+-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | Do |18|18|18|18|18|18|18|18|18|18|18|18|18|18|18|18|18|18|--| +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | Do |19|19|19|19|19|19|19|19|19|19|19|19|19|19|19|19|19|19|--| +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ {142} Applying this rule to the number 31,741, we have seen above that its division by 365 gives 351 as the numerator of the fractional part of its quotient. Assuming that the count is forward from the starting point, it will be necessary, therefore, to count 351 forward in Table XV from the position 8 Cumhu, the position of the day of the starting point, 4 Ahau 8 Cumhu. A glance at the month of Cumhu in Table XV shows that after the position 8 Cumhu there are 11 positions in that month; adding to these the 5 in Uayeb, the last division of the year, there will be in all 16 more positions before the first of the next year. Subtracting these from 351, the total number to be counted forward, there remains the number 335 (351-16), which must be counted forward in Table XV from the beginning of the year. Since each of the months has 20 positions, it is clear that 16 months will be used before the month is reached in which will fall the 335th position from the beginning of the year. In other words, 320 positions of our 335 will exactly use up all the positions of the first 16 months, namely, Pop, Uo, Zip, Zotz, Tzec, Xul, Yaxkin, Mol, Chen, Yax, Zac, Ceh, Mac, Kankin, Muan, Pax, and will bring us to the beginning of the 17th month (Kayab) with still 15 more positions to count forward. If the student will refer to this month in Table XV he will see that 15 positions counted forward in this month will reach the position 14 Kayab, which is also the position reached by counting forward 31,741 positions from the starting position 8 Cumhu. Having determined values for all of the unknowns on page 138, we can now say that if the number 31,741 be counted forward from the date 4 Ahau 8 Cumhu, the date 12 Imix 14 Kayab will be reached. To this latter date, i. e., the date reached by any count, the name "terminal date" has been given. The rules indicating the processes by means of which this terminal date is reached apply also to examples where the count is _backward_, not forward, from the starting point. In such cases, as the rules say, the only difference is that the numerators of the fractional parts of the quotients resulting from the different divisions are to be counted backward from the starting points, instead of forward as in the example above given. Before proceeding to apply the rules by means of which our fourth step or process (see p. 138) may be carried out, a modification may sometimes be introduced which will considerably decrease the size of the number to be counted without affecting the values of the several parts of its resulting terminal date.