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Disclaimer: not a surveyor.
Yes, the errors would indeed start to add up. ~~For latitude, this isn’t a problem because you can always measure that from the stars to verify it. For longitudes, not sure what they did~~ (Yeah, this isn’t accurate enough). My guess is that they also tried to start in the middle and work their way to both oceans rather than go in one long chain.
My friend used to work for a Texan civil engineering firm and even today, it is still common to have land disputes because the land was either surveyed wrong, or there are measurement errors from when they did it the old way. An error of a meter over a couple of miles of ranch land wasn’t a big deal back when it was first titled, but after being subdivided into small plots of land for houses, that error suddenly becomes huge. From I remember him saying, it was not unusual for both you and your neighbor’s surveying stake areas (Sorry, I forgot what these were called. They are rods that are put into the ground to demarcate the land) to be overlapping when checked against satellite positioning. So now both would need to go to arbitration to figure out the best way to fix it.
Yeah, it wasn’t perfect, but it was the best that could be done until surveying with aircraft or satellite came around.