Since maps are drawn under the presumption of a Round Earth, and since globes are inherently inaccurate due to form; we must conduct a query based purely on observational data - quotes from mariners who have personally sailed and charted the southern seas.
Specimen A:
In the "Cruise of the H.M.S Challenger," by W.J.J. Spry, the distance made from the Cape of Good Hope to Melbourne is stated to be 7,637 miles. The Cape is in latitude 34o 21' south and Melbourne in latitude 37o south, the longitude of the Cape being 18o 30' east and Melbourne 145o east. The middle latitude is 35.5o. Difference of longitude 126.5o, which makes the distance round the world at that latitude (35.5o) to be over 25,000 statute miles and as great as the equator is said to be. Thus we see on reliable evidence that the further we go south the greater the distance round the world. This latter distance is many thousand miles more than the purely theoretical measurement of the world at that latitude south. From the same work we find the distance from Sydney to Wellington to be 1,432 miles. The middle latitude is 37.5o, and the difference of longitude 23o 36', which gives as the distance round the world at latitude 37.5o south, 25,500 statute miles! This distance is again greater than the greatest distance round the 'globe' is said to be and many thousands of miles greater than could be the case on a globe. Thus, on purely practical data, apart from any theory, the world is proved to diverge as the south is approached and not to converge, as it would do on a globe.