Re the Mason Dixon line what exactly was an astronomer bringing to the table for a surveying job?
Prior to the development of accurate transportable clocks, the most accurate way to determine longitude was by astronomical observations. For example the moons of Jupiter comprise a wonderfully accurate clock, visible to anyone with a telescope and readable by anyone with an ephemeris.
John Harrison won the “longitude prize” for his invention of a clock with the required accuracy. For a good read, I recommend “Longitude” by Dava Sobel, which tells his story.
He would have been the one to measure the latitude and longitude with accuracy from various astronomical observations most likely.
If you survey just using distance and direction (compass or theodolite) the errors keep building up and next thing you know that line you shot due west say really isnt due west at the other end hundreds of miles away. And, for that matter, one end actually probably isnt the distance from the other you think it is.
Using astronomical observations to measure the four corners of your house lot is silly, even today probably. So, back in the day they did it with a compass and tape measure and an inclinometer. But once you start going miles and miles the astronomical observations make sense and keep the “drift” in control so to speak.
At the time of the survey, (1760s), there was still no efficient way in which to calculate longitude. The best efforts prior to the creation of an effective chronometer were based on observations of the stars together with almanacs and celestial tables to identify one’s East-West location relative to the sun and stars.
An astronomer would have provided invaluable leadership and direction on such a survey. (Dixon was also an (amateur) astronomer.)
The Mason-Dixon line runs east-west, so there wouldn’t be a need for measuring longitude, anyway. But latitude, now that you can measure quite straightforwardly from astronomical observations. At its simplest, you just measure the elevation of the North Star above the horizon, though this will still give you some small error, since the star isn’t exactly on the pole.
The Mason-Dixon Line turns a corner, forming both the Maryland-Delaware and Maryland-Pennsylvania borders.
To simply draw a straight line, one needs only latitude. To identify the points along that line and identify them as to their location, (with more accuracy than simply reckoning miles along the path walked), longitude is a definite plus. (And, as noted by Peremensoe, the actual Pennsylvania/Maryland/Virginia border included some angles that were not part of the simple East-West line, specifically, the western boundary of what is now Delaware.)
Actually for invention of a portable clock with the required accuracy.
Perhaps the OP confused “astronomer” with “astrologer”.
Indeed, that’s why I used the word transportable.
It would be an interesting demo of the device’s resolution to use a modern “total station” to survey a lot with an astronomical reference. This one claims an accuracy of five arc seconds. I’m not a surveyor, so I have no idea if that is sufficient.
Back of the envelope calculation (and based on logic I haven’t thought through carefully as the coffee hasn’t kicked in).
24,000 miles divided by 360 degrees divided by 60 minutes divided by 60 seconds then times 5 equals:
.092 miles or 488 feet
Note, 60 arc minutes in a degree and 60 arc seconds in an arc minute in case someone doesn’t know.
You underestimated a bit. The mean radius of the Earth is 3959 mi giving 24875 mi as a better circumference which works out to 0.096 mi or just under 507 ft.
Which is why Tennessee and Kentucky have that funny little notch between them.
And, of course, 5 arc seconds would be less in higher or lower latitudes.