Chinese Ancient Calendar "no Extinction Surgery" Research

The calculations of Mo and Mie in aneient Chinese calendars were invented by the Sifen Calendar of the Eastern Han Dynasty(A.D.85).A new difinition was given by Zhang Sui,a Tang Dynasty scientist who has a Buddhist name Yi Xing.Thus,the calculations of Mo and Mie in ancient Chinese calendars can be divided into two periods which have the Dayan Calendar(A.D.728)as their boundary.The mathematical fundamentals of Mo and Mie calculations in the two periods have been discussed.It also shows the understanding by the writer of this paper to the use of Mo and Mie.In the first stage,Mo and Mie gather in the calculation of designating names in “Jia Zi”(a cycle of sixty)of mean solar terms.In the second stage,Mo is also linked with the mean solar terms but Mie is linked with the mean conjunction.A conjecture about the meaning of the Mo and Mei methods is verified.They are a kind of intercalary system.The computation of the sum of the numbers for Mo and Mei days is related to the arrangement of the intercalary month.Interestingly,the definitions of Mo and Mei are the same as those in Indian mathematical astronomy.