The difference between magic, and mithril and adamantium weapons is that mithril increases the attack strength by one and adamantium by two besides the +1 chance to hit, while magic weapons don't increase the attack strength.
Once you've built the alchemists guild you can produce units with mithtril and adamantium weapons if the appropriate mines are in the city's cover area which is 2 blocks in each straight direction and 1 block in diagonal directions, I think.
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