19 Ashm 1931.137: Conclusion

As promised, we now will discuss how the unit sar fits into our existing System A. From Figure 21, we can see that sar is listed before ganá, thus the sar must be smaller than any of the units of ganá we have learned about previously. You may recall that the smallest unit of area in System A from the Early Dynastic period, iku ganá, was equal to 100 square ninda. This awkward gap between the units of length and units of area is filled by sar. 1 sar equals 1 square ninda. In other words, 1 sar is one hundredth of an iku ganá, or an iku ganá is 100 sar. The number of sar was specified using System S up to 50 sar, which equals 1 ubu ganá or one half of an iku ganá. The full relationship between sar and ganá, along with the the updated cuneiform symbols, is captured in Table 13.

Table 13. The expanded System A and its cuneiform symbols.

Symbol	Sumerian	Relative Value
	diš sar	1 sar
	u sar	10 sar
	ubu ganá	5 u sar
	iku ganá	2 ubu ganá
	èše ganá	6 iku ganá
	bùr ganá	3 éše ganá
	bùr’u ganá	10 bùr ganá
	šár ganá	6 bùr’u ganá
	šár’u ganá	10 šár ganá

The only other portion of Ashm 1931.137 that we have yet to discuss are that the first several entries of sar are actually fractions of 1 sar. At this point in time, System S was supplemented by a set of basic fractions accounting for the sixth parts of 1. Ashm 1931.137, however does not include one sixth.^[1]

Table 14. The fractions included in Ashm 1931.137.

Symbol	Value
	one third
	one half
	two thirds
	five sixths

The way an Old Babylonian metrology table is meant to be laid out is to start with the smallest possible units and then to increase by the smallest possible increments. Once the next unit is reached you then start counting using this new unit. Sometimes you might count by the smaller units one more time before incrementing up to larger steps. It is important that you not repeat equivalent amounts. Rather, you let the steps inform the reader how to convert from a smaller unit to a larger unit. For example, if we were making a metrology table for feet and inches. You would count from 1 inch up to 11 inches, and then the next amount would be 1 foot.