Spectroscope improvisation day!
Let's see if they can get this to the point where they can both see the lines of emitted spectra from heated materials, and also, see the corresponding absorption lines when you shine light through! That's because photons are emitted by electrons falling from orbitals energized above minimum, back down; and electrons can correspondingly absorb photons of that frequency to jump up.
Once they've got enough spectrographic detail, they can probably start to figure out where Golarion materials are on the Periodic Table; Keltham doesn't actually remember how the regularities work, but he knows they're there and don't require advanced math to notice.
Incidentally, do Golarion miners already have ways to tell exactly which minerals and metals are in which bits of ore? Because if not, they can just burn ores under a spectroscope and find out exactly which elements could be mined from that kind of ore, if only they could find a way to extract it.