Measuring and weighing

[Figleaf]

Globetrotter is making the excellent point that differences in coins should be quantified. "Small head" is about as informative as "stray dog". However, 2 mm from crown to edge is instantly verifiable in countries using the decimal system. A few thoughts.

Measurements are as good as the measuring instrument. Plastic callipers are horribly imprecise, because plastic bends. Laser distance measurers are horribly precise. The difference used to be price. No longer. High precision electronic scales are commonplace and cheap. Electronic callipers have come down in price to the point where they they have become a solution for the mathematically or eyesight challenged.

Good measurements must be reflected in good notation. Everyone understand the use of the zeroes in 0.09 cm, but what is the use of the zeroes in 9.00 mm? The zeroes indicate the precision of the measurement. A notation of 9 mm means that the diameter of the coin is between 8.9 and 9.1 mm, while 9.00 mm means that the diameter is between 8.996 and 9.005 mm.

Now consider the precision question again. Weigh the same coin 5 or 10 times. If your scales give you the same value at least 4 or 8 times, use all the digits on the read-out. Otherwise, use the last digit for rounding only. Do the same test for your callipers. Chances are that your callipers are less precise. Why? Because YOU position the coin in the calipers and gravity positions the coin on the scales.

Official weights are not one number, but a formula that comes down to a weight plus a margin above and below (the remedy). Coins that are outside the remedy should be rejected. A remedy is stil necessary. Take a number of coins struck according to the same specifications (e.g. a series of commemoratives) and you will find slightly different diameters and weight.

Observed coin weights are imprecise, because of wear and dirt. Observed weights (plural) are therefore a second choice for official weight. One observed weight only is third choice. The best way to divine the official weight is to have 1000 copies, weigh them, determine average and standard deviation (Excel will do this for you.) But what if you do not have 1000 coins? Weigh as many as you can, but at least five coins of the same type and take the average. Now find the weighing system used in the country of the coin at the time it was struck and express the average in that system. Round (preferably up) to the nearest likely weight.

When it comes to differences in design, I agree that quantifying them is important, especially for those who have only one copy and wonder which variety it is. Nevertheless, as collectors, we should not lose sight of other aspects, like spacing and alignment. I don't think designs are subtly changed because someone said "Mmmm, I think that lion should have a 1.7 mm chest". More probably, someone said "Mmmm, that lion looks too skinny. Look at how thin it is compared to the pedestal".

Peter

[THCoins]

I think you make a good point that quantification may remove some subjectiveness to a discription. Additionally i would like to stress that measurement should be repeatable. Luckily gravity does not vary very much, so weight is relatively easy. In a two dimensional design it is far more difficult to quantify elements in a reproducible one dimensional value like distance. So i do not really like discriptions as "2 mm from the edge" if there is a better way to describe the dimension of an element relative to another.
To extend your example of the "large head": In the British queen Victoria Jubilee shillng it is easy to distinguish the "large" and "small head" version. In the small head the last letter of "gratia" and the first letter of "britt" extend above the crown. In the large head these letters are to the side of the crown. This at itself ofcourse is also a quantification. But the reference of the measurement is in the coin. It is easily reproducible and i don't need my callipers and avoid measurement errors.

And if possible, showing two versions side by side on the forum can be very instructive sometimes !

[FosseWay]

showing two versions side by side on the forum can be very instructive

This is the key.

Measuring the distance between design elements on a coin's surface is imprecise (at least with any equipment I possess) and I'm unwilling to let the sharp pointy bits of my calipers anywhere near the surface of a coin in any case. Conversely, talking about relative positions of different design elements often falls down if you only have one variant in front of you.

The answer is to have decent-size, hi-res, annotated photos of the variants, so you can compare whichever you've got against all available variants. The book I use for Swedish coins is very good in this respect. KM, which I use for other world coins, is much less good, but clearly can't include pictures of every last variety in the whole world.

Therefore, WoC is ideally placed to show precisely this kind of information, and I second the suggestion that if we have both varieties in any given case, we should scan/photograph them and show the differences on here.

[GSDykes]

Here is a link (below) to view and print a free PDF file which I made. It is a handy chart of various coin alloys and their specific gravities. It also shows the S.G. of common elements as well as information on alloyed silver (Ag) coins. It is free to view, read, download and print (landscape format). Enjoy. Share.

www.Biblical-data.org/GSDykes_Specific_gravity_tests.pdf

Gary in Washington

[Bimat]

Here is a link (below) to view and print a free PDF file which I made. It is a handy chart of various coin alloys and their specific gravities. It also shows the S.G. of common elements as well as information on alloyed silver (Ag) coins. It is free to view, read, download and print (landscape format). Enjoy. Share.

www.Biblical-data.org/GSDykes_Specific_gravity_tests.pdf

Gary in Washington

This is very nicely done! Thanks for sharing!

Aditya

[EWC]

A couple of points:

Observed coin weights are imprecise, because of wear and dirt.

True of course but a few words of caution. 

Academics are sometimes impractical people who make mistakes on such matters.  Modest wear and dirt have a tiny effect on weight – a lot of the "wear" down from EF to GF seems often to be squashing rather than abrasion. 

In a paper on the weight of Charlemagne's pennies Miskimin assumed every known specimen was 10% low due to "leaching in the ground" or some such.  That is rubbish.  Many coins come from the ground exactly as the went into it

The big problem with old coins tends to be associated with clipping.  That makes very big differences. Clipped coins have to be carefully excluded from all samples if one is to estimate the initial intended weight.  This cannot be done by copying weights wholesale from museum catalogues.

The best way to divine the official weight is to have 1000 copies, weigh them, determine average and standard deviation  (Excel will do this for you.)

I think there are circumstances where standard deviation should be avoided.  It assumes distributions will be near normal, and can mislead badly where they are not.  It troubles me that almost the entire education system has ignored this problem for a whole century now.

[Figleaf]

In a paper on the weight of Charlemagne's pennies Miskimin assumed every known specimen was 10% low due to "leaching in the ground" or some such.  That is rubbish.  Many coins come from the ground exactly as the went into it

That's a bit sweeping. I have seen coins that had lost over 50% of their weight due to copper leaching.  Not one. Many. The main culprit is over-fertilisation, especially with artificial fertiliser. Maximum leaching depends on the amount of copper in the coin, of course.

The point is rather the acidity of the soil. Coins that were lodged in sand (beach, river) or gravel show no leakage, while those that stayed in woodland or agricultural land that was heavily treated with artificial fertiliser suffered heavily. I don't think find data bases have info on the acidity of the soil in which the coin was found, so a rough estimate is the best you can do. If the Charlemagne coins were found all over Western Europe, and the coins are of reasonably good quality (say 80% silver, 20% copper), a 10% average would seem about right.

Peter

[Figleaf]

I think there are circumstances where standard deviation should be avoided.  It assumes distributions will be near normal, and can mislead badly where they are not.  It troubles me that almost the entire education system has ignored this problem for a whole century now.

Why would the distribution not be (near) normal?

Peter

[EWC]

If the Charlemagne coins were found all over Western Europe, and the coins are of reasonably good quality (say 80% silver, 20% copper), a 10% average would seem about right.

I too have seen and weighed a lot of coins, and 10% via corrosion looks high to me, regarding specimens largely in national collections.  But that is not the  important point.

The important point is that Miskimin was not discussing the average, he is discussing a big shortfall in every single surviving specimen.  And I stand by my judgement that that suggestion is rubbish.

[EWC]

Why would the distribution not be (near) normal?

Could be lots of reasons - swindling, or picking over, inside, or outside the mint are 4 possiblities for starters.

[Figleaf]

OK. I thought you might be worrying over populations too small to draw conclusions, which is my usual problem with bell curve analysis. If the sample is too small, you may easily be overlooking a "twin peak", caused by the same coin being struck on different standards, or the whole graph may be unrepresentative in the first place.

Picking over newly struck coins was standard procedure in Renaissance times. It does not invalidate the approach. The right tail of the graph will become significantly shorter than the left tail and the distribution will be skewed. The skewedness of a graph can be spotted on sight. Similarly, swindling will produce a graph that is skewed to the left. There is a problem only when the two occur at the same time. However, this is unlikely, because picking over makes no sense when the coins are lightweight or do not contain enough precious metal.

Peter

[EWC]

The skewedness of a graph can be spotted on sight.

Yes exactly right - that gets to the heart of my point.  Distributions are 2 dimensional objects and there are an infinite number of them (actually more than a countably infinite number of them.)

Reducing their characteristics to a single number, any single number, is going to give an impoverished 1 dimensional account of what is going on.  You have to make a graph of a fairly big representative sample to get the real picture.

Within that, I dislike standard deviation, and prefer absolute deviation.  For non-normal curves, SD will  give misleading results.  I made this point in a class about 40 years ago, and the lecturer got pretty annoyed with me.  It was not till we got the internet and search engines that I discovered the history of the matter.  Eddington was objecting to the use of SD right back when it was first mooted (1920's I think), for just the reasons I did.

On the history of such matters.  I seeem to recall Italian bankers turning down a recoining contract (perhaps in Spain?) because their calculations depended upon further clipping the old coins themselves as a major part of their profit.  They discovered the old coins were already so clipped that their sums did not add up.  Do I recall this correctly?  There were lots of stories about clipping and excess profits in the English 1696 recoinage too.