INTKODUCTION. 



commencement of a 13-katun period — of which I have not a particle of doubt — the era 

 must extend backward until by stages of 949 katuns (the number in a grand round) 

 the beginning of a great cycle is reached. A simple table will most clearly show the 

 result. 



Beginnings of the Katun Rounds in a Grand Era. 



No. of 

 Rounds. 



Katuns. 



Great 



Cycles. 



Cycles. 



Katuns. 



1. 



949 



3 



8 



9 



2. 



1,898 



7 



3 



18 



3. 



2,847 



10 



12 



7 



4- 



3,796 



14 



7 



16 



5. 



4,745 



18 



3 



5 



6. 



5,694 



21 



11 



14 



7. 



6,643 



25 



7 



3 



8. 



7,592 



29 



2 



12 



9. 



8,541 



32 



11 



1 



10. 



9,490 



36 



6 



10 



11. 



10,439 



40 



1 



19 



12. 



11,388 



43 



10 



8 



13. 



12,337 



47 



5 



17 



14. 



13,286 



51 



1 



6 



IS. 



14,235 



54 



9 



15 



16. 



15,184 



58 



5 



4 



17. 



16,133 



62 







13 



IS. 



17,082 



65 



9 



2 



19. 



18,031 



69 



4 



11 



20. 



18,980 



73 











The table is made to cover the entire grand era, in order to show that at no point 

 but the start does the beginning of a katun round correspond with that of a great 

 cycle, and that in the 54th great cycle only does the round begin with the 15th katun 

 of the 9th cycle. This showing is conclusive to my mind as fixing the position of the 

 date in question. That position accords with a pre-existing requirement of the 

 calendar; it fulfils a conjuncture of cycle and katun dates against odds of thirteen to 

 one ; it explains why the occasion was regarded as of such great importance ; and it 



