It follows from the foregoing that the sum of all the black numbers multiplied by the number of day signs in the column—the number of main divisions in the tonalamatl—will equal exactly 260. If any tonalamatl fails to give 260 as the result of this test, it may be regarded as incorrect or irregular.
The foregoing material may be reduced to the following:
Rule 2. To find the coefficients of the beginning days of succeeding divisions and subdivisions of the tonalamatl, add the black numbers to the red numbers immediately preceding them in each case, and, after subtracting all the multiples of 13 possible, the resulting number will be the coefficient of the beginning day desired.
Rule 3. To find the day signs of the beginning days of the succeeding divisions and subdivisions of the tonalamatl, count forward in Table [I] the black number from the day sign of the beginning day of the preceding division or subdivision, and the day name reached in Table [I] will be the day sign desired. If it is at the beginning of one of the main divisions of the tonalamatl, the day sign reached will be found to be recorded in the column of day signs, but if at the beginning of a subdivision it will be unexpressed.
To these the test rule above given may be added:
Rule 4. The sum of all the black numbers multiplied by the number of day signs in the column of day signs will equal exactly 260 if the tonalamatl is perfectly regular and correct.
In plate [27] is figured page 12 of the Dresden Codex. It will be noted that this page is divided into three parts by red division lines; after the general practice these have been designated a, b, and c, a being applied to the upper part, b to the middle part, and c to the lower part. Thus "Dresden 12b" designates the middle part of page 12 of the Dresden Codex, and "Dresden 15c" the lower part of page 15 of the same manuscript. Some of the pages of the codices are divided into four parts, or again, into two, and some are not divided at all. The same description applies in all cases, the parts being lettered from top to bottom in the same manner throughout.
The first tonalamatl presented will be that shown in Dresden 12b (see the middle division in pl. [27]). The student will readily recognize the three essential parts mentioned on page [251]: (1) The column of day signs, (2) the red numbers, and (3) the black numbers. Since there are five day signs in the column at the left of the page, it is evident that this tonalamatl has five main divisions. The first point to establish is the day with which this tonalamatl commenced. According to rule 1 (p. [252]) this will be found by prefixing the first red number to the topmost day sign in the column. The first red number in Dresden 12b stands in the regular position (above the column of day signs), and is very clearly 1, that is, one red dot. A comparison of the topmost day sign in this column with the forms of the day signs in figure [17] will show that the day sign here recorded is Ix (see fig. [17], t), and the opening day of this tonalamatl will be, therefore, 1 Ix. The next step is to find the beginning days of the succeeding subdivisions of the first main division of the tonalamatl, which, as we have just seen, commenced with the day 1 Ix. According to rule 2 (p. [253]), the first black number—in this case 13, just to the right of and slightly below the day sign Ix—is to be added to the red number immediately preceding it—in this case 1—in order to give the coefficient of the day beginning the next subdivision, all 13s possible being first deducted from the resulting number. Furthermore, this coefficient will be the red number next following the black number.
Applying this rule to the present case, we have: