The level of accuracy you need scales with the problem you have. If you want to measure the distance between to points in a city something like a meter is quite ok, if you want to make an accurate drawing of something, maybe a millimeter is sufficient, a biologist investigating some cell material needs a micrometer scale, and in the semiconductor business you go down to some angstroms.
If you do standard optics, you don't have to solve the Schrödinger equation for the photons involved, but if you're playing with single photons it could be necessary.
There is no universal rule for the level of accuracy.
This was questioned in an earlier thread. ‘Accurate’ is relative, of course. There is accuracy down to the molecular level, and there is accuracy for the purpose of everyday measurement.They both look like levels to me, though once checked for accuracy they may be suitable to do part of what you want.
With the help of my late father-in-law’s theodolite, which I am just beginning to understand, I can determine this. The first picture below shows the whole instrument. It was made by Clarkson and co Holborn, and the case says it was inspected 17th April 1962. Incidentally, my father-in-law worked for the British government, travelling to distant places to check the amount of land the government owned or controlled. I don’t know if he was in on the conspiracy, he never mentioned it.
You should just be able to see the bubble in the spirit level, which I set level before the photo was taken. This was done by turning the dial in the second picture. The idea is that when the bubble is in the centre, the optical tube is absolutely level, i.e. on a line perpendicular to the force of gravity, and any object appearing in the horizontal crosshair will lie on that line. It follows that if the horizon appears below the horizontal crosshair, it does not lie on that line. Rowbotham claimed that there were ‘collimation’ distortions in such instruments, but haven’t seen any evidence so far.
(http://www.logicmuseum.com/w/images/a/a9/Theodolite.JPG)
(http://www.logicmuseum.com/w/images/4/4d/Level.JPG)
This https://en.wikipedia.org/wiki/Theodolite#/media/File:Theb1982.jpg shows a theodolite with 0.2 arcsecond precision, i.e. 60 times the precision of the instrument I have.That's fine if you need it, but from only 10 ft above sea-level the horizon dip is 0.056° or over 3 arcminutes so your 30 arcseconds, or 0.5 of an arcminute would tell you a lot.
That's fine if you need it, but from only 10 ft above sea-level the horizon dip is 0.056° or over 3 arcminutes so your 30 arcseconds, or 0.5 of an arcminute would tell you a lot.
One thing a theodolite can do is to flip the telescope 180° and rotate 180° using the horizontal scale and so do a self-check on level.However this wouldn't correct for Rowbotham's 'collimation error' i.e. the tendency for the instrument to show the horizon lower than it truly is.
This was questioned in an earlier thread. ‘Accurate’ is relative, of course. There is accuracy down to the molecular level, and there is accuracy for the purpose of everyday measurement.
One thing a theodolite can do is to flip the telescope 180° and rotate 180° using the horizontal scale and so do a self-check on level.
If the theodolite can flip through 180 degrees in a vertical arc, then measuring the arc of the sky (as i did with a sextant) would be a doddle.
A nice high point on an island, or headland would be great, and measure both opposite horizons to get the arc of the sky...
Anyway, as to the original question, i believe it is, and is as accurate as need be.
For example, chart surveying for cartography does not need to be defining objects to a precision of better than a metre in the horizontal datum, as the users (ships) wont be needing them that accurate, (most GPS systems are not more accurate than that) so the methods and standards reflect that.
However i am sure the surveying methods for building bridges are a bit more accurate, as it would be a bit of a pain if the 2 ends were built to meet in the middle, and they were a few feet off! Therefore the methods and accuracy required are determined by the end result.
I would expect someone can detail some other instances where the siting of equipment etc is required to be much more precise, even closer than 1 MM tolerances.
The reason the world is not surveyed not the same accuracy is 1, cost, and 2, need, amongst other things.