedel1 ,ethnol4 des ,soussous1 ,bull4 ,soc4 ,anth4 ,paris1 #ahib1 p4 #ahe4 #bee ,mller1 ,sprachwissenschaft1 ,i4 ii4 p4 #aad4 ,the ,temne scale is from the same page4 ,these two languages are closely related4 #bef ,op4 cit41 ,i4 ii4 p4 #aee4 #beg ,op4 cit41 ,i4 ii4 p4 #ee4 #beh ,long1 ,c4,c41 ,central ,africa1 p4 #ccj4 #bei ,mller1 ,sprachwissenschaft1 ,,iv4 i4 p4 #aje4 #bfj ,pott1 ,zhlmethode1 p4 #da4 #bfa ,mller1 op4 cit41 ,i4 ii4 p4 #adj4 #bfb ,mller1 ,sprachwissenschaft1 ,,iv4 i4 p4 #ha4 #bfc ,pott1 ,zhlmethode1 p4 #da4 #bfd ,mller1 op4 cit41 ,i4 ii41 p4 #baj4 #bfe ,pott1 ,zhlmethode1 p4 #db4 #bff ,schweinfurth1 ,linguistische ,ergebnisse1 p4 #ei4 #bfg ,mller1 ,sprachwissenschaft1 ,i4 ii4 p4 #bfa4 ,the ten is not given4 #bfh ,stanley1 ,through the ,dark ,continent1 ,vol4 ,,ii4 p4 #dij4 ,ki-,nyassa1 the same page4 #bfi ,mller1 op4 cit41 ,i4 ii4 p4 #bfa4 #bgj ,du ,chaillu1 ,adventures in ,equatorial ,africa1 p4 #ecd4 #bga ,mller1 ,sprachwissenschaft1 ,,iii4 i4 p4 #fe4 #bgb ,du ,chaillu1 ,adventures in ,equatorial ,africa1 p4 #ecc4 #bgc ,mller1 op4 cit41 ,,iii4 ii4 p4 #gg4 #bgd ,balbi1 ,a41 ,l',atlas ,eth41 ,vol4 ,i4 p4 #bbf4 ,in ,balbi's text #g and #h are ansposed4 ,taru for #e is probably a misprint for tana4 #bge ,du ,chaillu1 op4 cit41 p4 #ecc4 ,the next scale is op4 cit41 p4 #ecd4 #bgf ,beauregard1 ,o41 ,bull4 ,soc4 ,anth4 de ,paris1 #ahhf1 p4 #ebf4 #bgg ,pott1 ,zhlmethode1 p4 #df4 #bgh ,op4 cit41 p4 #dh4 #bgi ,turner1 ,nineteen ,years in ,polynesia1 p4 #ecf4 #bhj ,erskine1 ,j4,e41 ,islands of the ,western ,pacific1 p4 #cda4 #bha ,op4 cit41 p4 #djj4 #bhb ,codrington1 ,melanesian ,languages1 pp4 #bce1 #bcf4 #bhc ,peacock1 ,encyc4 ,met41 ,vol4 #a4 p4 #che4 ,peacock does not specify the dialect4 #bhd ,erskine1 ,islands of the ,western ,pacific1 p4 #cfj4 #bhe ,turner1 ,g41 ,samoa a ,hundred ,years ,ago1 p4 #cgc4 ,the next three scales are from the same page of this work4 #bhf ,codrington1 ,melanesian ,languages1 p4 #bce4 ,the next four scales are from the same page4 ,perhaps the meanings of the words for #f to #i are more properly more #a1 more #b1 etc4 ,codrington merely indicates their significations in a general way4 #bhg ,hale1 ,ethnography and ,philology1 p4 #dbi4 ,the meanings of #f to #i in this and the preceding are my conjectures4 #bhh ,mller1 ,sprachwissenschaft1 ,,iv4 i4 p4 #abd4 #bhi ,aymonier1 ,e41 ,dictionnaire ,francaise-,cambodgien4 #bij ,mller1 ,op4 cit41 ,,ii4 i4 p4 #aci4 #bia ,mller1 ,sprachwissenschaft1 ,,ii4 i4 p4 #abc4 #bib ,wells1 ,e4,r41 ,jr41 and ,john ,w4 ,kelly1 ,bureau of ,ed41 ,circ4 of ,inf41 ,no4 #b1 #ahij4 #bic ,pott1 ,zhlmethode1 p4 #eg4 #bid ,mller1 ,op4 cit41 ,,ii4 i4 p4 #afa4 #bie ,petitot1 ,vocabulaire ,franaise ,esquimau1 p4 lv4 #bif ,mller1 ,sprachwissenschaft1 ,,ii4 i4 p4 #bec4 #big ,mller1 ,op4 cit41 ,,ii4 ,i4 p4 #agi1 and ,kleinschmidt1 ,grnlandisches ,grammatik4 #bih ,adam1 ,l41 ,congres ,int4 des ,am41 #ahgg1 p4 #bdd 7see p4 #afb infra74 #bii ,gallatin1 ,synopsis of ,indian ,tribes1 ,trans4 ,am4 ,antq4 ,soc41 #ahcf1 p4 #ceh4 ,the next fourteen lists are1 with the exception of the ,micmac1 from the same collection4 ,the meanings are largely from ,trumbull1 op4 cit4 #cjj ,schoolcraft1 ,archives of ,aboriginal ,knowledge1 ,vol4 ,,ii4 p4 #baa4 #cja ,schoolcraft1 ,archives of ,aboriginal ,knowledge1 ,vol4 ,v4 p4 #ehg4 #cjb ,in the ,dakota dialects #aj is expressed1 as here1 by a word signifying that the fingers1 which have been bent down in counting1 are now straightened out4 #cjc ,boas1 ,fifth ,report ,b4,a4,a4,s41 #ahhi4 ,reprint1 p4 #fa4 #cjd ,boas1 ,sixth ,report ,b4,a4,a4,s41 #ahij4 ,reprint1 p4 #aag4 ,dr4 ,boas does not give the meanings assigned to #g and #h1 but merely states that they are derived from #b and #c4 #cje ,op4 cit41 p4 #aag4 ,the derivations for #f and #g are obvious1 but the meanings are conjectural4 #cjf ,boas1 ,sixth ,report ,b4,a4,a4,s41 #ahhi4 ,reprint1 pp4 #aeh1 #afj4 ,the meanings assigned to the ,tsimshian #h and to ,bilqula #f to #h are conjectural4 #cjg ,hale1 ,ethnography and ,philology1 p4 #fai4 #cjh ,op4 cit41 loc4 cit4 #cji ,hale1 ,ethnography and ,philology1 p4 #fai4 #caj ,mller1 ,sprachwissenschaft1 ,,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 ,the meanings given for the words for #g1 #h1 #i are conjectures of my own4 #cad ,mller1 ,sprachwissenschaft1 ,,ii4 i4 p4 #big4 #cae ,pott1 ,zhlmethode1 p4 #ij4 #caf ,mller1 op4 cit41 ,,ii4 i4 p4 #cgi4 #cag ,gallatin1 ,semi-,civilized ,nations of ,mexico and ,central ,america1 ,tr4 ,am4 ,ethn4 ,soc41 ,vol4 ,i4 p4 #aad4 #cah ,adam1 ,lucien1 ,congres ,internationale des ,americanistes1 #ahgg1 ,vol4 ,,ii4 p4 #bdd4 #cai ,mller1 ,sprachwissenschaft1 ,,ii4 i4 p4 #cie4 ,i can only guess at the meanings of #f to #i4 ,they are obviously circumlocutions for #e-a1 #e-b1 etc4 #cbj ,op4 cit41 p4 #dch4 ,mller has transposed these two scales4 ,see ,brinton's ,am4 ,race1 p4 #ceh4 #cba ,marcoy1 ,p41 ,tour du ,monde1 #ahff1 #bme sem4 p4 #adh4 #cbb ,op4 cit41 p4 #acb4 ,the meanings are my own conjectures4 #cbc ,an elaborate argument in support of this theory is to be found in ,hervas' celebrated work1 ,arithmetica di quasi tutte le nazioni conosciute4 #cbd ,see especially the lists of ,hale1 ,gallatin1 ,trumbull1 and ,boas1 to which references have been given above4 #cbe ,thiel1 ,b4,a41 ,vocab4 der ,indianier in ,costa ,rica1 ,archiv fr ,anth41 xvi4 p4 #fbj4 #cbf ,these three examples are from ,a4,r4 ,wallace's ,narrative of ,travels on the ,amazon and ,rio ,negro1 vocab4 ,similar illustrations may be found in ,martius' ,glos4 ,brasil4 #cbg ,martius1 ,glos4 ,brasil41 p4 #agf4 #cbh ,adam1 ,l41 ,congres ,international des ,americanistes1 #ahgg1 ,vol4 ,,ii4 p4 #bdd4 ,given also supra1 p4 #ec4 #cbi ,o',donovan1 ,irish ,grammar1 p4 #abc4 #ccj ,armstrong1 ,r4,a41 ,gaelic ,dict41 p4 xxi4 #cca ,spurrell1 ,welsh ,dictionary4 #ccb ,kelly1 ,triglot ,dict41 pub4 by the ,manx ,society4 #ccc ,guillome1 ,j41 ,grammaire ,franaise-,bretonne1 p4 #bg4 #ccd ,grber1 ,g41 ,grundriss der ,romanischen ,philologie1 ,bd4 ,i4 p4 #cji4 #cce ,pott1 ,zhlmethode1 p4 #hh4 #ccf ,van ,eys1 ,basque ,grammar1 p4 #bg4 #ccg ,pott1 ,zhlmethode1 p4 #aja4 #cch ,op4 cit41 p4 #gh4 #cci ,mller1 ,sprachwissenschaft1 ,i4 ii4 p4 #abd4 #cdj ,op4 cit41 p4 #aee4 #cda ,op4 cit41 p4 #adj4 #cdb ,op4 cit41 loc4 cit4 #cdc ,schweinfurth1 ,reise nach ,centralafrika1 p4 #be4 #cdd ,mller1 ,sprachwissenschaft1 ,,iv4 i4 p4 #hc4 #cde ,op4 cit41 ,,iv4 i4 p4 #ha4 #cdf ,op4 cit41 ,i4 ii4 p4 #aff4 #cdg ,long1 ,c4,c41 ,central ,africa1 p4 #ccj4 #cdh ,peacock1 ,encyc4 ,met41 ,vol4 ,i4 p4 #chh4 #cdi ,mller1 ,sprachwissenschaft1 ,,iii4 ii4 p4 #fd4 ,the next seven scales are from op4 cit41 pp4 #hj1 #acg1 #aee1 #ahb1 #bac4 #cej ,pott1 ,zhlmethode1 p4 #hc4 #cea ,op4 cit41 p4 #hc1--;,akari1 p4 #hd2 ,circassia1 p4 #he4 #ceb ,mller1 ,sprachwissenschaft1 ,,ii4 i4 p4 #adj4 #cec ,pott1 ,zhlmethode1 p4 #hg4 #ced ,mller1 ,sprachwissenschaft1 ,,ii4 ii4 p4 #cdf4 #cee ,op4 cit41 ,,iii4 i4 p4 #acj4 #cef ,man1 ,e4,h41 ,brief ,account of the ,nicobar ,islands1 ,journ4 ,anthr4 ,inst41 #ahhe1 p4 #dce4 #ceg ,wells1 ,e4,r41 ,jr41 and ,kelly1 ,j4,w41 ,eng4 ,esk4 and ,esk4 ,eng4 ,vocab41 ,bureau of ,education ,circular of ,information1 ,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 ,sixth ,report on the ,northwestern ,tribes of ,canada1 p4 #aag4 #cfa ,boas1 ,fr41 ,fifth ,report on the ,northwestern ,tribes of ,canada1 p4 #he4 #cfb ,gallatin1 ,semi-,civilized ,nations1 p4 #aad4 ,references for the next two are the same4 #cfc ,bancroft1 ,h4,h41 ,native ,races of the ,pacific ,states1 ,vol4 ,,ii4 p4 #gfc4 ,the meanings are from ,brinton's ,maya ,chronicles1 p4 #ch et seq4 #cfd ,brinton1 ,maya ,chronicles1 p4 #dd4 #cfe ,simon ,rmi1 ,dictionnaire de la langue nahuatl1 p4 xxxii4 #cff ,an error occurs on p4 xxxiv of the work from which these numerals are taken1 which makes the number in question appear as #bgi1iii1iii instead of #a1bgi1iii1iii4 #cfg ,gallatin1 ,semi-,civilized ,nations of ,mexico and ,central ,america1 ,tr4 ,am4 ,ethn4 ,soc4 ,vol4 ,i4 p4 #aad4 #cfh ,pott1 ,zhlmethode1 p4 #hi4 ,the ,totonacos were the first race ,cortez encountered after landing in ,mexico4 #cfi ,op4 cit41 p4 #ij4 ,the ,coras are of the ,mexican state of ,sonora4 #cgj ,gallatin1 ,semi-,civilized ,nations1 p4 #aad4 #cga ,humboldt1 ,recherches1 ,vol4 ,,ii4 p4 #aab4 #cgb ,squier1 ,nicaragua1 ,vol4 ,,ii4 p4 #cbf4 #cgc ,gallatin1 ,semi-,civilized ,nations1 p4 #eg4