True Standard & Some Silver References

  Cupellation appears to be the most accurate assay method for silver but there are some losses, on the order of 0.1%, in the process which requires an adjustment to determine the fineness on the scale of a true standard. This points out the difficulty in specifying a definitive test for the fineness of silver and the care that needs to be taken.

Here are some books and links concerning silver and its history, alloys, assay and metallugy:

aes - Wiktionary  Harper's Dictionary of Classical Literature and Antiquities

Pliny - The Natural History of Metals c. 79 AD

Arbuthnot - Tables of Ancient Coins, Weights and Measures 1727, proportion of gold & silver in coins

Phillips - A Manual of Metallurgy 2nd Ed 1859, assay of the alloys & ores of silver

Phillips - The Mining and Metallurgy of Gold and Silver 1867, concentration of precious metals in lead, smelting

Percy - The Metallurgy of Lead 1870, lead-smelting

Hill - A Handbook of Greek & Roman Coins 1899, quality of metals used

Del Mar - A History of the Precious Metals 1902

Scientific American Cyclopedia of Formulas 1915, silver and copper alloys  dwt

Phase diagram - Wikipedia

Provisional and Definitive Tests

  I've been trying to come up with a good example from the History of Science to illustrate the comparison of test procedures and one is the assessment of the purity of metals. One test might be the use of Archimedes' principle to test the specific gravity of a given sample. On the other hand one might take cupellation as the definitive test for purity but he disadvantage of cupellation is that it is destructive so one might prefer a provisional test like the use of Archimedes' principle.

Cupellation is used in the Trial of the Pyx for the assay of coinage. This method dates from ancient times. Modern silver standards are well regulated. For example sterling silver is required to have a fineness of 925.

A modern example of the purification of metals similar to cupellation is the Czochralski process. X-rays can also be used for assaying metals.

Using Concurrence Counts for Comparisons

  In the last couple of blogs I tried to show how the expected number of good items in a sample can be estimated if the agreement and disagreement of two testers were known for correct assessments on the same set of items. One just needs the counts of the concurrence since from them one can determine what the testers observations were as indicated in this diagram. The counts in the last column are just the sum of the counts for the two path leading to the combined counts.

If one tries to make an estimate N_G using the actual observations one ends up with an estimate of N₀, the number of items in the sample instead.

So the testers' assessments themselves don't help us very much. In general we need a table of the concurrence of the actual number of good and bad items. We can alter the problem by asking how well a pass/fail function test will predict whether an item will function for a specified length of time with those that do being the number of "good" items. So we need to consider diagrams like these for the two testers.

After the true counts of concurrence have been determined on can use them to get the conditional probabilities for the testers which in turn allow us to evaluate the testers and their tests.

Supplemental (Oct 4): The reference to a concurrence matrix above would be more properly be called a concurrence table. The conditional probabilities are part of a matrix since they allow one set to be used to compute the other if one set of probabilities is known. The reason for the failure of the testers' concurrence estimate is due to the presence of false positives in the counts used.