Are there any early industrial age methods capable of determining diamond or graphite's crystalline structure?

I'm writing a fictional story with early [industrial age](https://en.wikipedia.org/wiki/Industrial_Age) technology where a chemist discovers not only that diamond and graphite are made of the same substance, but that they [differ by crystalline structure](https://en.wikipedia.org/wiki/Allotropes_of_carbon) (cubic vs hexagonal). However, I'd like this to be a realistic depiction if possible and the chemist does not have access to electron tunneling microscopy or advanced spectrographic methods. The farthest spectroscopy has gotten is [Fraunhofer](https://en.wikipedia.org/wiki/Joseph_von_Fraunhofer)'s spectroscope and John Herschel's evaporogram, with visible light and the beginnings of an understanding of [infrared](https://en.wikipedia.org/wiki/Infrared#History_of_infrared_science) and ultraviolet. Would 1850's level spectroscopy or other technology of the time be able to demonstrate the crystal structures of carbon (specifically graphite and diamond) without a 1900's understanding of atomic structure?





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> Would 1850's level spectroscopy or other technology of the time be able to demonstrate the crystal structures of carbon (specifically graphite and diamond) without a 1900's understanding of atomic structure?
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Yes, using visible light and petrographic microscopes. The field of optical mineralogy was mature enough by the mid-1800's for one to determine the crystal structure of minerals. In particular, the work of Sir William Nicol is worth investigating (thin but useful [Wikipedia](https://en.wikipedia.org/wiki/William_Nicol_(geologist)) article).


I will add that there's a pretty simple way to determine whether or not the crystal structure of a mineral is the same or different than that of another mineral - the so-called [crystal habit](https://en.wikipedia.org/wiki/Crystal_habit).


Finally, diamond exhibits [conchoidal fracture](https://en.wikipedia.org/wiki/Conchoidal_fracture), and graphite does not. This might be the easiest way to tell that the two minerals have different crystal structures.


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