Actually in regards to finding more Orichalcum, the fact that we now have access to magic-users and the fact that it is anti-magic (in that active magic fizzles out whenever it gets near) possibilities arise.
@Questor
Process of elimination
Orichalcum. Out of all the materials Archimedes had ever worked with, it was by far the one with the most potential he had ever seen. Incredibly tough and heat resistant, the potential uses for the metal in every walk of science constantly danced in his mind, whether as an alloy or pure metal. By far however was it's most incomprehensible property: it's ability to disrupt magic. Considering the mad sorcerer-king to the south, this aspect was what the Emperor and the council tended to focus on. Unfortunately the Empire only had in it's possession one seam of the material and no idea if it existed anywhere else.
Claw and beak, they'd only found said seam by pure chance (and the miners getting enthusiastic with black powder). Fortunately with the Emperor managing to entice some Neighponese Magic-Experts to the court, new options had become available. For while he might never be able to use said energies, Archimedes had eagerly devoured any and all texts relating to magic in an attempt to how it worked.
Which was why he was working with Yakō-Nogitsū in a large map room fluttering around one one of the most detailed and extensive maps ever made of the empire. The kitsune meanwhile was standing on a metal framework suspended above the map, holding out what at first glance would be a fishing rod. Only instead of a hook at the end of the string was a large crystalline divination pendulum, glowing softly with a mystical light.
"Are you sure this is a good idea, Archimedes? I don't want to damage this map and it looks like it costs more than my yearly wage." Yakō-Nogitsū asked with a nervous tone.
"Actually I'm pretty sure its commission cost about 5.642 times your yearly wage." Archimedes distractedly replied, ignoring the choking gasp from above. "Frida however is always interested in finding new mineral deposits or similar sites of interest and this is the best reference map in the Empire. Now, are we ready?"
"Y-yes. Whenever the pendulum passes over a region containing a seam of a particular mineral, its color should change to match the reference set we previously came up with."
"Excellent. Let us see what we can see then."
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The results of the next half hour however were decidedly mundane. Oh they recorded several potential mining sites (granite, marble, several metal seems) but nothing special like Archimedes had hoped. Until an oddity occurred; the pendulum seemed to be pushing away from a particular point on the map in defiance of gravity, it's glow actually dimming slightly.
"Here now, what's this? Your dowser appears to be acting up."
Yakō-Nogitsū leaned over looking more closely at the abnormal behavior of the pendulum. "Looks like a dead zone. They're spots in the world where magic is weakened or just not present for some reason. Nothing valuable in such places and nobody ever would want to live in such an ill-omened location."
"Really? Well best mark it and any others off so we know for the future." Archimedes said, doing so even as they continued their work. What he didn't say to the young kitsune was that the 'dead zone' that the pendulum had avoided was indeed inhabited. Namely by the Gryphus Empire's heavily defended (and fairly secretive) Orichalcum mine and forge.
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Later that night one of Ravenburg's agents quietly slipped a small packet of paper into the Emperor's private in-box with a deceptively simple title: Potential sites for mineral seams containing Orichalcum.