This is a demonstration of an instrument used to measure “cephalic index,” or how big a person’s head was. This was, at this point in the 1800s, deemed important so that we’d know how smart the person was and, generally, what kind of person he or she was.
The same pamphlet, translated into English in the 1920s, also describes a device used to map out 3D models of solid objects… so the kind of modeling that, like, made Gollum and Jurassic Park‘s dinosaurs come to life.
You can read how they work here, at archive.org.