Interpreting in the same way the glyphs in figure 85, we have the record that Kin 4 of Uinal 4 of Tun 9 of Katun 15 (of Cycle 9, unexpressed) fell (or ended) on the date 9 Kan 12 Kayab. Changing this Period-ending date into its corresponding Initial Series and solving for its terminal date, the latter date will be found to be 13 Kan 12 Ceh, instead of 9 Kan 12 Kayab. At first this would appear to be even farther from the mark than our preceding attempt, but if the reader will admit a slight correction, the above number can be made to reach the date recorded. The date 13 Kan 12 Ceh is just 5 uinals earlier than 9 Kan 12 Kayab, and if we add one bar to the four dots of the uinal coefficient, this passage can be explained in the above manner, and yet agree in all particulars. This is true since 9.15.9.9.4 reaches the date 9 Kan 12 Kayab. On the above grounds the writer is inclined to believe that the last three Serpent numbers on plate 32, which were shown to have proceeded from a date 9 Kan 12 Kayab, were counted from the date 9.15.9.9.4 9 Kan 12 Kayab. {276} TEXTS RECORDING ASCENDING SERIES There remains one other class of numbers which should be described before closing this chapter on the codices. The writer refers to the series of related numbers which cover so many pages of the Dresden Codex. These commence at the bottom of the page and increase toward the top, every other number in the series being a multiple of the first, or beginning number. One example of this class will suffice to illustrate all the others. In the lower right-hand corner of plate 31 a series of this kind commences with the day 9 Ahau.[264] Of this series the number 8.2.0 just above the 9 Ahau is the first term, and the day 9 Ahau the first terminal date. As usual in Maya texts, the starting point is not expressed; by calculation, however, it can be shown to be 1 Ahau[265] in this particular case. Counting forward then 8.2.0 from 1 Ahau, the unexpressed starting point, the first terminal date, 9 Ahau, will be reached. See the lower right-hand corner in the following outline, in which the Maya numbers have all been reduced to units of the first order: 151,840[266] 113,880[266] 75,920[266] 37,960[266] 1 Ahau 1 Ahau 1 Ahau 1 Ahau 185,120 68,900 33,280 9,100 1 Ahau 1 Ahau 1 Ahau 1 Ahau 35,040 32,120 29,200 26,280 6 Ahau 11 Ahau 3 Ahau 8 Ahau 23,360 20,440 17,520 14,600 13 Ahau 5 Ahau 10 Ahau 2 Ahau 11,680[267] 8,760 5,840 2,920 7 Ahau 12 Ahau 4 Ahau 9 Ahau (Unexpressed starting point, 1 Ahau.)