39. An Almanac published in the 1870's stated a distance between Sydney and Nelson that disagrees with current maps

“Practical distance measurements taken from “The Australian Handbook, Almanac, Shippers’ and Importers’ Directory” state that the straight line distance between Sydney and Nelson is 1550 statute miles. Their given difference in longitude is 22 degrees 2’14”. Therefore if 22 degrees 2’14” out of 360 is 1550 miles, the entirety would measure 25,182 miles. This is not only larger than the ball-Earth is said to be at the equator, but a whole 4262 miles greater than it would be at Sydney’s southern latitude on a globe of said proportions.”

Incorrect historical information and Dubay does not know how to do trigonometry.

Once again Eric Dubay resorts to historical sources, in this case The Australian Handbook, Almanac, Shippers’ and Importers’ Directory” which was published between 1872-1879.

The distance it is reported as quoting between Sydney and Nelson is 1550 miles which is incorrect. The Almanac might not have been quoting the mileage as the crow flies, or maybe they just got the distance wrong but the accurate distance is 1309 miles.

In addition Dubay has forgotten to take into account that Sydney and Nelson are not both sitting on the equator, which is the only place where his crude 22 degrees 2’14” calculation would work.  Latitude matters.

Sydney co-ordinates are Latitude -33.87° (-33° 52' 7"), longitude 151.21° (151° 12' 33")
Nelson co-ordinates are Latitude -41.27° (-41° 16' 14"), longitude 173.28° (173° 17' 2")

So Dubay has an incorrect distance and an incorrect number of degrees between the two locations.  It is not surprisingly he gets a figure that does not match the known diameter of the globe.

The correct formula to work out the angle between two points A and B on a sphere is:
acos(
          sin( latitudeA ) * sin( latitudeB ) +
          cos( latitudeA ) * cos( latitudeB ) * cos( longitudeB - longitudeA )
)
Note if you want to try this in a spreadsheet you need to convert the longitude and latitude to radians for the formula to work.  The answer is given in radians.
Using the correct calculation the angle between Sydney and Nelson is 18.9 degrees  If we take the correct mileage between Sydney and Nelson, 1309 miles, our calculated circumference of the Earth is (1309 * 360 ) / 18.9 = 24,901 miles.  Surprise surprise this agrees EXACTLY with what scientists say the circumference of our spherical Earth is.

Back to school for you Mr Dubay.


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