Nowadays, the crystal structure of some solids can be determined by using X-ray diffraction techniques based on Bragg's law and so on. However, after reading the timeline of crystallography, it seems that physicists had some clear geometric ideas about crystals way before X-rays were discovered.
I'm aware of the work of Bravais and Barlow at the end of the 19th century, but those are more mathematical rather than experimental. On the other hand, crystallography has been developing since the 18th century by the hand of Jean-Baptiste L. Romé de l'Isle and Abbé René Just Haüy, establishing some geometrical aspects of crystals and symmetry laws based on experimental data. Also, it seems that people working on crystallography assumed that crystals were composed by atoms/molecules, maybe based on Dalton's atomic theory and Bernoulli's kinetic theory.
My question is about how did they come up with that before X-ray diffraction. What kind of experiments did scientists perform to study the structure of crystals? How did they know about a periodic arrangement of atoms/molecules in crystals? I think the latter question also addresses the introduction of the concept of a "crystal" in the modern sense.