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 Manik Cib Chicchan Ix Chuen Ahau Muluc Ezanab Men Kan Been Ik Cauac Lamat Caban Cimi Akbal Eb Ymix Oc Connected with these numbers is a line of alternate black and red numbers running along over the figures of Plates 32 to 39, division _a_. There are several breaks and some partially obliterated characters in it which must be restored in order to use it. It has been selected partly on this account, that the method of filling such breaks and making such restorations may be seen.