<div dir="ltr">This is an interesting problem, and as such, I have spent more time than I probably should have thinking about it. <div><br></div><div>The first issue is the manufacture of the links. At first glance, it seems like it would be difficult to come up with a way to quickly and accurately mass produce enough of these links to be useful for currency. However, after thinking about this for a while, I came up with a relatively simple solution. The pure metals in their proper proportions would be melted down and mixed together to form an alloyed metal. This metal would then be drawn into a wire of the right thickness. It would be rough cut to length and then trimmed down till the weight matches that of a standard link of that alloy. It would then be formed into a the shape of a link and soldered shut around previous lengths to make a chain. The excess trimmings would be melted down into the next batch of the same alloy. </div>
<div><br></div><div>So now that we know how these links are going to be manufactured, we need to figure out what proportions of metal to make the alloys out of to ensure the links have the right value. As Chris and Charles have already stated, that's best determined by weight, and here in lies the next problem; you've specified these links by their spatial dimensions giving us links of constant volume, not weight. Fortunately, a ring like what you've specified is a torus, and it's rather trivial to find the volume of a torus. Simple that is provided you know calculus, which I'm assuming the people in the universe Metamor do not. I'm just going to assume through trial and error or coincidence that they came up with a standard size of link that matches the dimensions you've specified. That leaves each link a volume of 0.206 cubic inches. Now we can relate the volume of the links to the weight of precious metals given the densities of the metals. The following are the densities of the possible component metals given in troy ounce per cubic inch. </div>
<div class="gmail_extra"><br></div><div class="gmail_extra"><div class="gmail_quote"><div class="gmail_quote">Gold<span class="" style="white-space:pre"> </span>10.2 t.oz/in^3</div><div class="gmail_quote">Silver<span class="" style="white-space:pre"> </span>5.527 t.oz/in^3</div>
<div class="gmail_quote">Copper<span class="" style="white-space:pre"> </span>4.721 t.oz/in^3</div><div class="gmail_quote">Tin<span class="" style="white-space:pre"> </span>3.851 t.oz/in^3</div><div class="gmail_quote">
<br></div><div class="gmail_quote">Now we still need to know the relative cost of each metal so we can determine the composition of each link, and we also need the composition of each Metamorian coin to figure out the exchange rate. Fortunately, <a href="http://mkworld.wikidot.com/writers-guidelines#toc12">the Wiki has a table</a> that specifies the weight and composition of each Metamorian coin and its approximate buying power in US dollars. Unfortunately, that table is very, very wrong. First off, the approximate buying power of the Copper Penny, the Silver, and the Bronze Crescent don't line up with the previously stated definitions of their value. The correct value for buying power should be $0.60, $3.00, and $6.00 respectively. With those fixed we can now solve for the approximate value of the metals in US dollars per troy ounce (I'm assuming troy ounce because that's the proper US customary unit for precious metals). Now we run into another much bigger problem. The values start off reasonably enough. Gold is worth $585.66 per troy oz. Silver is worth $37.82 per troy oz. Then we get to copper. In order to make the values given in the chart work, Copper must have a value of -$40.43 per troy oz. That's right; copper has a negative value, a very large negative value, as in, if you ended up with an ounce of copper in your possession, just by throwing it away you gain more value than if you picked up an ounce of silver. This is clearly an enormous problem. </div>
<div class="gmail_quote"><br></div><div class="gmail_quote">I'm currently trying to figure out a way to rectify this. It would be best to define the relative values of each metal first and then derive coin composition from there. Historically, from the 15th to the 19th century the ratio of the price of silver to gold was fairly constant at 15:1. That closely matches the ratio derived from the table so that's a good place to start. The value of copper has fluctuated a lot throughout history mostly based on its utility. The ratio of the value of copper to silver has fluctuated wildly being any where from 10:1 to 350:1. Currently it is about 120:1. Around the middle ages it was about 300:1. However, the value of silver compared to gold has dropped significantly since then so that ratio makes more sense. If we assume the approximate buying power of gold has stayed constant a 300:1 ratio of copper to silver and a 15:1 ratio of silver to gold gives us a ratio of copper to gold of 4500:1. compared to the current ratio of 5344:1, this makes copper worth a little bit more in Metamor than it is today. The value of tin would be closely related to copper thanks to it's primary use in the making of bronze. Let's give in a ratio of 2700:1 which makes tin worth about half of what it is now. </div>
<div class="gmail_quote"><br></div><div class="gmail_quote">If we continue to assume that gold has an approximate buying power in Metamor similar to what it does on modern day Earth we can give dollar values to precious metals in Metamor and use the approximate buying power of Metamor coins to determine their composition. Gold is about $1350/t oz., so that leaves us with the following prices for Metamorian metals:</div>
<div class="gmail_quote"><br></div><div class="gmail_quote"><div class="gmail_quote">Gold<span class="" style="white-space:pre"> </span>$1350/t oz</div><div class="gmail_quote">Silver<span class="" style="white-space:pre"> </span>$90/t oz</div>
<div class="gmail_quote">Copper<span class="" style="white-space:pre"> </span>$0.30/t oz</div><div class="gmail_quote">Tin<span class="" style="white-space:pre"> </span>$0.50/t oz</div><div class="gmail_quote"><br></div>
<div class="gmail_quote">Now we have enough information to work out the composition of our various currency; however I'm too busy at the moment to do that right now, so I'll try to work those out and post them later tonight. </div>
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