y 4-2-3 ^. ^ . a^2/^ y-T'i^^ NOTE ON THE ANCIENT MEXICAN CALENDAR SYSTEM BY ZELIA NUTTALL. COMMUNICATED TO THE TENTH INTERNATIONAL CONGRESS OF AMERICANISTS. STOCKHOLM 1894. NOTE ox THE ANCIENT MEXICAN CALENDAR SYSTEM BY ZELIA XUTTALL. COMMUNICATED TO THE TENTH INTERN ATION AT. CONGRESS OF AMERICANISTS. STOCKHOLM 1894. PRINTED BY BRUNO SCHULZE, DRESDEN. PREFACE. When I communicated the results of my investigations of the Ancient Mexican Calendar System to the International Anthropological Congress at Chicago, August 1893, I an- nounced their speedy publication by the Peabody Museum, Hai-vard University, Cambridge, Mass. It was then my intention to publish my communication -as it stood and I forwarded it to the Salem Press without ■delay. When, after some weeks, I received the j)roof- sheets and read them through, I realised the serious drawbacks of publishing as a permanent memoir a paper originally inten- ded for a spoken address to a Congress. The necessity of making tliis as short as possible had obliged me to treat certain points of the intricate subject supei-ficially and to •omit desirable references to the writings of previous investi- gators. I saw that T would be doing an injustice to my subject and to myself were I to publish, in permanent form, the bare outlines of an investigation that I could not even regard as tei-minated. For J had not come to any definite -conclusion regarding several obscure problems and could only hope to do so after a pi'olonged and close research. AVith Prof. Putnam's kind approval I decided to delay my publication until 1 had completed my investigations .satisfactorily. I returned my rcNised manu.st-npt to Cambridgt' in February, but then an unexpected delay of several months — 4 — occuiTcd in the printing of* proof-sheets. This delay has proved to be of utmost vahie to me, for it afforded me leisure to continue and extend my researches. Tlie results I have recently gained are of stuh definite interest that I am tempted to submit them to the International Congress of Americanists as my complete work is in press and is not likely to appear for several montlis. In presenting these results I am somewhat at a dis- advantage, for I am not able to refer my readers to the 4 large and 10 small analytical tables of the Mexi'-an Calendar System, that accompany my publication. Nor am I able to discuss the opinions of previous wi'iters as tho-. roughly as in niv work. On the other hand the results 1 desire to make Ivnuwn are solid facts that, to a great measure, explain themselves and can be readily verified. I am therefore encouraged to present tliem, in as plain and brief a manner as possible, on the present memorable occasion. J_t is a well-known fact that the Ancient Mexican Calendar S^^stem was based on a combination of 20 day signs with numerals ranging from 1 to 13. The ritual year of 260 days contained every possible combination of 20 and 18 and formed therefore an unit. An unbroken series of such units formed the ground- work of the Solar Calendar. Among the 20 day -signs there are four that are known as year- symbols, the years being invariablj' named after them n rotation. The reconstruction of the Calendar System tJiat I exhibited at the Huelva Meeting of the Congress and at the Madrid and Chicago Expositions, constituted a demon- stration of the harmonious results obtained when the solar year was made to commence on a day bearing its symbol and number. I based my reconstruction on the following distinct statement contained in the Anonymous Ms. of the Biblio- teca Nazionale, Florence: "The year always begins with one of four day -signs and takes its name accordingly. Wlien it begins on a day Acatl the year is named Acatl, when it begins on Tocpatl the year is named Tecpatl, and so on." Boturini and Veytia likewise record this order of days, but not one of these three authorities mentions any connection between the numeral of a year and tliat of its first da}'. As far as I know Siguenza is the only one to state that "the year must always begin on a day of its number." This authority is quoted by Orozco y Berra, Historia Antigua de Mexico, vol. II p. 54. — 6 — "While my reconstruction exemplified both of the- above rules relating to day- signs and numerals it taught me that what I will tei-m the law of concordant numeration was the prime factor in producing a metho- dical and harmonious development of the system. Thus the year I Acatl, for instance, beginning with a day 1 acatl, naturally divided itself into 4 quarters headed by a day numbered 1. After 365 days the day 2 tecpatl began the year II Tecpatl that contained 4 quarters headed by days numbered 2. Moreover by beginning a count of solar years on the (Uiy 1 acatl and allowing it to develop itself according to the laws of the system, a Great Epoch of 1040 years is formed, containing 20 cycles of 52 years, each beginning with a day and year numbered 1.^ Impressed though 1 was A^dth the harmony and plausibility of the method of beginning a year with a day of the same name I nevertheless realised that the mass of authentic evidence established the employment of a solar Calendar in which the years Acatl, Tecpatl, Calli and Tochtli^ began respectively on days Cipactli, Miquiztli, Ozomatli and Cozcaquauhtli. This order is recorded by Sahagun^ Duran, Gama, Humboldt, Ramirez, Orozco y Berra and Chavero who remarks (Anales del Museo Nacional II p. 245) that it is observed in the Vatican, Borgian and Telleriano Remensis Codices and is adopted by their interpreters,. Fabregat, Rios and others. Having duly tested and examined the evidence of the- foregoing authorities and found it as firm as tliat main- taining the employment of the first method I was forced to conclude that both methods must have been used. In my endeavour to account for the existence of two orders of days 1 was inclined to believe, at an early stage of my 1 In his valuable contribution: Ensayo sobre los simbolos cronograficos. de los Moxicanos, Anales del Museo Nacional, vol. 11, p. 346. Senor Francisco del Paso y Troncoso first demonstrated that the period of 1040 years was^ the natural outcome of the Mexican <.'alendai' Svstem. investigation, that the Calendar had served in a demotic and an hieratic form. But recent researches lead me to the firm conviction that one method was as much tlie natural outgrowth of the system as the other and that both were employed, in turn. Before proceeding to present the facts upon which I base my conviction, I must state that it differs widely from the views of recent writers on the sub- ject who advocate the employment of one method only. The distinguished Mexican historian, Orozco y Berra maintained that the years began with the days: cipactli, miquiztli, ozomatli and cozcaquauhtli, and he demonstrated that the year III Calli (A. D. 1521) must have begun with the day 2 ozomatli and the month Itzcalli at a date corre- sponding to January 30 *h. On the other hand Dr. Ed. Seler, in a recent publi- cation^ denounces Orozco y Berrn's views as erroneous and states his belief that the years began on days of the same name only. His final conclusion is: "that the Mexican year took its name from the first day of its fiftli month!" and that the year III Calli, for instance, began with the month Atlacahualco on a day 1 Calli, corresponding to Febru- ary 12 tb. While both of these investigators Avere equally justified in respectively upholding the employment of both orders of days it is remarkable that neither of them seem to have recognised the fundamental law of the system requiring that the number of a year and of its first day shonM be identical. In my reconstruction according to Order I, in which the year begins with a day of the same name, the impor- tance of the numerals as factors in regulating the succession of years and cycles is apparent. The same results are ob- tained by observing concordant numeration in Order II, as exemplified on the accompanying plate to which I now refer. 2 Die Mexikanischen Bilderhandsebrifteii . . . in der koniglicben Bililio- thek zu Berlin . . . Berlin 1893. p. 20. — 8 — In the first case the year I Acatl, beginniug on a day 1 Cipactli is foimd to hold, in tlie centre, a complete ritual year beginning with the day 1 Acatl. It is 2)ro(-p(l(Ml and followed by a period of 4X13 = 52 days and forms, so to speak, the kernel of the solar year. The years TI Tecpatl, beginning witli a day 2 Miquiztli and III Calli, beginning with 3 Ozomatli, respectively enclose ritual years beginning with 2 Tecpatl and 3 Calli, and so on. Now as it is well known that in Ancient Mexico the religious festi- vals anil observances were regulated by the ritual year, it is extremely significant to find that there was a definite connection between the name of the solar year and of the first day of the ritual year it enclosed. What is more, the solar year divides itself into four quarters beginning with days bearing the numeral of the year, a point to whicli T will revert. Having verified these striking and significant facts on my tables, I next determined the date, according to our Al- manach, of the day that the system itself seemed to designate as the first of the year. In order to do this it was merely necessary to refer to the historical dates that were recorded by Spanish and Mexican historians according to their respective Calendars. The best known of these, the date of the surrender of the last Mexican ruler, the unfortunate Quauhtemoc, was first adopted by Orozco y Berra and tlien by Dr. Ed. Seler as a starting point for their widely divergent investigations and conclusions. According to Spanish historians the event took place on August ISth 1521 (Julian Calendar). Chimalpahin and Sahagun relate that it occurred on the day 1 Coatl, in tli(> month Tlaxochimaco, vear TIT Calli. With an Almanach in liand it can be easil}' verified that if the day 1 Coatl corresponded to August 13*^, the day 3 Ozomatli corresponded to March 1]H' (Julian Calendar) and consequently, with the vomkiI (Mpiinox. It is scarcely necessary to recall the well-known fact that, at the time of the Gregorian reformation in 1582, the Julian Calendar had gained 10 complete days upon the equinox since A. D. 325, when the Council of Nice was held. During the 16 th century, therefore, before 1582. the vernal equinox corresponded sometimns to the 10 H' but generally to the IV^ of March. After the Calendar had been reformed by the suppression of 10 days, March 21^-' was adopted as the fixed date of the equinox. It may be well to state here that A. D. 1520 was a leap-year, conse- quently 1519 and 1521 were ordinary years and coincided in length with the Mexican year. It was a striking fact that the day 3 Ozomatli that I had reason to look ujDon as the first of the year III calli should correspond to the period of the vernal equinox. But this did not acquire its full importance until I had connected it with the following state- ment contained in a curious old chronicle dated 1547 and known as the Codex Fuenleal:-^ "They reckoned the year from the equinox in March, when the sun casts a straight shadow, and as soon as it was observed that tho Sun began to rise they counted the first day. And from the day of the equinox they counted the da3"S for their feasts and thus the feast of bread, in commemoration of tlie birth of Huitzilopochtli , occured when the sun was in its decline and in the same way the other festivals (were counted)." Nothing could seem more natural and plausible than that the Mexicans, who are known to have been Sun- worshippers, should have dated the commencement of their solar year from the vernal equinox and held festivals to celebrate other marked periods of its eourse. But, strange to say, with the single exception quoted above, the Sun as a factor in regulating the solar Calendar, lias been entirely ignored by all writers on the subject down to the present day. 3 Published in the Aiiales del Museo Nacioiial, vol. 11 \>. S5. — 10 — The accompanying list of tlie dates assigned to the commencement of the Mexican year by the best authorities, will show the variety of opinions held: Janiiary 1. MS. attributed to Olmos. „ 9. Gama. Humboldt. „ 30. Orozco y Berra. February 2. Sahagun, Torquemada, Veytia, Vetancourt. Fray Martin de Leon. 12. Dr. Ed. Seler. „ 24. Interpreters of the Vatican and Telleriano- Remensis Codices. „ 26. Acosta and Clavigero. March 1. Duran, Valades, Anonymous Author of the Biblioteca Nazionale MS. and Motolinia. „ 20. Ixtlilxochitl. Referring tlie reader to the works of these writers containing their reasons for fixing upon these dates. I will but remark that the majority of them were influenced, in doing so. by tlieir views as to which of the native months was the first of the year. Sahagun is a notable exception. AVriting in 1577. he relates that he had at some previous time, assembled a number of the oldest and wisest Indians at Tlatelolco and confronted them with the most able of the Spanish c;ollegiates in order to discuss the Ancient Calendar sj^stem. "After spending many days in altercation they finally concluded that the Mexican year began at a date corre- sponding to February 2"*^." Sahagun further states, however, that he had observed great discrepancies in the testimony that he had collected in different localities. In some he was informed that the native year began in January, in otliers on the pt of February, in other places he was told that it began in !\[arch. it is mucli to be regretted that absolutely no ( hu' is furnished to the reasons that influenced the Spanish coUe- giates and native elders to tlecide that the Mexican year — 11 — began on Feb. 2"'^. It is evident that tlie matter must have seemed a complicated and difficult one since many days had to be spent in discussion and altercation before any conclusion was reached. It is improbable that any of the old priest- astronomers should have been among the converted Indians present at the consultation, for the privileged ruling caste had been the first to perish in the Conquest. The secrets of the Calendar system had been rigidly guarded by the initiated and the Anonymous Friar, quoted by Sahagun, records that "the Indians who knew the secrets of the Calendar taught or revealed them to very few, for through their knowledge they gained their livelihood and were esteemed as wise and learned men. Now although nearly all adult Indians knew the correct name of the year, of its number and symbol, it was only these master calculators who knew the many secrets and counts that the .... calendar (;ontained." All matters considered it is admissible to question tlie value of the Tlatelolco decision, for it would seem as tliougli the native elders assembled had exemplified an ancient proverb: "Those who spoke, knew not and those who knew, spoke not." Again, in their case, no liiut is given of a connection between the solar Calendar and the marked periods of tlie Sun's course. Upon close examination some of the dates on the list given above prove to harmonise with my demonstration that the year III Calli and the year preceding it began March 11 (Julian Calendar) and the statement by the author of the Fuenleal Codex, that the Mexicans datcil tlicir solar year from the vernal equinox. In order to demonstrate this agreement I must revert to the accepted fact that the Mexicans employed the vague solar year in their Calendar and rectified retrogression at the end of 52 years by adding a group of 13 days. As bissextile intercalation was employed in the Julian Calendar it is evident that a diverp-ence at the rate of one day every four years would necessarily occur m any sniuu- — 12 — taneous count of Mexican and Julian years. The fact that the year ITT CalH began on a day corresponding to the vernal equinox enables us to determine that the year II Acatl. the first of the Cycle, must have begun three days after the vernal equinox, a fact T will discuss later. On the other hand the first day of the S'i^'i year of the cycle would correspond to March 1 and fall 10 days before the vernal equinox. It is recorded that as the Spaniards had subjugated and occupied Mexico in 1559 no celebrations were held in that year at the beginning of the new Cycle, accordinu' to the ancient custom. The native Calendar was not adjusted to the equinox in that year, as formerlj^ and consequently the divergences between the Mexican year, the equinox, and the Julian Calendar went on increasing proportionately. Thus when Duran, Motolinia, Valades and the Anony- mous Author of the B. N. MS. state that the Mexican year began on March 1, they were perfectly right-but this date held good for 1546 — 1550 only. From 1550 — 1554 the Mexican year began on Feb. 29 or 28, from 1562 — 1566 on Feb. 25 and so on. It must also be borne in mind that the refor- mation of the Julian Calendar by the suppression of 10 days took place in 1582 and that the different dates on the list above were partly assiiined according to the Julian and partly according to the Gregorian Calendars. Ixtlilxochitl. the native historian, who died in 1648, naturally recordetl the date March 20 according to the Gregorian Calendar — it reads March 10 in the Julian Calendar and coincides, in either case, with the period of the equiii<)X. I thuik that 1 have sufticicntly demonstrated the fruitlessness of all attempts to connect the Mexican New Year's Day with a fixed date of our Calendar. For its relation to this and to its own Calendar was subject to respective changes by the shifting of a day every four years. But while 1 have exposed the duiditful value of — 13 — t]ie fixed dates assigned 'by various writers I liave also shown tliat tliose given by the rehable autliorities: Duran, Motolinia, Ixthlxochitl, Valades and the An. Author of tlie B. N. MS. connect the commencement of the year with tlie vernal equinox. Further evidence corroborates tliis connection, moreover Sehor Troncoso (op. cit.) has amply proven tliat tlie Mexicans were acquainted with the use of the gnomon. He also quotes the following extremely interesting though some- what confused passage from the MS. Historia de los Indios by Padre Motolinia. "The festival or month Tlacaxipehua- liztli, in lionour of Tezcatlipoca, fell when the Sun occupied the centre of Huitzilopochtli, wdio was the equinox. Because it (a statue or column?) was slightly crooked, Montezuma wished to fell it and have it straio-htened." The same writer further states : "At tlie time when the Spaniards entered and (conquered New Spain the natives began their year at the connnencement of March; but as they did not employ bissextile intercalation their yeai's and months are subject to variation." In the Biblioteca Nazionale MS. the description of the feast Tlacaxipehualiztli is accompanied by the date: March 21, a fact that further connects this festival with the vernal equinox. Gomara, Gemelli Careri and Diego Valades state that it was the first of the year, but Sahagun, Duran, Torquemada, Betancourt, Fray Martin de Leon, Rios and Clavigero agree that the jeRv began with the previous month Atlacahualco or as it is also named, Quahuitleloa or Xilomaniztli. Both views are compatible, for supposing that tlie cycle and its first 3^ear began with the vernal ecpiinox on the first day of Tlacaxipehualiztli it naturally followed that the first daj^ of the vague solar year would gradually recede from this date and fall in Atlacahualco. Indeed after the fourth year of the cycle the years would always begin in this month until the intercalation of 13 days, at the end — 14 — of 52 years would adjust New Year s Day to Tlacaxipe- hualiztli. Let us next consider the fixed order of months as given by Sahagun, collated with Gama and the Anon. Author of the B. N. MS. — Sahao'un. Grama. Xilomaniztli. Anon. Author. Xilomaniztli Aicauaio. Miccailhuitontli. Miccailhuitl. Pachtli. Hueypachtli. Miccailhuitontli. Miccailhuitl. PachtU. Hueypachtli. I. AtlacahualcO Quauitleloa. 11. Tlacaxipehualiztli. III. Tozoztonlli. IV. Hueytozoztli. V. Toxcatl. VI. Etzacualitztli. VII. Tecuilhuitoutli. Vm. HueitecuiJhuitl. IX. Tlaxochimaco. X. Xocohuetzi. XL Ochpaniztli. Xll. Teotleco. XIII. Tepeilhuitl. XIV. Quecholli. XV. Pauquetzaliztli. XVI. Atemoztli. XVll. Tititl. XVIII. Itzcalli. It is generally assumed that each of these 17 "months" contained 20 days, that the eighteenth had 25 and that these periods had special names just like our months. M}^ investigations lead mc to believe that this was not exactly the case. According to Sahagun' s own statements* "the divisions of the year arose from the custom of dedicating to each deity a period of 20 days during whidi feasts and saxni- fices occurred in bis honor. But there were two months during which foui- deities were feasted, ten days being dedicated to each. Thus, although there were 18 months, 20 feasts wci-e celebrated."" * op. cit. ed. Bustaniante p. 338. — 15 — This being the case it Is evident that none of tlie above lists are complete, since each gives the names of 18 instead of 20 festival-periods. A clue to the names and positions of the two missing- festivals is perhaps furnished by the circumstance tliat the three lists united, assign four names to months IX and X and four names to months X and XI. At the same time it must be noted that several months, the first for instance, are known to have been designated by several names. It is therefore im- possible to venture an opinion on this intricate subject without going further into details than I can at present. It suffices for my purpose to show that, contrary to the current view, the Mexican year contained not 18 but 20 festival- periods. Reference to Sahagun's and Duran's descriptions ' of the festivals reveals the irregularity with which they fell in their respective fixed periods. Indeed in an appended note, Sahagun himself states that these feasts were only in so far fixed, that they alway occurred during the "month" or a day a two before it. He adds that there were moveable feasts that were regulated by the cycle of 260 days and that these varied and fell in a different month each year. Referring to Sahagun's list of the moveable feasts "that usurped the places of some of the Calendar festivals in some 5 Thus Sahagun records that in Months I, XIU and XYII the festival was celebrated during- the month. In Months H, III, IV, V, VI? on first day. In Months VIII, XIV and XVIII on tenth day. „ „ IX two days previous. „ „ XI five days previous to this aU the festivaties of the tenth month ceased. After its beginning certain ceremonies were observed for eight days, making thirteen days in all, after which another feast occurred, lasting four days. „ „ XII Festival began on fifteenth day. The great festival of the month was held on eighteenth and nineteenth days. ,, „ XV Second, ninth and sixteenth days. „ „ XVI Sixteenth and last days. — 16 — years as sometimes liappeus with us", we find tliat the first given is in honor of the Sun and invariably fell on tlie day 4 Ollin. a day- sign s\mbolising the "4 movements of the Sim."" We further learn that on each day 1 Acatl a great festival was held in honor of Quetzalcoatl. On the days 1 ]\Iiquiztli and 2 Coatl Tezcatlipoca was feasted. TliH (lay 1 Teepatl was dedicated to Huitzilopochtli and 1 Irzcniurli to Xiuhtecuhtli, the god of fire, or of the year. On the latter day they also "held the elections of their chieftains . . . and decided upon wars against their enemies." As Sahagun describes the feast 1 Quialiuitl twice, his list actually consists of 13 moveable festivals. Besides these lie describes the great feast held every four yeai'S on a fixed day and another held exery eight years, previous to which a fast of eight days was observed. Padre Duran"s Historia de las Indias de Nueva Espana contains an extremely important chapter on the native Calen- dar, dated 1579. It shows that Sahagun' s list of 13 move- able feasts was incomplete for, "in order to honor each of"' "the 20 days -signs the first day of each period of 13 days" "was observed as a solemn feast like Sunday. When the" "same day occurred twice in the year it was not observed" "the second time." This being the case it is but logical to infer that the series of such festivals in the year T Acatl. foi- instance, began with the day 1 Acatl and were concentrated in the central ritual year, each festival occurring on a day combined with number 1. When the same day recurred before or after this ritual year it was not celebrated in the same way. On the other hand the first and twentieth day of each Calendar festival were specially solemnised and "many feasts had what was an equivalent to the octaves" of thf Catholic church festivals. A most important and little knovxu feature of the ancient Calenilar system is recorded by Duran. He states that on the first day of each period of 20 chiys in the solar year a complete rest from all manual labor was rigorously enforced, so muc^h so that "all houses had to be swept and all food prepared and cooked on the previous day." Accordingly, in the year I Acatl on my table, each day of the sign Cipactli would be a day of rest, in the year II Tecpatl each Mi(|iuztli day and so on. Duran likewise relates that an old woman who had formerly been a priestess and enjoyed a reputation for wis- dom, had drawn his attention to the curious fact that the most important of ancient native festivals used to be held at the same times of the year as Easter, Corpus Christi and Christmas. She pointed out further coincidences of the kind but the friar, unfortunately, does not record them. From the testimony of this ex-priestess it is not difficult to gather that the principal feasts of the native year coincided with the equinoxes and solstices. Duran remarks (p. 155) that Tlacaxipeliualiztli was the first feast of the native Calendar and fell on Mar(;h 21. He laments that it seriously interfered with the celebration of Easter, as it was difficult to discriminate which of the ■festivals the Indians were observing. The above and fore- going testimony suffices to establish Tlacaxipehualiztli as the feast of the vernal equinox and the first religious festival of the year. The festival Toxcatl is designated as the fourth and greatest of all festivals of the native Calendar and it presumably corre- sponded to Corpus Christi and began in May. Its 20th day was the climax of the festival and coincided with the summer solstice. An idol or image of Huitzilopochtli was solemnly bonie in procession aroimd the courtyard of the great temple on the 20*'' day and. "with uplifted arms the pai'ticipauts iuij)lored the Sun for water, for it always happened that there was a scarcity of water at this time of the year On tliis day, every fourth year, prisoners were sacrifit-ed at mid-day. o — 18 — The above aud further fragmentary evidence that I cannot attempt to include in this brief shetch, definitely establishes the connection between the festival Toxcatl and the sunmier solstice, and it is extremely interesting to note- that it was considered the greatest festival of the entire year. This is not sni-pi-isiug for, as Prof. Norman Lockyer lias remarked: (Nature July 2. 1891) "the solstices and their accompaniments are the most striking things in the natural world to people wlio live in tropical and subtropical countries a summer solstice is a very much more definite thing than it is with us." An extremely valuable and suggestive detail in preserved to us in the official report of Alvarado's trial for the un- authorized massacre of the native chieftains whilst they were assembled during the inaugural festivities of the festival Toxcatl. Alvarado states that on the morn of the festival li<' saw that a number of poles had been raised in the court- yard of the Great Temple and that one, taller than tlic rest surmounted the principal pyramid. I do not hesitate in assuming that these poles had been set up for the purpose of serving as gnomons and observing the approaching sunmier solstice which is the day when the shortest shadoW is thrown at noon. That such observations were actually made by tlic Mexican priest- astronomers has already been provcil by the Codex Fuenleal and also by the statement, by Path-e Rios: (Vatican Codex, Kingsborough YI. p. -ior^) "They alledge that the cause of winter beinp- so disagreeable is the absence of the Sun and that summer is so delightful on account of its presence and that the return of the Sun to our zenith is nothing else but the approach of their god to coiifer favors upon them." He further states that th(> Sim reigned over the sign 1 Tecpatl. Since Huitzilopochtli was supposed to liave been born on this day the connection — 19 — is suggestive aud tends to identify Huitzilopoclitii as a Sun- god. At the end of the month Pachth in September, the "advent of HuitzilopochtU" was celebrated with great solemnity and human sacrifices. At this time a certain constellation was also observed. The "advent of the god" during the festival Pachtontli undoubtedly coincided with the autumnal equinox, and I except to be yet able to identify the constellation observed at that time. In the month Atemoztli, in December, another „ advent of Huitzilopoclitii" was commemorated. Duran, who wrote in 1579 states that this feast fell on the day of St. Stephen, or the day after Christmas. This native feast was unques- tionably in connection with the winter solstice, as I will more fully prove elsewhere. Any lingering doubts as to whether the Mexicans feasted the Sun difring its apparent annual course are dispelled on studying attentively the significance of the curious cere- mony always performed on the day Naliui Ollin, a name meaning, as authorities agree in stating, the four move- ments of the Sun. This feast was always celebrated with equal splendor, even when it occurred twice in a year, as sometimes happened. Duran alludes to a year in which it fell on the 17^^ of March and the 2""! of December as it doubtlessly may have done about the time he wrote. Only wai'riors and chieftains took part in the festivities that were held in the court-yard of the temple of the Sun, where its painted image was preserved. Incense was usually bui-nt bofoi-o this four times during a night and day. On the day of the festival, towards noon, tlic priests assembled the people by blowing on conch shells. A richly attired prisoner or slave, the chosen messenger to the Sun was sent to the sunnuit of the temple to deliver an invo- cation, acting as the mouthpiece of the people. 2- — 20 — "He ascended the high liight of steps slowly, making "long delays. He remained standing for a while on "each step then mounted another and halted again, accoi"- "ding to the instructions given him. This ceremony "denoted the slow ascent of the Sun in liis course "and this was the reason why the messenger lin- "gered on each step. When lie ad attained the "summit he went and mounted on a great circular stone "in the centre of which were the arms of the Sun. Standing "on tliis and addressing himself partlyto the painted image "that hung in the open temple and partly to the Sun itself, "he delivered his message. After this he was sacrificed "and his heart was offered to the Sun in tlie presence "of the entire population who were obliged to fast until "then. The ceremony was so timed that the victim mounted "on the sacrificial stone at noon precisely." Referring again to the accompanying table I draw attention to the correspondence and probable connection between the four quarters of the Mexican solar year, headed by daj^- signs united to tlie numeral of the year, and the solstices and equinoxes. Of course the correspondence would be approximate only and subject to alteration, but is would never amount to more than 13 days in 52 years. It is tlierefore admissible to connect these 4 signs and the ]2 days preceding them witli the solstitial and equinoctial periods. Deferring a closer examination of these signs as they occur in the different years, I must now view the solar year of the Mexican Calendar from a secular stand -point. Hitherto I have concentrated attention on the festivals of a more or less religious character. I have verified that Sun-worship prevailed and I'uled the religious Calendar and til at the true beginning of the solar year was the vernal equinox. Every four years this receded one day from the first day of the civil or Calendar year, followed by a shifting of other Sun festivals as well. But the ritual year preserved its central position throughout, so that the feasts in honor of — 21 — tlie 20 day -signs remainetl unaltered. Moreover the 18 periods of 20 days each, began with days of enforced rest. Occasionally, as we are told, one of the moveable feasts fell on one of these days of rest and then it was solemnised with double splendor. Besides, the above the solar year possessed one per- manent feature of utmost importance that was not affected by the shifting of religious festivals. Whilst they moved, according to a mysterious law whose secret was known to the priest-astronomers only, this feature remained intact and made the Calendar system act like a giant heart whose regular beat caused a vivifying force to circulate through the entire Mexican commonwealth. I allude to the remarkable and admirable institution of the macuiltianquiztli, or market that took place every five days. The entire weal of the communal government depended upon the apportionment of labor, the active exchange of products and the payment of tributes. Just but cruel and severe laws regulated the production, collection and distri- bution of all the necessities of life. In the centre of each town there was a large market-place to which broad, well kept roads led from the four quarters, and it was imperative that all adult members of the community should assemble there on the market-day. I find strong indications that these invariably fell on the days bearing year names. It is well known that these symbolised the four quarters and the elements as follows: Acatl (Ilccd) — east, water Tecpatl (flint) = north, fire Calli (house) = west, air Tochtli (rabbit) south, earth. It is impossible not to realise how admirably the periodical collection of tribute and the assortment or choice of products for the market, according to season and necessity, could be regulated by means of the rotation of the above oo symbolic names applied to market days. Thus on each ot these day- signs respectivel}-, at convenient intervals, the tribute from the subjugated tribes to the east, north, west or south of the City of Mexico might fall due ajid thus the produce from each quarter would arrive regularly at set intervals. lu the tribute -rolls of Montezuma, contained in the Mendocino Codex, it is noted that (certain tributes were payable every 20, 40, or 80 days respectively, in each case a period being designated on which the same day- sign would inevitably recur. On the other hand, supposing that a division of all labour performed in the community be divided into four cate- gories, according to the elements with which each industry or pursuit was connected, it would naturally follow that on Acatl market-days aquatic or vegetable products, on Tecpatl days mineral products etc., on Calli days, (the element air Ijeing symbolised by a house) all manufactured articles? on Tochtli days all j)roducts of animal life, should predominate in the market place. Of course any such distribution would necessarily vary according to climate, season or necessity and the result would often be a different division of labor in each com- munity. In my forthcoming publication I will jiroduce evidences showing how these circumstances explain and account for the peculiar fact recorded by various writers, that in each locality the year began on a different day- sign and the markets were held on different da3^s. There are strong indications proving that the different branches of industry or pursuits were identified with certain day-signs and that in this way the entire population of Mexico was sub-diA'iilcd into 20 castes or kinships, grouped under four heads. The fact that four day- signs were always ruled over by one of the element symbols established a further conne(!tion between these. From a practical point of view nothing — 23 — <'Ould be more simple and admirably adapted f'oi- a com- munal government than sucli a distribution of labour or occupation into categories connected with day- names. By this means a thorough control of all the jiuman activity and the products of the land was in the hands of the rulei'S and could be easily regulated as required. I must defer entering deeply into this subject, a further presentation of whicli would require much time and space. Suffice it to maintain here the paramount importance of the market as an institution of the communal government and the fact that the regular rotation of market-days ami the day of enforced rest every 20 days, were the prominent and permanent features of the civil solar year. The market day, a(;cording to Padi'e Duran, (op. cit. II pp. 21.5 and 21G) used to be connected with many obscure superstitious observances and the custom of resorting to tlic market-places was so deeply rooted and liad been so rigo- rously enforced in ancient times that the Spaniards found it extremely difficult to extirpate it. In Ancient Mexi(;o no one was allowed, under severe penalties, to barter or exchange tlio pi'odiico of their labour elsewhere than in the market- place where all such transactions were superintended by appointed inspectors. Duran relates a curious instance of the survival of the ancient custom. Taking pity on a naked half frozen Indian who was carrying a heavy load of wood to the market on a frosty November morning, he bestowed the price of the load upon him and bade him return to his home and warm Jiimself by burning Jiis load. But the Indian showed his preference to relint[uish the friar's gift sooner than the performance of what he considered his sacred duty. There can be no doiiht tliat the regular oi-dci- of market- days, regulating as they did the distribution of all of the necessities of life, could not be int('i-i-u])t(Ml without serious, widely felt consequences. It must tlici-rt'orc have ])een impe- rative that the religious festivals should not interfei-c with — 24 — the fixed order of market days, aud doubtlessly this eircuiu- stance exerted an influeuce over the positions of the religious festivals. What is more: since the first day of the solar year and of each of its "montlis" or periods of 20 days was a day of enforced rest it would also he necessary to avoid beginning tlie year with a day that liad become identified, through rustoui. \^^t]l the market. If this had been the case with the days Acatl, Tecpatl, Calli and Tochtli. for instance and that the years were made to begin witli these element symbols after they had become identified witli market days, it is evident that a change would have to be made, and that it would be advisable to preserve the sequence of market days intact. in this connection it is suggestive to learn that the alleged reason why Montezuma the Elder transferred the commencement of the cvcle from I Tochtli to II Acatl iji 1507, was that there had always been a dearth of food in the year I Tochtli. I draw attention to the fact that in a year 1 To(-;htli beginning with a day 1 Tochtli all the enforced days of rest would fall on this sio'n that is connected with the products of animal life. Undoubtedly an irregular supply of animal food would make itself felt more readily than in the case of vegetable products that can be more easily preserved. Since the alteration was made in order to avert a scarcity of food I am inclined to suspect that the order of days adopted was preferable for the practical reason that it did not cause interference with the periodi(;al market'^ At all events the year II Acatl began, with the day 2 Cipactli. On the other hand, as I will demonstrate further on, there wcm-c astronomical reasons of utmost importance that designati'd this day as the first of the new Epoch that began in 1507. I have defined the permanent features of the civil year; its market-days and days of rest, and also shown how the great festivals of the religious Calendar shifted — 25 — their positions at the rate of a day every four years and were rectified once in 52 years. Let us now verify certain historical dates on the accom- panying table and ascertain what light they throw upon the positions of the religious festivals in the years 1519 to 1521. Returning to the date of Quauhtemoc's surrender. August 13, 1521, we verify this day as 1 Coatl, year III Calli. Since native historians state that this day fell in Tlaxochimaco ^ we see that this would be the eighth an* I Tlacaxipehualiztli the first. The latter position agrees perfectly with the testimony of Duran and others and with the establislied connection between this festival and the vernal equinox. Provisionally adopting therefore the following order the festivals, we will proceed to examine further dates: I. Tlacaxipehualiztli. II. Tozoztontli. III. Hueytozoztli. IV. Toxcatl. V. Etzacualiztli. VI. Tecuilhuitontli. VII. Hueitecuilliuitl. YUI. Tlaxochimaco. IX. Xocohuetzi. X. (.)chpauiztli. XI. Teotleco. XII. Tepeilhuitl. Xm. Quecholli. XIV. Patiquetzaliztli. XV. Atemoztli. XVI. Tititl. XVII. Itzoalli. XVIll. Atlacahualco. s ''la a chronicle, supposed to have been written by one of the Me.vicaii warriors -who had taken part in the siege, the author refers to the month as Xexochimaco", an alteration of the name Tlaxochimaco, conveying the meaning unlucky. (See Gania, Dos Piedras, notes pp. 79 and 80 also p. 83.) < 'himalpahin designates Tlaxochimaco also. Dr. Seler quotes these authorities but his conclusion is that tlie day 1 coatl was tiie thiixl day of the month Xocohuetzi. — 26 — Tlio only date kno\^ai at present, in wliicli the position of the day in its mouth is recorded with its name, is tliat of the entry of the Spaniards into the City of Mexico. Bernal Diaz dates this event November 8, 1519, Cliimalpahin gives the native date: 8 Ehecatl, the eve of tlie lOth day of the montli Quecholli, year I Acatl. It can be easily verified on my table that there is a discrepancy of one day between these statements. For the day 8 Ehecatl corresponds to November 9*'\ I endorse Dr. Seler's view that this mnst have arisen from a confusion between the eve and the day of the occurrence, or from an omission to take the leap-year 1520 into consideration whilst fixing the native date. At the same time there undoubtedly existeii the tradition that the eventful day bore the sign Ehecatl, because this is also recorded in Sahagun's Historia, but through an evident mistake, it is accompanied by the numeral 1 instead of 8. Now the day 8 Ehecatl could only have been the eve of tlic l()th day of Quecholli if this month began on the day 13 ocelotl. I am inclined to accept this indication as a most valuable proof of the position of the festival Quecholli in the year 1 x4.catl. I note that the day 13 Ocelotl occurs precisely 40 days before the day 1 Ocelotl, the sign of the autumnal equinox. I also notice that 8 Ehecatl is the 10 "i day after 12 acatl tlie sign that heads the periods of the c;entral ritual year beginning with 1 Acatl. If thei-ofore 8 Ehecatl had been designated as the 10 th instead of the eve of the IQth day, we would have an established comiection between tli(^ periods of the ritual year and the religious festival. The subject is difficult and intricate and demands most careful investigation. A step in this direction is the further examination of other liistorical dates. The cruel massacic ul' tlic "flower of Mexican nobility" by Alv;ii-;i(lo and his followers, during the inaugural festivities of the month Toxcatl took place, according to Ixtlilxochitl 27 on May 19, 1520; to Bustamante ou Whitsunday May 25 or 27, to Ramirez on May 16. A follower of Alvarado testifies that it was on a Thursday. From Sahagun's Historia we learn, however, that 40 days elapsed between the massacre and the Noche Triste, or June 30, 1520, corresponding to 8 Cozcaquauhtli, year II Tecpatl. Calculating that a period of 40 days lay between these two (critical days we might fix the date of the massacre as May 21, or the day 7 Cozcaquauhtli. But to fix a historical date by intervening periods of days is scarcely a precise or satisfactory metliod and I prefer to seize the occasion and put my conclusion: that the feast Toxatl coin- cided with the summer solstice, to a crucial test. If this was the case, the massacre of the dancers on the first day of the feast must have taken place precisely 20 days before the sign of the summer solstice. Referring to my table it will be seen that tlie latter was 2 Ollin, (corresponding to June 11 Jul. Cal. The true date of the solstice was June 12. Therefore the inaugural dance must have been celclu-ated on the day 9 Tecpatl corresponding to May 23 and this establishes, beyond doubt, a connection between the periods of the central ritual year and the religious festival. For the ritual year II tecpatl consisted of 13 periods of 20 days each and the day 9 tecpatl heads the second of these. This connection is further proven by a (careful verification of the fact recorded in Sahagun's Historia, "that the Spaniards fled during the night of the festival Tecuilhuitontli." Now if Toxcatl and Etzalcualiztli contained 20 days each it is evident that the festival-period Te(;uilhuitontli would only have commenced 2 days after the recorded (bite, (ui the day 10 Tecpatl or July 2. But a reference to Sahagun's description of the religious festivals (ed. Bust, vol I. p. 59) teaches that celebration of Tecuilhuitontli began on the eve of its first day and lasted throughout the night. It is therefore clear tliat the Spaniards, fled from the — -28 — city (luring the uiglit of June 30. or the eve of tlie inaugural celebration of TecuilhuitoutH. This explanation reconciles the dates recorded on both sides, and fiii-nishcs us with two well authenticated instances of a religious festival beginning on the first day of a di\asiou of the ritual year. These instances are in perfect agreement witli a mass of evidence tliat I cannot attempt to analyse at present, but duly take into account while formulating the following conclusions : The religious festival-peidods of tlie Mexican year must not be confounded, as heretofore, with the 18 so-called "months" of the civil solar year. Each of the latter were headed by a day of enforced rest and (contained set market-days, at intervals of .5 days. The religious festival-periods were partly mo- veable and partly ruled by the central ritual year contained in each solar year. In three wel 1-authen- ticated instances the beginning of a festival-period is shown to have coincided with the first day of one of the 13 periods of 20 days contained in the ritual year. Tlie subject demands further study and nmcli has to be ascertained before an attempt can bo made to define the exact order and relative lengths of the Mexican festival- periods and to determine whether and in what maniiei- the "month names" preserved applied to the civil or religious periods, or to both combined. Let us merely glance at a few more historical dates of special interest. Spanish historians relate " that their brigan- tines were launched and Cortes mustered his forces on April 28, l.'r21. This date corresponds to 11 Tecpatl, year III Calli and falls 108 days before 1 Coatl. the day of (^Miauhtemoc-'s sun'r-nder. « See 11. 11. IJancroft'.s History of Mexico vol. J. i>ii. 017 and (i8!>. — 29 — Tliey further date the actual begirming of the siege from May 30, a day corresponding to 3 Atl ami falHng 76 days before 1 CoatL Cortes (Cartas and (xrant to Cortes) states tliat tlie siege lasted 75 days, Duran and Txthlxochitl extend it to 80, Chimalpahin to 90 and Bernal Diaz to 93 days. I consider that the evidence of Cortes is decisive in this matter moreover it agrees exactly with tlie number of days l)etween May 30 and August 13. At the beginning of this communication i stated my conviction that the method by which the years began wath the days Acatl, Tecpatl, Calli and Tochtli was as much the natural result of the system as the method by which tlie years began with Cipactli, Miquiztli, Ozomatli and Cozca- quauhtli. I will now proceed to demonstrate my assertion with the assistance of the accompanying table, regretting that I cannot refer to the set of analytical tables of my publication. Designating the day 1 Acatl, in the table of the year I Acatl (third column) as a point of departure I request the reader to imagine that a count of vague solar years is started on this day, even with vernal equinox. Following the development of the system we ascertain that after Tvi vague solar years, of 365 days each, the day 1 Ac;atl once more resumes its position as the first of the year. But, as the years have been counted as of 365 days only, and bis- sextile intercalation has not been employed, the day 1 Acatl, at the end of the cycle, is precisely 13 days behind tlie equinox. At is it known that, in order to right tlu' Calendar the the missing 13 days were added to the Cycle, it can be easily verified that this circumstance would make the next Cycle begin on tlie day 1 Miquiztli, thirteen days latei- than 1 Acatl. A repetition of this rectification causes a third Cycle to begin with 1 Quiahuitl and so on, until 20 Cycles, each beginning with one of the 20 day-signs in suc-c(>ssion. — •5<' — have completed tJiemselves. I carmot pause licie to refer to the pi-ogression of the Calendar, amouuting to nearly 9 days at tlie end of this Great Cycle of 1040 years, for it is the order of the cycles that concerns us at present. At a first piance it would seem as thouo-h 20 different orders of days were produced by the above rotation of day-sions. Biit a careful study shows that this is not the case and that only 5 oi'ders of day-signs prevailed. For when 4 cycles had succeeded the cycle Acatl beginning with the day 1 Acatl, a cycle Tecpatl occurred, beginning with the day 1 Tecpatl, and throughout this cycle the same oi'der of days as in the Acatl cycle would necessarily prevail. After 5 cycles the cycle Calli beginning with i Calli and then the cycle Tochtli beginning with 1 Tochtli would follow and thus, in 1040 years, four cycles would exhibit precisely the same order of days, each year beginning with a day bearing the name of the year, a method 1 will designate as Order I. The following tables exhibits this and the other four Orders, two of which are also known to have been employed: Order II, in which the years begin with the days Cipactli, Miqidztli, Ozomatli and Cozcaquauhtli is that whose existence is recorded by the majority of histoi'ians. My reconstruction, moreover, is a demonstration that it was in a(;tual use at the time of the Conquest. Order ITl is known to have been employed by the Mayas and is that recorded with one variation in tlie ceiiti-e of the famous Calendai- Stone of the City of Mexi(;o. It is an open question whether the Calendar- makers began the cycles with the four year-synd^ols in rotation, as fodows: 31 1 ACATL Great Symetrical Cycle consisting of 4X 5X52 = 1,040 solar years — 379,860 days. Acatl Age Tecpatl Age Oalli Age Tochtli Age Order: 1 First day n First day 111 First day IV Acatl — Acatl 1 acatl Tecpatl— Tecpatl 1 tecpatl Calli— Calli 1 calli Tochtli— Tochtli 1 tochtli Tecpatl — Miquiztli 1 mi([uiztli Calli — Quiahuitl Tochtli — Cuetzpaliii 1 quiahuitl 1 cuetzpaliii Tochtli— MahnaUi icatl— OUin Calli — Ozomatli Tochtli — Cozcaquauhtli Acatl — Cipactli 1 ozomatli 1 cozca(|uauhtli 1 cipactli First day 1 nialinaUi First dav Acatl — Coatl 1 coatl 1 oUin Tecpatl — Itzcuintl 1 itzcuintli Acatl- Atl 1 atl Tecpatl — Ehecatl 1 ehecatl Calli — Quauhtli 1 quauhtli Tecpatl— Ocelotl 1 ocelotl Calli— MazatI 1 mazatl Tochtli— XochitI 1 xochitl or grotiped live cycles under the head of one year -symbol after which the following year - symbol would naturally succeed, as follows: Acatl cycles Older I Acatl — Acatl Calli cycles Tochtli cycles Calli— Calli TochtU- -Tochtli Calli — Cozcaquauhtli Tochtli— Cipactli Calli— Atl Calli— Ehecatl Calli— Quauhtli Tochtli— Ocelotl Tochth -Mazatl Tochtli Xochitl Tecpatl cycles Tecpatl — Tecpatl II Acatl— Miquiztli Tecpatl — Ozomatli J II Acatl — Quiahuitl Tecpatl — Cuetzpalin I V Acatl— Malmalli Tecpatl— Olliu V Acatl — Coatl Tecpatl — Itzcuintli In either case Order 1 remains the same while in Orders II — V a mere difference in the combination of identical sia'ns residts. The above tables constitute the first demonstration of the method by which one cycle could have been distin- guished from another in this remarkable Calendar System. It clearly shows how easily and effectually this could have been done by adopting a combination of the signs of the first day and the symbol of the first year as the name of the cycle. Tlius one might be known as the Acatl-Acatl another as the Acatl-Coatl cycle and so on. A feature that fiiuulv establishes the law of — 32 — concordant numeration is tlie peculiarity that if the first cycle be started on a day number 1, for instance, the 20 cycles infallibly follow suit. It is therefore evident that one epoch or Great Symetrical Cycle of 1,040 years could have been distino-uished from anothci- bv its rulinir numeral merely. Now is it a historical fact that a Cycle began in 1507 with the year II Acatl. The given results of iny investi- gation establish that it began on a day 2 Cipactli, con- sequently with Order II. For a cycle to be ruled over by the number 2 it is obvious that it followed an epoch in which cycles were ruled by number 1, therefore it may be safely inferred that the cycle II Acatl that c;onunenced in 1507, formed part of a cycle that had been preceded, at its ontset, by a period of 1,040 years. This unavoidable inference constitutes the first firm step backwards into the mysterious past of American civilisations, and it carries us furtlier than may be realised at first sight. For it establishes the adoption of a highly perfected and artificial Calendar system at a remote date and this must have been preceded by a pro- longed period during which the intricate and adniii-ablc system had slowly developed froui its primitive form. It would be premature to venture now to express an opinion as to the position, in Epoch II. of the cycle II Acatl -Cipactli. during which the Conquest of Mexico and the destruction of its ancient civilisation took place. But I see the possibility of being able to dotcrmiuo this ulti- )nately. I will now cite some important verifications of astro- iiomical dates tliat I have recently obtained froui the dis- tinguished astronomer Dr. A. Berberich of Berlin. Nothing could form a more convincing endorsement of my assertion that the year III Calli must have begun on the day 3 Ozomatli, corresponding to March II. jr)21 and coinciding with the vernal ('(piinox, than the following verifications kindly made at my request: — 6o — ,,Venial equinoxes occurred in 1507 M-AvrU 11 7^' rrZ^ 151!) Maicli 1 1 51' '57.2'" |». lu. 1520 Maivh 10 1 i 20 )). m. 1521 :\Iar(li 1 1 5 15 a. iii. 1522 :\raiv|i II 11 4 a. iii. The above dates ai'e ojven in (xreenwicli time. For Mexico tlie precise time of tin- ('(juiiiox was (\^ ."Mi arlier."" On page 12 of this coiiniiunicatioii 1 stated tliat the fact that the' Mexican yeai- III ('alii Ix'^aii even v.itli the xci'nal equinox enabled us to (h'tenniue that the yeai' IJ Acatl. the first of the Cycle, must have connnenced tliree days after tlie equinox, or on a day (-(u-responchno; to March 14. For the day 2 Cipacth coincided with tliis date. This fact puzzled \nr somewhat at hi'st. for 1 was inchned to expect that the Cycle would have naturally staited exactly even with an e(|uiuox. Tlie asseitions of several old wi'itej-s. to the effect that the Caleiidai- system was based on observations not only of the Sun hut also of the Moon and Planet Venus, afforded me a hint as to the causes that might have determineil the Calendar-makei-s to begin a new Cycle three days aftei- the veilial equinox. Referring to Dr. Berberich he infoi'med me tliat acccn-- (ling to calculations madi' with w ( )i)j)olzer"s Tables a new Moon f'll on :\raivh i;}. 1507. at 11. 40 a. m.l It is well known that the solemn I'ite of kindling New Fii-e with which the high-priest aniioun<-ed the beginning of the new Cycle was performed at midnight on a certain hill near the City of Mexico. Sahaguii relates that at sunset till' priests began their prej)aratious for t he I'eligioiis observances aud that at nightfall they began \i> march m slow and solenni ])rocession towards Huixachtlan. It is now evident that the delicate crescent of the new Moou, becoming first visible for a little while after sunset on March 14. 15o7 was the signal fir tlu' Mexican priest- — .u — asti-uiioiucrs to perfoiMii . t'oi- what \v,is destiiKMl to ln^ the last tiiuf. the imprt'ssixi' (•.(M'ciuony of iisluM-iiii;' in the new era. Throiiii;li Di". Bcrhci-idi I lia\-e asccrtaiiicil that (»ii this same (r'veiiin^ rhr Phim't \Ciuis was clearly \-isil)l«^ as cx'oiiini;- star anil set ";)| iiiinutcs attcr thr Siiii. Fi-oni ^lardi 14 to Man'h IS it is possible that the Phuict \'fiuis was v'isiblo both as luorniuo- and evciiinj^' stai- from the City ot' .Mi-xico where the twilight is very shoil, but it is also possibh' that it was U:»st in tin- sph'iuh>i- ef the Sim's rays, it is certain however, that X'eniis must have been visible as e\(!ning star after .Alaich -l-I." it is thus ch'arly proved that on the (h^y 2 Cipac^tli, or March 14, loOT. the Xew Moon and the Planet Venus were visible together m the west immediately after sunset. Was it in order to wait for this striiang phenomenon that Montezuma transferrfMJ the beginning of the cycle to 2 Acatl-Cipac-tli instead of Ix-iiinniim the vear with the rea'ular registration of the vernal iMpiinox? On the othei- hand if the statement in the Codex Kueii- jeal l)e carefully studied, it sh(»ws us that it was not custo- marv to date the beeiixninu- of the year from the exact time when the Sun cast a straight shadow. For it was only "after this, when tlu; Sun was observed to rise, that the}' counted the tirst day""." Now the exact date of the vernal eipiinox in I .")07, furnishe(| me l)y Dr. Berbei-ich, is: March 11. 7. 52 p. ni. (consequently it was probably ol)served in the great temj)le of Mexico at noon on ^fari-li 12. After this the shadow would shorten daily at the rate of three inches a day and on March 14. at noon, it would be 6 inches shorter than on March 12. It nuiy he. that custom recpiin-il that this difl'erence shoidd be noted before "the tirst dav beo'an". It is not ' "luego cuando se sintia que el sol subia. contavau el primer dia" op. et loo. cit. — 85 — impossible, in fact, tliat the falliiio- of tlie shadow at noon, across a certain altar or sacred synil)ol in tlic^ (In-at Teiiiph;, may have been the given signal for the commencement of the new cycle Therefore it may well l)c that the Mexican rehgioiis solar year actually began about thi-cc days after the true vernal equinox, on March 14. Avhen the Moon and the Phmet Y(nius also occupied exceptional positions. On the other hand it is just as possible that thy Calen(Uir-mak(n's may liave delayed the commenceuKMit of the New Cycle until the (hiy 2 Cipacth on account of its sign and number aiul of the given position of tlie Moon and Venns. Tlie adoption of this day may even liave been an attempt at a rectification of the Calendar, for it is qnite obvious that by beginning the cycle 8 days after the eqninox there would only be a reti-ogressiou of 10 instead of 18 days at the (>nd of the cycle of ."r2 years. Besides, as I)i-. Berberich has (carefully demonsti-ated. the effect of commencing the year 8 days aftei- the equinox would tend to make the 4 di^'isions of the Mexic-an year coincide moi-e closely with the solstices and autumnal e(|uinox. 1 regret that I cannot entei- more fully into this inter- esting subject at pi'csent. without exceeiHng tlie limits of this brief connniinication. The foregoing data will suffice to prove beyond a doid)t that historical evidence, the law of concordant numeration that a prolonged study of the Calendar-system enabled me to recognise and astronomical facts cojicur in establishing that the Mexican solai- yeai" began with the \-ei-nal equinox. Tliey also prove that the native Calendar system attempted to Ijidng into at-cord thf ap- parent movements of the Sun, Moon and Planet Venus, which fact agrees with my obsei-\ ation and also with my convicticni that tli(> astrononiei- priests enq)loyed a lunar calendar, consisting of periods of 2()o (hiys each, for the rep'istration of asti'onomical and historical dates. The' role of the Planet Venus and the adaj)tation of the — 3(i — Calendar to ;i systematic rt^f^istration of its synodie periods and those of otlier planets have been desc;ribed by Senor Tronc.oso y Paso and will be found demonstrated, by means of tabh's and fnrtlicr I'labonitions. in my forthcoming pid)li- ciition. This will also show the intricacy of other Hncs of in- vest io;at ion that T am steadily pnrsnino- and how much tinjc and labor these involve. 1 trust that the recognition of these facts will explain and excuse the delay that has occnrred and is likely to occur ill the appearance of the pnblications I had announced as speedily fortln^oming. little knowing what proportions iriy task was about to assume. I cannot close without stating that, iu this brief presen- tation of small portion only of my work. I have not been able to even allude to many important facts that should be ^keu into consideration in weighing some of my conclusions. In \-iew of this I request my felloAv- scientists to look upoii this as a pi-eliminary note merely, that will be followed, in time, by a complete presentation of the results 1 have ob- tained throngh my prolong(Ml stu20. ^EAR I ACATL MONTHS: j_i - .— 1> > >■ VII VIII ■:: ^. X ^ XIII XIV > > X ■y. C'lPACTrj 1 S 2 9 3 10 1 11 f) 12 () 13 7 1 8 2 9 EllECATL 2 !) 3 10 4 11 ;■) 12 G 13 7 1 2 i) 3 10 4 YB Calli 3 10 4 11 5 12 (i 13 7 18 2 9 3 10 4 n 5 CUETZPALIN 4 11 5 12 (J 13 7 1 8 2 9 3 10 4 11 5 12 G COATL 5 12 (i 13 7 1 8 2 9 3 10 4 11 5 12 G 13 7 »— - " :: > ;: MlQUIZTI.I (i 13 7 1 8 o f» 3 10 4 1! .-) 12 G 13 7 1 8 2 9 > 10 4 1 Mazatl 7 1 8 2 9 3 10 4 11 5 12 G 13 7 1 8 2 9 •> 10 4 115 1 TOCHTLI 8 2 9 3 10 4 11 5 12 6 13 7 1 8 2 9 3 10 4 11 5 12 G 1 Atl 9 3 10 4 11 5 12 13 7 1 8 2 9 3 10 4 11 5 12 G 13 7 1 iTZCUINTLI 10 4 11 5 12 V) 13 7 18 2 9 3 10 4 11 5 12 G i;i 7 1 8 i OZOMATLI 11 f) 12 i; 13 i 1 8 2' 9 3 10 1 11 r. 12 G 13 ' i 1 8 9 _r Malinalli 12 () 13 7 1 8 2 9 3 10 4 11 5 12 G 13 1 1 8 2 9 3 10 A ACATL 13 V 1 8 2 9 3 10 4 11 5 12 6 13 7 1 8 2 9 3 10 4 11 f; OCELOTL 1 8 2 9 3 10 4 11 5 12 G 13 7 1 8 2 9 3 10 4 11 f) 12 (• QUAUHTIJ 2 9 3 10 4 11 b 12 G 13 7 1 8 2 9 3 10 4 11 Ti 12 G 13 : COZCAQUAflUJ 10 4 11 ,') 12 (1 13 7 18 2 9 3 10 4 11 5 12 G 13 m 1 E Ollin 4 11 5 12 6 13 7 1 8 2 9 3 10 4 11 5 12 G 1:; 1 1 S '4 '. Tecpatl f) 12 6 13 7 1 8 2 9 3 10 4 11 5 12 G 13 7 1 8 9 :! 1 QUIAHUITL 6 13 7 1 8 o 9 3 10 4 11 5 12 G 13 7 1 8 it 3 10 4 1 XOCIIITL 1 1 8 2 9 3 10 -1 11 5 12 G 13 7 I'll 1 8 Ai TI.I 2 9 10 3 ■1 10 11 4 11 -) 1 12 G 1 EllKCATl. 11 .") 12 G 13 7 1 Cai.i.i 12 G 1.'. 1 1 8 2 CUETZl'AI.lN 13 i 1 S 2 9 3 COATL 1 8 • ) 9 3 10 A N T E. THE DAY 8 EHECATL, YEAR I ACATL, COKRESPoNnS TO NOV. 9. 1510. 7 COZCAQUAUIITM, YEAR II TECI'ATI,, TO MAY 21. 1520. 8 COZCAQUAUHTLI, YEAR II TECPATL, TO JUNE 30. 1520. 11 TECPATL, YEAR III CALLI, TO APRIL 28. 1521. 8 CIPACTLI, YEAR II! (AM. I, T'l MAY 22. l.V.'l. 3 ATL, YEAR III CALLI, TO MAY 30. 1521. 1 COATL, YEAR 111 CALLI, TO AUfiU.ST 13. iri2I. JCTION TH A DAY CORRESPONDING TO MARCH 12. ^LLI AVITH ]\rARCH 11. JUL. CAL. :'-YEAR. A. D. 1521. A.D. 1522. II TECPATL. : 2 ^ ^ ^ S ^ > > ? ? ^ k< ;^ ^ ;>< X 2 i\ 13 7 I 8 2 9 3 10 4 3 7 1 S 18 2 9 3 9 3 10 4 11 .0 10 4 IJ 5 12 G YEAR III CALLI. ? 9 3 10 3 10 4 11 4 5 11 5 12 6 13 7 12 G 13 7 1 8 ,»_ XIII XIV > > >^ > 'y, •^, X, i^. t 11 5 12 G 13 7 18 2 9 3 10 4 11 .^ 12 G 13 7 1 8 2 9 3 10 4 11 .0 ) 12 6 13 7 I 8 2 9 3 10 4 11 5 12 6 13 7 1 8 2 9 3 10 4 11 5 12 6 ) 13 7 1 8 2 9 3 10 4 11 12 G 13 7 1 8 2 9 3 10 4 11 5 12 6 13 7 '18 2 9 3 10 4 11 .5 12 G 13 7 1 H 2 9 3 10 4 11 .5 12 6 13 7 1 8 i 2 9 3 10 4 11 5 12 6 13 1 1 8 2 9 3 10 4 11 .0 12 6 13 7 18 2 9 ) 3 10 4 11 .5 12 G 13 7 1 8 2 9 3 10 4 11 5 12 G 13 7 1 8 2 9 3 10 4 11 .-. 12 G 13 7 18 2 9 3 10 4 11 5 12 G 13 7 1 8 2 9 3 10 4 11 1 .") 12 (i 13 7 1 S 2 9 3 10 4 [mJ .5 12 G 13 7 1 8 2 9 3 10 4 11 5 12 2 G 13 7 1 8 2 9 3 10 4 11 5 12 ti 13 7 1 8 2 9 3 10 4 11 5 12 6 13 3 7 18 V 9 3 10 4 11 5 12 6 13 7 1 8 2 9 3 10 4 11 5 12 6 13 7 1 s 2 9 3 10 4 11 .5 12 G 13 7 10 2 9 3 10 4 11 .5 12 G 13 7 18 2 ; 9 :! 10 4 11 .5 12 G 13 7 1 s 2 9 3 10 4 11 .0 12 G 13 7 1 8 2 9 3 ! 11) 4 11 .) 12 G 13 7 1 8 o 9 3 10 4 11 f) 12 G 13 7 1 8 2 9 3 10 4 11 ."j 12 () 13 7 1 8 2 9 3 10 4 11 .-) 12 G 13 7 1 8 2 9 3 10 4 11 .0 > 12 G 13 i 1 8 2 !) 3 10 4 11 5 12 G 13 7 CU 8 2 9 3 10 4 11 5 12 G MlQUIZTLI 11 5 12 G 13 7 ) 8 2 9 3 10 4 11 5 12 6 13 7 Mazati, 12 G 13 7 1 8 2 9 3 10 4 11 5 12 G 13 7 1 8 TociiTi.i 13 7 1 8 2 9 3 10 4 11 5 12 6 13 7 18 2 9 ATI. 1 8 2 9 ODlO 4 11 .5 12 G 13 7 1 8 2 9 3 10 IT/.CIINTU 2 9 3 10 4 11 5 12 G 13 7 1 8 2 9 3 10 4 11 OZOMATLI 12 Maunali.i 13 ACATL 1 OCELOTL 2 QUAniTI,! 3 *3/-^5^'/v