KUMEEAL VALUE OF THE DAT SYMBOLS. 55 



Instead of being disconcerted by the fact that in the above instances the factors are not 

 all multiplied into each other, as in the case of compound and separate characters, I 

 am guided by it to the deduction of two important rules, which I believe will be found 

 applicable to all Maya multiplication : first, to find the numerative value of a simple 

 character, multiply the value of its factors singly by the number of factors if alike, 

 and together if unlike ; second, to find the numerative value of separate or compound 

 characters, multiply the values of the different parts into each other. Thus I would 

 account for the numerative values of Kan, Ix, and Chuen ; and, finding the cleft 

 inclosure appropriately used as a sign for multiplication in these symbols, I deem it 

 fairly reasonable to suppose it may have the same significance elsewhere. 



This deduction, whether true or false, very naturally suggests a search for indices of 

 other arithmetical processes. The circle, with a dot or smaller ring in the center, 

 cannot have failed to attract the attention of every student, its use is so common, 

 especially upon all forms of the hand. I had thought that it simply indicated the 

 character to be a numeral, but the detection of what there was reasonable ground for 

 supposing might be a sign for multiplication led me to investigate whether this circle 

 and dot might not also signify some particular process ; and the result is that I am now 

 inclined to the belief that, apart from its possible conventional use at times in connec- 

 tion with the hand — and even there, perhaps, indicating that all numbers represented 

 by the hand are to be added — it implies addition. For instance, in the symbol for 

 Manik the hand is closed until the space between the thumb and fingers resembles a 

 reversed ik sign, to which, if it signifies 6, add the 5 that the hand itself may mean 

 and the sum is 11, the number represented by Manik in the day series. I shall speak 

 more fully of this when I come to the symbol for that day. In this sign for 20, 



the implication is plain that the two signs for 10 are to be added together. 



I do not consider that the use of these signs to indicate addition and multiplication 

 can by any means be regarded as proved, but a fair degree of probability is established 

 by the examples I have given and others in keeping with them. The fact that in the 

 codices, especially on heads, the two signs are combined, does not necessarily militate 

 against the theory. The combination might mean that both processes were to be 

 made use of — as, indeed, both are nearly always involved — or it may be one of the 

 many conventionalisms whose original significance is lost. Nor do the further facts 

 that the employment of these signs is inconstant and irregular, and that no signs for 

 subtraction and division appear anywhere, weigh very heavily against it. The entire 

 Maya graphic system is marked by irregularity and capriciousness, and subtraction and 

 division were of so rare occurrence that there may have been no signs for them, or, if 

 there were, they may have escaped my notice. 



