People keep quoting the statement that refraction lies as the key reason that Rowbotham's experiments succeeded. However, the truth remains that differences from vacuum to air and angles of light entry into the atmosphere result in refraction patterns. Such refraction is responsible for even the setting sun and changes in color. The sky being blue during the day proves refraction occurs as well... In Rowbotham's case, every single experiment used a hygromoter (measures water vapor levels), thermometer, and barometer (measures air pressure). We desire not to explain away refraction. We embrace the aforementioned atmospheric phenomena as being probable and realistic.
Plus, when the experiment was done well above the water, it's results perfectly coincided with a round Earth. One of those results is wrong, obviously. Could it be the one that's much closer to the water, where much more severe temperature gradients are comment, and thus is much more susceptible to refraction. Or is it the one that isn't as susceptible to any known phenomena and must then be explained by magic?