thoughts

There is a great deal we don't know about Islamic and Byzantine weights. They don't always weigh what they "should" and the usual reasons (excessive cleaning, corrosion, adhesions) often do not explain unusual masses.

How can we attribute weights? Almost always the time period and location of a weight's production and use is obscure. We rarely know where they were found. Sometimes the mass doesn't seem quite right for the denomination. What can explain why a weight does not neatly fit the usual expectations?

For example, consider this well-preserved weight.

#103
The shape two truncated cones back-to-back.
7.83 grams. It is squat at
13.2 mm in diameter and only 8.7 mm high.
Assuming it is Islamic and Fatimid, as seems likely,
the shape makes it is on the dinar standard.
It is 2 dinars at 3.92 grams/dinar.
That's light--maybe even very light, given dinars supposedly average 4.16 grams or more.
Why is it so "off"?
Corrosion doesn't seem to be a problem. Does the shape mean it is from a different time-period? Could it be Roman or Byzantine on a different standard?

How about this one?

#102
13.2 mm and 3.0 mm thick.
3.58 grams.
The discoid shape implies it is on the dinar standard. One bird's eye might suggest 1-dinar. But the dinar is over 4.0 grams and this piece is only 3.58 grams.
If we decide to omit it from consideration because it is so "wrong," what are we missing? Is it criminally made? From a different place or time?

The next one is light but has lettering that might turn out to be legible and so we might (eventually) be able to attribute it.

#104
13.2 by 12.8 by 4.4 mm thick.
5.26 grams.
5.26 /2 = 2.63 grams/dirham, if this is a 2-dirham piece, which the two bird's eyes suggest. (Not all 2-dirham weights have two bird's eyes. Some have four and some have none.)
If so, it is very light. Why?
I don't think corrosion has reduced the weight. If anything has changed its weight, it might be the small adhesions which increase it slightly.

If the legend could be read it might give us a hint.

I've seen polygonal pieces offered with listed weights well off their expected value. I can see collectors choosing not to buy those and scholars omitting them from calculations of typical masses. Does that produce a bias?

#107
After looking at this piece closely from every angle I can't make out a design. The shape suggests it is a weight.
8.92 grams. 16.9 by 16.1 by 4.3 mm.
With only that for evidence, I attribute it as a
Byzantine 2-nomismata piece.
at 4.46 grams/nomisma.
Given the weight is just right for that Byzantine denomination, I decide that is the attribution.
I use its weight to decide it is Byzantine and its denomination, so I shouldn't use that decision (its denomination) to decide what the weight of a nomisma should be.

#101
13.1 by 12.9 mm by 3.8 mm thick.
5.68 grams. (I don't think corrosion has affected this number.)
If this is a 2-dirham weight, and I think it is, it is a bit light at only 2.84 grams/dirham.
Note how, in addition to the central dot, there are 12 dots in the corners. 12 dots at 6 dots per dirham makes 2 dirhams.

Does the different design and light weight mean it is from a different place or time-period? We don't know (and won't until laws are changed to reward finders who report find spots and contexts.)

#2573
5.26 grams (very light at 2.63 grams/dirham)
14.3 by 12.2 by 3.8 mm thick.
A long horizontal line with two vertical strokes at each end.
This mark is also seen on 2-dinar weight (the flat weights page, #1085). That one is full weight, unlike this one.
What can explain why this weight is so underweight?

We assemble lots of weights, see how much each weighs, determine its denomination, and do the division (the actual weight of a 5-dirham piece is divided by 5 to get "grams/dirham") and think about the implications. It is clear that larger denominations tend to produce higher grams-per-dirham results.

Bias. One problem is the tendancy to reject weights that don't conform to the pre-supposed standard.

Should it be averaged in with other 2-dinar weights?
We might omit this weight from consideration, which is a type of circular reasoning. To find the weight-standard we look at the the weights but omit the ones that don't conform to our pre-conceived opinions.