36 “During Captain James Clark Ross’s voyages around the Antarctic circumference, he often wrote in his journal perplexed at how they routinely found themselves out of accordance with their charts, stating that they found themselves an average of 12-16 miles outside their reckoning every day, later on further south as much as 29 miles.”
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.