All mid-19th century-explorations relied heavily on celestial navigation, which, over long distances, only works on a spherical model of earth (we'll have more on that later). It is also known that atmospheric refraction (deviation of light through differently dense air layers) increases the further you go into polar regions because of higher gradients in temperature. Furthermore, there is also the huge problem of the antarctic circumpolar current, which until today is a big issue for sailors because of its high forces and speeds, however, it was not fully understood at that time. These three facts combined provide a perfect explanation of how sailors at that time COULD circumnavigate around Antarctica, but many times experienced an offset to the position where they expected to be. Let's say you are today sailing around Antarctica and you only use a sextant for navigation. Trying to determine your position and finding yourself a little off by only 20 miles from where you expected to be, any sailor in the world will tell you that you are actually in quite good shape. It is within your margin of error. Using these methods AND understanding these phenomena, in no way does an offset of 20 miles concern you (geometrically) as a sailor, nor does it dispute a spherical earth.
#37 See #36
#38 See #36
#39 False claim (incomprehension of the model).
The distance between Sydney and Nelson is roundabout 2100 km or 1300 miles or 1135 sm or 18.9°. And 360°*2100km/18.9° is how much? Right, 40,000 km.
I suspect that the cited 1877 "The Australian handbook and almanac, and shippers' and importers' directory" was either not stating a perfectly straight line or that is was just off by a certain amount; unfortunately I don't have a copy of my own. Needless to say, these distances and durations of travel don't work on the flat earth azimuthal map.
I also just found out how to mistakenly get the value of 22°. It is the difference in longitude between these two places. There are two big problems in taking this value as a reference for distance:
1st Sydney and Nelson are not on the same latitude. That means you have to go southeast from Sydney to Nelson and not just east. It's just the wrong line to begin with.
2nd Even if they were on the same latitude, the shortest distance between them wouldn't follow the latitude and the true angular distance wouldn't be 22°. That is because no latitude (except for 0° at the equator) represents the true diameter of earth. If you were to calculate the distance between these two places following the latitude, you would have to use the diameter of your latitude and not the diameter of earth. Anyway, take a piece of string and try to connect two places on the same latitude (except 0°). You will see that the line will NOT follow the latitude, but actually spans an arc around it. It only works for places that lie exactly on the equator.
#40 False claim & incomprehension of the model
The distance between Cape Horn and Port Philip is roundabout 9130 km or 5675 miles or 4930 sm or 82°. And 360°*9130km/82° is how much? Right, roundabout 40,000 km. Same problem as in #39: The true angular distance between two places is not their difference in longitude (except when both lie exactly on the equator). As stated above, this value of 143° is false for more than one reason (since Cape Horn and Port Philip are not on the same latitude either) and will give you false results if you take it as a reference for distance measurement on a sphere.
#41 False claim & incomprehension of the model
Again, phony numbers. The distance between Cape of Good Hope and Melbourne is roundabout 10,300 km or 6,400 miles or 5,560 sm or 92.5°. And 360°*10300km/92.5° is how much? Right, roundabout 40,000 km.
Finally, Mr. Dubay has found two places that are roughly on the same latitude. Unfortunately, that doesn't change the fact that the latitude in no way describes the shortest distance between the two places, nor can it be used as reference for the true angular distance between them. The reasons have been made clear in the above two examples. The following image gives a nice demonstration of the problem:
#42 Incomprehension of the model.
If these numbers should be a disproof of a globe in any way, then you could expect these two cited gentlemen to have allegedly circumnavigated Antarctica, roughly describing a circle around it on a proposed globe. You could then take these described distances and show how they were not consistent with a spherical earth. However, looking at the expedition of Sir Ross, you will find something like this:
For James Cook something like this:
And for the challenger something like this:
The described paths are nowhere near circular. So, in what way do they contradict a spherical earh? If you were circumnavigating Antarctica in the same fashion, these are the exact same distances you would expect on a spherical earth. By the way, none of these explorers has ever claimed that earth was flat.
#43 False claim.
Here it is again, the infamous flight Santiago-Sydney. And yet again, the map problem (#34 & 35). We have previously seen that the azimuthal map of earth is absolutely worthless when it comes to angles, surface-areas or even distances that are not measured directly through its centre.
We see a line with a measured distance of roughly 11,360km (~7,050sm). Coincidentally, this line/distance is perfectly consistent with Qantas Air flights taking off three times a week and directly connecting both of these locations. The "shortest, quickest" route southernly passes New Zealand while it is clearly nowhere near the mainland of Antarctica. As of today, the flight Ident is QFA27 and you can check it here:
To be honest, there would be ONE connection that actually had to directly cross Antarctica with less than 5° away from the south pole. It's Perth-Buenos Aires. Well... nobody flies that route. So, here's the question: How many people can you find to at least once a week fill a large passenger aircraft on that route so Qantas would not direct it over its normal international flight hubs Sydney/Melbourne? If you can explain how Qantas could actually make real profit out of this direct connection, you might have an argument (leaving out the contradictory flat earth distances, of course).
#44 see #43
#45 False claim.
a) South African Airways fly directly from Perth to Johannesburg and back, once every day (as of now: Flight SAA281) . Straight over the Indian Ocean, South of Madagascar and nowhere near Indonesia, India or Dubai.
b) The flight duration doesn't work on the flat azimuthal map (map problem #34&35).
#46 False claim.
As of this day, there is no airline flying directly from Buenos Aires to Cape Town. However, if you compared the flight durations, you would opt for a shorter connection from Buenos Aires right across the Atlantic to Johannesburg and from there back to Cape Town (yes, back! It's shorter and it works!) instead of taking the detour over London. These flight durations don't work on the flat azimuthal map (map problem #34&35).
#47 False claim.
a) South African Airways fly directly from Johannesburg to Sao Paolo and back (as of now: Flight SAA223). Straight over the Atlantic Ocean, once every day.
b) The flight duration doesn't work on the flat azimuthal map (map problem #34&35).
#48 False claim.
As of this day, there is no airline flying directly from Santiago to Johannesburg. However, if you compared the flight durations, you would opt for a shorter connection from Santiago to Sao Paolo and from there straight across the Atlantic to Joburg instead of taking the detour over Dakar. Need I mention, these flight durations don't work on the flat azimuthal map (map problem #34&35).
#49 False assumption.
Nobody says that different temperatures on earth are due to different distances to the sun. These differences are indeed negligible. Conducting a simple experiment will show you how it works:
If you hold your hand perpendicular to a bonfire, it will get warm. Now, keeping your hand at the same distance, tilt it by say, 64° (same angular displacement between Johannesburg and the South Pole). You will feel that your hand gets much less warm. That should tell you that thermal radiation on a certain area is dependent on the angle of impact, which in fact is the main reason for different temperatures on different latitudes on earth.
By the way, even Johannesburg is never exposed at 90° and the exposure of either pole is always below 23.5° and 0° for about half a year. That's why it's so cold up and down there.