By their aid another method of numeration was in vogue for counting time. For "eighty-one years," they did not say _hutuyokal haab_, but _can kal haab catac hunpel haab_, literally, "four score years and one year." The copulative _catac_ is also used in adding a smaller number to a _bak_, or 400, as for 450, _hun bak catac lahuyoxkal_, "one _bak_ and ten toward the third score." _Catac_ is a compound of _ca tac_, _ca_ meaning "then" or "and," and _tac_, which Dr. Berendt considered to be an irregular future of _talel_, to come, "then will come fifty," but which may be the imperative of _tac_ (_tacah_, _tace_, third conjugation), which means to put something under another, as in the phrase _tac ex che yalan cum_, put you wood under the pot. It will be seen that the latter method is by addition, the former by subtraction. Another variety of the latter is found in the annals. For instance, "ninety-nine years" is not expressed by _bolonlahutuyokal haab_, nor yet by _cankal haab catac bolonlahunpel haab_, but by _hunpel haab minan ti hokal haab_, "one single year lacking from five score years." § 7. _The Calendar._ The system of computing time adopted by the Mayas is a subject too extensive to be treated here in detail, but it is indispensable, for the proper understanding of their annals, that the outlines of their chronological scheme be explained. The year, _haab_, was intended to begin on the day of the transit of the sun by the zenith, and was counted from July 16th. It was divided into eighteen months, _u_ (_u_, month, moon), of twenty days, _kin_ (sun, day, time), each. The days were divided into groups of five, as follows:-- 1. _Kan._ 6. _Muluc._ 11. _Ix._ 16. _Cauac._ 2. Chicchan. 7. Oc. 12. Men. 17. Ahau. 3. Cimi. 8. Chuen. 13. Cib. 18. Imix. 4. Manik. 9. Eb. 14. Caban. 19. Ik. 5. Lamat. 10. Ben. 15. Eɔnab. 20. Akbal. The months, in their order, were:-- 1. Pop. 2. Uo. 3. Zip. 4. Zoɔ. 5. Zeec. 6. Xul. 7. Ɔe-yaxkin. 8. Mol. 9. Chen. 10. Yaax. 11. Zac. 12. Ceh. 13. Mac. 14. Kankin. 15. Moan. 16. Pax. 17. Kayab. 18. Cumku. As the Maya year was of 365 days, and as 18 months of 20 days each counted only 360 days, there were five days intervening between the last of the month Cumku and the first day of the following year. These were called "days without names," _xma kaba kin_ (_xma_, without, _kaba_, names, _kin_, days), an expression not quite correct, as they were named in regular order, only they were not counted in any month.