A number of weeks in the past I discussed that I used to be studying Stephen Ambrose’s account of the Lewis & Clark expedition and wrote a submit about their astronomical measurements. James Campbell left a remark recommending Edwin Danson’s ebook [1] on the historical past of the Mason-Dixon line. I ordered the ebook, and now that work has slowed down for Christmas I’ve had the time to open it.
Along with figuring out their eponymous line, surveyors Charles Mason and Jeremiah Dixon had been additionally the primary to measure a level of latitude in 1767.
What precisely did they measure? We’ll get to that, however first we want some background.
The form of the Earth
To first approximation a level of latitude is solely 1/360th of the Earth’s circumference, however Mason and Dixon had been extra correct than that. Isaac Newton (1643–1727) deduced that our planet was not an ideal sphere however fairly an oblate spheroid. The perfect measurement in Mason and Dixon’s time was that the Earth’s semi-major axis was 6,397,300 meters with flattening 1/f = 216.8.
It’s a little bit of an anachronism to explain the gap in meters for the reason that meter was outlined in 1791. The meter was initially outlined as one ten-millionth of the gap from the equator to the North Pole alongside a terrific circle via Paris.
What precisely is a level of latitude?
If the Earth had been an ideal sphere, a level of latitude could be 1/360th of its circumference. Utilizing the unique definition of the meter, this could be precisely 10,000,000/360 meters. However as a result of the Earth is just not an ideal sphere, every diploma of latitude has a barely completely different size. To place it one other approach, the size of a level of latitude varies by latitude.
One other complication because of the flattening of the Earth is that there are a number of methods to outline latitude. The 2 commonest are geocentric and geodetic. The geocentric latitude of some extent P on the Earth’s floor is the angle between the equatorial airplane and a line between the middle of the earth and P. The geodetic latitude (a.ok.a. geographic latitude) of P is the angle between the equatorial airplane and a line perpendicular to the Earth’s floor at P. Extra on the distinction between geocentric and geodetic latitude right here.
What did Mason and Dixon measure?
Because the size of a level of latitude varies, we have to say at what latitude they measured the size of a level. In brief, they measured the size of a level close to what we now know because the Mason-Dixon line, the border between Pennsylvania and Maryland.
To be extra exact, the start line was Stargazer’s Stone, a stone positioned by Mason and Dixon on John Harland’s farm close to Embreeville, Pennsylvania, to some extent a few diploma and a half due south close to what’s now Delmar, a city on the Deleware / Maryland border.
I’ve had some issue figuring out how correct Mason and Dixon had been. Some sources I’ve discovered are clearly mistaken. I haven’t verified this, but it surely appears Mason and Dixon overestimated the size of a level of latitude at their location by solely 465.55 ft or about 0.13%, a exceptional feat given the know-how of their day.
Associated posts
[1] Edwin Danson. Drawing The Line: How Mason and Dixon Surveyed the Most Well-known Border in America. John Wiley & Sons. 2001.
