MORLBT] INTRODUCTION TO STUDY OF MAYA HIEEOGLYPHS 139 



Taking u]) the number, 31,741, which we have chosen for our first 

 example, let us deduct from it the highest multiple of 13 which it 

 contains. This will be found by dividing the number by 13, and 

 multiplying the wliole-numher part of the resulting quotient by 13: 

 31,741^ 13 = 2,44l3§3. Multiplying 2,441 by 13, we have 31,733, 

 which is the highest multiple of 13 that 31,741 contains; consequently 

 it may be deducted from 31,741 without affecting the value of the 

 resulting day coefficient: 31,741—31,733 = 8. In the example under 

 consideration, therefore, 8 is the number which, if counted from the 

 day coefficient of the starting point, will give the day coefficient of 

 the resulting date. In other words, after dividing by 13 the only 

 part of the residting quotient which is used in determining the new 

 day coefficient is the numerator of the fractional part.^ Hence the 

 following rule for determining the first unknown on page 138 (the day 

 coefficient) : 



Rule 1. To find the new day coefficient divide the given number 

 by 13, and count forward the numerator of the fractional part of the 

 resulting quotient from the starting point if the count is forward, 

 and backward if the count is backward, deducting 13 in either case 

 from the resulting number if it should exceed 13. 



Apphdng this rule to 31,741, we have seen above that its division 

 by 13 gives as the fractional part of the quotient -^. Assuming that 

 the count is forward from the starting point, 4 Ahau 8 Cumliu, if 8 

 (the numerator of the fractional part of the quotient) be counted 

 forward from 4, the day coefficient of the starting point (4 Ahau 

 8 Cumliu), the day coefficient of the resulting date will be 12 (4 + 8). 

 Since this number is below 13, the last sentence of the above rule has 

 no application in this case. In counting forward 31,741 from the 

 date 4 Ahau 8 Cumhu, therefore, the day coefficient of the resulting 

 date will be 12; thus we have determined our first unknown. Let 

 us next find the second unknown, the day sign to which this 12 is 

 prefixed. 



It was explained on i>age 37 that the twenty day signs given in 

 Table I succeed one another in endless rotation, the first following 

 immediately the twentieth no matter which one of the twenty was 

 chosen as the first. Conse([uently, it is clear that the highest mul- 

 tiple of 20 which the given number contains may be deducted from it 

 without affecting in any way the name of the day sign of the date 

 which the number will reach when coimted from the starting point. 

 This is true because, no matter what the day sign of the starting 

 point may be, any multi]ile of 20 \vill always bring the count back to 

 the same day sign. 



1 The reason for rejecting all parts of the quotient except the numerator of the fractional part is that this 

 part alone shows the actual number of units which have to be counted either forward or backward, as the 

 count may be, in order to reach the number which exactly uses up or finishes the dividend— the last unit 

 of the number which has to be counted. 



