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Yes, and it is a basic demand that the instrument itself be accurately leveled- there are built in spot and cylindrical levels on true theodolites- as well as plumb bobs on the older instruments, and optical plummets to establish the vertical on modern ones. The theodolite, the quintessential engineering instrument, is a highly refined variant of the simpler surveying Transit. Non-optical transits existed in Classical times and it is certainly plausible the word itself came from an approximation of the Greek- The Eye of God- for Theodolite. There are all different types - it can get very mathematically involved. There are some specialty types such as the spot-averaging theodolite which can be used in motion studies of such objects- as -and one emphasizes from a safe distance, the dimensions of tidal waves. The spot-averaging mechanism is similar to a movie camera but takes only two shots a second over a two-minute period and strikes a mechanical average- used also for aircraft and submarine navigation-through periscopes, a periscopic theodolite, so to speak. there are all different kinds- as there are varieties of compasses.
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Is levelling spelled like this if not how is it spelled?
levelling
