It looks like a very robust tool to measure length and distance. A long time ago, tape measures were unreliable, so people used these folding measuring sticks, although I've only ever seen wooden ones. Brass doesn't rust, so it has that advantage over steel.
I don't think the measurements are "non-sequential;" Maybe it appears like that because the numbers go "back and forth" in the photo so that they measure correctly when the thing is unfolded.