This series terminates with I, as it should according to the theory. The sum of the black numerals--16, 9, 20, 5, 2--is 52, a multiple of thirteen, and the interval between the successive days, reading downwards, is 52, agreeing in these particulars with the theory. It will also be observed that the symbol represented by S answers to the number 20. In the lowest division of the same plate is another similar series, as follows: XII Ezanab } Akbal } 20 + 9, II; 11, XIII; 18, V; 7, XII. Lamat } Been Ezanab This terminates with XII, the number over the column; the sum of the black numbers is 65, a multiple of thirteen and precisely the interval between the successive days of the column, taking the week numbers into consideration, which is always to be understood in speaking of these intervals unless the contrary is expressly stated. [Illustration: FIG. 361.] In the middle division of Plate 8 is a short series connected with a day column containing the following days, reading downwards, as usual: Manik, Cauac, Chuen, Akbal, Men. The symbol for Akbal (Fig. 361), is a very unusual one, reminding us strongly of a skull, which may possibly have given origin to the symbol. The numerals of the series are as follows: 20 + 6, VIII; 20 + 6, VIII; the number over the column, VIII; and the interval between the days, 52. In Plate 15, division _c_, is the following series, which differs from those given in having two day columns instead of one: III III Lamat Ix Ahau Cimi } Eb Ezanab } 12, II; 14, III. Kan Oc Cib Ik The final number is the same as that over the columns; the sum of the black numbers is 26, which is a multiple of 13; but in this case in counting the intervals the days are to be taken alternately from the two columns. Commencing with 3 Lamat on our calendar and counting 26 days brings us to 3 Ix; 26 more to 3 Ahau; 26 more to 3 Cimi, and so on to the end. In the lower division of Plate 9 is a series arranged as follows: III III VI VIII Cauac Been 3 2 {XI II Chuen Chicchan { 3 4 {VI VII Akbal Caban { 4 1 Men Muluc I III Manik Ymix 7 2 The sum of the black numerals is 26 and the final red number is III, the same as that over the columns. The interval between the days, taken alternately from the two columns, as in the preceding example, is 26. The numbers are also to be taken alternately from the two number columns. It is apparent that these examples sustain the theory advanced. This will also be found true in regard to all the series of this type in this and the other codices where the copy is correct. Brasseur's copy of the Manuscript Troano is so full of mistakes that no satisfactory examination of this codex can be made until a photographic copy is obtained; nevertheless a few examples are given as proof of the above statement.