Strum, this thread has gotten pretty big and probably a little confusing to you, you are getting a lot of advice.
You asked how surveying works. That is kind of like asking how does a diesel engine work. You could describe that in one sentence, or write a 500 page book about it. A short summary is that we look for evidence. This evidence could be fence, an iron rod, a stone wall, a old surveyors rock etc. We try to match all the angles and distances up and make it fit the persons deed as best as possible. Its like so many other things, its not always black and white and is often a lot of judgement on the surveyors part.
At one time, we used to try to set up on the corners and measure the angles and distance between them. We don't do that very often anymore. You can imagine all the problems with things on line, such as trees and other things that get in the way. Instead we run what is called a random traverse. This is points we set in the ground, set our equipment up on, and measure the angles and distances between these points and then the property corners. We often run this traverse and make a closed loop to check the math for errors. Computers have really helped out and make the computations much simpler.
As far as a surveyor making a bad measurment? A good surveyor does good self checking techniques. .... Mistakes can get made, but a good surveyor will minimize the chance of this.
..... Often the most important tool is a spade and a locator and tile probe. This is how we look for evidence, which is really the important thing.
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What often seems simple to a layman, is often complicated and takes a lot of work on the surveyors part.
..... If he is like so many other surveyors, he is hard working and has the best intersest of the public in his heart.