MORLEY] INTKODUCTION TO STUDY OF MAYA HIEROGLYPHS 253 



cient of the beginning day of the second subdivision of the first divi- 

 sion, the second Hack number is to be counted forward in order to 

 reach the third red number, which is the coefficient of the day begin- 

 ning the third subdivision of the first division. This operation is 

 continued until the hist black number has been counted forward from 

 the red number just preceding it and the last red number has been 

 reached. 



This last red number will be found to be the same as the fij'st red 

 number, and the day which the count wiU have reached wiU be shown 

 by the first red number (or the last, since the two are identical) used 

 with the second day sign in the column. And this latter day will be 

 the beginning day of the second division of the tonalamatl. From 

 this day the count proceeds as before. The black numbers are 

 added to the red numbers immediately preceding them in each case, 

 until the last red number is reached, which, together wdth the third 

 day sign in the column, forms the beginning day of the third division 

 of the tonalamatl. After this operation has been repeated until the 

 last red number in the last division of the tonalamatl has been 

 reached — that is, the 260th day — the count will be found to have 

 reentered itself, or in other words, the day reached by counting for- 

 ward the last black number of the last division will be the same as 

 the beginning day of the tonalamatl. 



It foUows from the foregoing that the sum of all the black numbers 

 multiplied by the number of day signs in the column — the number 

 of main divisions in the tonalamatl — wiU equal exactly 260. If any 

 tonalamatl fails to give 260 as the result of this test, it may be regarded 

 as incorrect or irregular. 



The foregoing material may be reduced to the following: 



Rule 2. To find the coefficients of the beginning days of succeeding 

 divisions and subdivisions of the tonalamatl, add the black numbers 

 to the red numbers immediately preceding them in each case, and, 

 after subtracting all the multiples of 13 possible, the resulting num- 

 ber will be the coefficient of the beginning day desired. 



Uule 3. To find the day signs of the beginning days of the suc- 

 ceeding divisions and subdivisions of the tonalamatl, count forward 

 in Table I the black number from the day sign of the beginning day 

 of the preceding division or subdivision, and the day name reached 

 in Table I will be the day sign desued. If it is at the beginning of one 

 of the mam divisions of the tonalamatl, the day sign reached will be 

 found to be recorded in the column of day signs, but if at the begin- 

 ning of a subdiidsion it will be unexpressed. 



To these the test rule above given may be added: 



Rule 4- The sum of all the black numbers multiplied by the 

 number of day signs in the column of day signs wiU equal exactly 260 

 if the tonalamatl is perfectly regular and correct. 



