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These are cool details and I'd love to have them in, but to my dissatisfaction, I can't find out what techniques Berzelius used on a quick look. Apparently I'll have to search for the papers he published.--R8R (talk) 18:29, 12 July 2016 (UTC)
See, this is why this whole thing is murky: there is the xenotime story, that everyone parrots, and then there is also this thing about gadolinite now. I can believe that he thought it was in both minerals, but this is really encroaching on interpreting the sources to one's convenience. (This is where we really need Berzelius' papers.) Double sharp (talk) 08:40, 14 July 2016 (UTC)
Nothing really murky for me, I have a coherent picture of what happened, correct me if I'm missing something: B was studying a gadolinite sample and found a white mineral impurity, which he assumed was an earth of another new element. No source says gadolinite had this thorium on it. That impurity, howe, turned out to be xenotime.--R8R (talk) 08:57, 14 July 2016 (UTC)
http://ntl.inrne.bas.bg/workshop/2011/proceedings/apostolova.pdf -- also see this: "In 1815 Berzelius observed thermoluminescence in gadolinite caused by the α-decay of U and Th traces ." that  actually reveals the original 1815 paper; unfortunately, I can't find it online (also, it's apparently in Swedish, but we could ask a Swede for help if we had the paper to work with; anyway, I got some info already)--R8R (talk) 21:50, 12 July 2016 (UTC)
Not early 19th century, but here's minor detail missing: the German physicist discovered Th's radioactivity before Curie did: "Thorium was discovered to be radioactive by Gerhard Schmidt in 1898 – the first element after uranium to be identified as such. Marie Curie also found this, independently, later in the same year. (3)" http://www.chemicool.com/elements/thorium.html --R8R (talk) 21:59, 12 July 2016 (UTC)