It will be noticed in each of the tonalamatls given in the following examples that the record is greatly abbreviated or skeletonized. In the first place, we see no month signs, and consequently the days recorded are not shown to have had any fixed positions in the year. Furthermore, since the year positions of the days are not fixed, any day could recur at intervals of every 260 days, or, in other words, any tonalamatl with the divisions peculiar to it could be used in endless repetition throughout time, commencing anew every 260 days, regardless of the positions of these days in succeeding years. Nor is this omission the only abbreviation noticed in the presentation of the tonalamatl. Although every tonalamatl contained 260 days, only the days commencing its divisions and subdivisions appear in the record; and even these are represented in an abbreviated form. For example, instead of repeating the numerical coefficients with each of the day signs in (1), the coefficient was written once above the column of day signs, and in this position was regarded as belonging to each of the different day signs in turn. It follows from this fact that all the main divisions of the tonalamatl begin with days the coefficients of which are the same. Concerning the beginning days of the subdivisions, a still greater abbreviation is to be noted. The day signs are not shown at all, and only their numerical coefficients appear in the record. The economy of space resulting from the above abbreviations in writing the days will appear very clearly in the texts to follow. In reading tonalamatls the first point to be determined is the name of the day with which the tonalamatl began. This will be found thus: _Rule 1._ To find the beginning day of a tonalamatl, prefix the first red number, which will usually be found immediately above the column of the day signs, to the uppermost[242] day sign in the column. From this day as a starting point, the first black number in the text is to be counted forward; and _the coefficient_ of the day reached will be the second red number in the text. As stated above, the _day signs_ of the beginning days of the subdivisions are always omitted. From the second red number, which, as we have seen, is the {253} coefficient of the beginning day of the second _subdivision_ of the first division, the _second black number_ is to be counted forward in order to reach the third red number, which is the coefficient of the day beginning the _third subdivision_ of the first division. This operation is continued until the last black number has been counted forward from the red number just preceding it and the last red number has been reached.