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bring us to 1 Ymix. In like manner we find the fourth day to be 1 Cib and the fifth 1 Ymix. The numbers in the figure columns are to be taken alternately, thus: 5, VI; 8, I; 5, VI; 8, I, &c. These examples are sufficient to show that the series of the Manuscript Troano are arranged upon the same plan and based upon the same system as those of the Dresden Codex. The following examples from the Codex Cortesianus prove the same thing to be true in reference to the series found in it. The first is taken from the lower division of Plates 10 and 11, Rosny's reproduction: XIII Ahau } 11, XI; 5, III; 5, VIII; 5, XIII; 9, IX; 3, XII; 6, V; Chicchan } 1, VI; X, XIII. Oc Men The S in the line of numerals represents the usual symbol for 20. The sum of the black numbers is 65, the interval between the days 65, and the last red numeral the same as that over the day column, thus agreeing in plan with those in the other codices. The following double column series is found in the middle division of Plate 30: XI XI Ahau Ymix } Eb Been } 20 + 6, XI; 20 + 6, XI. Kan Caban } Cib Chicchan Lamat Manik The number 20 is denoted by the usual symbol. The sum of the black numbers is 52 and the interval between the days in each column 52, but in this case there does not appear to be any connection between the columns, there being, in fact, two distinct series. In the upper division of the same plate is this series: XI Ezanab { VI XI { 8 5 Oc { VI XI { 8 5 Ik { VI XI { 8 5 Ix { VI XI { 8 5 Cimi The order in which these numerals are to be read is as follows: 8, VI; 5, XI; 8, VI; 5, XI, &c., which gives, as the final red number of the series, XI, the same as that over the column. The sum of the black numbers is 52 and the interval between the days 52. Taking for granted that the correctness of the theory advanced is conceded, some attempts at its further application, especially its use in making restorations and corrections in defective series and in settling doubtful questions relating thereto, will now be presented. In the upper division of Plate 32, Dresden Codex, are the four day columns and lines of numerals over them here represented: 1 4 13 9 4 15 13 2 11 XIII XIII XIII XIII
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