OK, I know they’re probably not telescopes; more than likely some sort of directional compass and perhaps level. What the heck are people looking for or at specifically when they peer through these things at someone holding a stick a few hundred yards away?
Are they using plain, ordinary magnetic compasses to position (presumably with a great deal of accuracy) the flag pole at the other end?
I asked this question a long time ago but can’t find the thread. The device is called a Theodolite.
Basically, they’re doing a lot of triangulation based on optical rangefinding and other means of measuring distances and angles - both elevation and compass heading.
In the old days, surveyors had to physically drag known-length chains from the instrument to a target location. Not so bad on open ground, but on the other side of a river? Or across a highway? Not so good. As soon as optical rangefinding became accurate, the old chains were rapidly abandoned.
Now, the state of the art is represented by devices known as “total stations”. Optical rangefinding is replaced with lasers and calculating distances based on the speed of light and how long it takes for a reflection to come back.
Total station setup is much simpler than older transits or theodolites. The operator no longer has to painstakingly level the device - thanks to internal gyros, they are now self-leveling.
The basic math involved to say, measure the height of a building is simple.
Take a distance reading to a marker at ground level, then take a reading of a marker at roof level. The total station now has the angle from level for the two targets, so it can calculate the angle between the two points, and it also knows the distances of those two legs. A little seventh-grade trig to find the other leg’s length, and there’s the hight of the building. It takes longer to read this than it does to actually do.
Surveying (the old way) used two optical instruments atransit and a level.
When you saw someone looking through an instrument he was doing one of two things. 1) locating a point relative to a known location by measuring the angle from true north or some landmark. Or 2) he was determining the difference in elevation between the point where the instrument was located and the point where the rod (stick) was located.
In the first instance, in order to locate the point the distance from the location of the instrument to the rod (stick) needs to be measured. The transit can be used to do this in one operation to an accuracy of about 1 part/100. If that isn’t good enough you must measure the distance using a surveyor’s chain (a metal tape measure), or these days a laser range finder. I’m unsure of the accuracy of laser range finders however I believe that for real precision a chain still must be used.
The ordinary land survey for things like farms or residential building lots a precision of 1 in 1000 to 1 in 5000 is good enough. For surveying in Manhattan where land sells for stratospheric prices that’s not even close and I wouldn’t want to guess at what precision is good enough. I do know that for such precision surveying zero temperature coefficient metal chains were used and they were pulled to a calibrated tension using calibrated scales to measure the pull on the chain.
As an added note. All surverys must be closed. You start from asurvey monument or benchmark, which is a known location. After you have completed the survey you must continue the survey either back to the original benchmark or to another benchmark in order to compute the error of closure. Otherwise you have no idea how accurate your survey is.