Kopper Ken When one is dealing with SG vs Density the "confusion" you point to is of no real consequence. Water the unit reference for Specific gravity in the metric system is 1 gram per cubic centimeter so the difference is merely terminology provided the conversion to g/CC is made in the calculations which I did. The answer is 9.1 either way. Density (weight divided by volume) is expressed as 9.1 grams per cubic centimeter and SG which is expressed as a number without units. However the units are only eliminated in last step where the density is divided by the reference to the standard unit. 9.1 g/cc divided by 1 g/cc which produces 9.1.
You say:
Quote:
I refined your calculations and the volume of the "good" coin would be 2.5238 cubic centimeters. You need to change out of scientific notation for decimal numbers. I used the formula (V=pie x radius squared x h). for the "counterfeit" coin the volume was 2.6784 cubic inches.
You use "Scientific notation" where I think you mean significant figures. I used the same standard formula for the volume of a cylinder and reached the same mathematical answer but we differ on how many digits are actually significant in the result. The mathematical answer may be 2.5238 but that is a false level of precision. You should not express the result in 4 decimals when the measurements were taken only to thousandths of an inch (two significant figures). So the result can be no more specific than Two significant figures 9.1.
Since the diameter of BOTH coins is identical by measure - the only true variable is the thickness measurement. One coin is 92/1000 ths and the other 98/1000 ths. That difference is VERY significant - you simply can not ignore it because it does effect density and makes the difference between 900 fine silver and some sort of debased metal.
You also say:
Quote:
I believe that the "reeding" caused the increase in thickness (height variable) at the rim only, and that a truer reading would be gotten using a micrometer, taking a reading from the middle of the coin.
There is no evidence in the photos that the thickness was increased by the application of reeding. That is a supposition without any actual evidence and should not alter the result.
What we ideally need is the actual volume of the coin not any single thickness. However, I still maintain that the difference between 92 and 98 thousandths is adequate to generate a conclusion that the coin is NOT genuine.
A ratio of the measurement taken at the rim will accurately describe the ratio of volumes if the contours and diameter of the coin match.
Your conclusion based on the above supposition is:
Quote:
I still believe that this is a damaged original coin...there is not sufficient variation in the density. Which is what you have shown also.
If one coin is 98/92 thicker - How does that actually effect the density?
The volume of the coin (B) using your numbers is 2.6784 cc.
The volume of the coin (A) is 2.5238 cc.
If the weight of both is identical then the density is reduced by the ratio of those two numbers. 2.6784/2.5838 or 1.0469 - 5%. So there is a 5-6% change in Volume, Density and ?.
Coin silver 900 fine has a density of 10.3 g/cc. Reducing that to 95% (average of ratios) reduces the density to 9.785 which is NOT 900 fine silver but something less than 650 fine silver IF IT CONTAINS actual silver. The alloy could be bronze coated with silver and achieve that density.
Anyone familiar with Riddell's 1845 book should recall that Riddell found that his melt averages were only 5% short in total silver, but that 5% difference led to his cataloging the first ever book on circulating counterfeits. Perhaps the coin that began this thread is actually a CCC type.
Albert You make a great suggestion. I do the same thing for anyone asking and do not charge for it. In hand it is easier of course you can look closely at the coin and settle the open issues by accurately weighing the coin in air and immersed in water. The loss of weight in grams equals the volume of the coin in cc's. Density is weight in air - divided by the weight loss. Remove units and you have SG. Just that simple.
Loruca You say:
Quote:
this sort of calculation is exactly why significant digits are taught in high school, the alleged difference is irrelevant given the original standard of precision of the measurements.
You are right significant digits are critical but your conclusion is flawed. The use of significant digits actually supports my conclusion and can not be ignored without a valid reason. A change in volume of 5% is precisely what is often seen with counterfeit coins made for circulation. You ignore a 5% variance at your peril.
I would ask why you believe that the concept of significant digits applied correctly eliminates concern for a 5% change in volume? That is not something actually based in science.
The you say:
Quote:
These coins were worth their weight in silver, the only contemporary counterfeits I am aware of are made of base metals, a silver counterfeit would have defeated the purpose of faking the coin!
Silver counterfeits using the identical silver alloy as genuine coins were made and in many coin series that circulated in the 1890s and 1930s are in fact very common. You are unaware of them perhaps but they do exist in very large numbers. The reason - in 1893 world silver values dropped to about 30 cents an ounce (same thing happened again in 1933). A coin like the 5 Lira had a silver value of only 21.7 cents. In 1893 a dollar coin cost about 5 cents to make. So for 26.7 cents a counterfeiter could make and circulate a genuine silver coin at a profit of nearly 5 times more than cost. That is a cold hard fact.
Most collectors are unfortunately unaware of that fact and often own ccc coins believing them to be genuine.
Examples of this happening are US
Morgan dollars, Spanish 5 Pesetas and Peruvian Sols. When discovered - ccc's of this type are melted to get them out of circulation (See historic records for Spain in 1895 and the massive redemption of millions of ccc 5 Pesetas that happened.) There are many other coins copied in a similar way in history.