Rowbotham was a victim of a superior mirage. When flat-earthers hear this, they normally respond by dismissing this as impossible, because mirages supposedly are inverted images, but Rowbotham saw the boat right side up the entire time. However, this confuses superior and inferior mirages. What is the difference? First we must discuss the physics of light a bit.
66) Dr. Rowbotham conducted several other experiments using telescopes, spirit levels, sextants and “theodolites,” special precision instruments used for measuring angles in horizontal or vertical planes. By positioning them at equal heights aimed at each other successively he proved over and over the Earth to be perfectly flat for miles without a single inch of curvature. His findings caused quite a stir in the scientific community and thanks to 30 years of his efforts, the shape of the Earth became a hot topic of debate around the turn of the nineteenth century.
In the past 60 years of space exploration, we’ve launched satellites, probes, and people into space. Some of them got back, some of them still float through the solar system (and almost beyond it), and many transmit amazing images to our receivers on Earth. In all of these photos, the Earth is (wait for it) spherical. The curvature of the Earth is also visible in the many, many, many, many photos snapped by astronauts aboard the International Space Station. You can see a recent example from ISS Commander Scott Kelly's Instagram right here:
The Rev. D. Olmsted, in describing a diagram whish is supposed to represent the Earth as a globe, with a figure of a man sticking out at each side and one hanging head downwards, says "We should dwell on this point until it appears to us as truly up," In the direction given to these figures as it does with regard to a figure which he has placed on the top! Now, a system of philosophy which requires us to do something which is, really, the going out of our minds, by dwelling on an absurdity until we think it is a fact, Cannot be a system based on God's truth, which never requires anything of the kind. Since, then, the popular theoretical astronomy of the day requires this, it is evident that it is the wrong thing, and that this conclusion furnishes us with a proof that the Earth is not a globe.
Astronomers tell us that, in consequence of the Earth's "rotundity," the perpendicular walls of buildings are, nowhere, parallel, and that even the walls of houses on opposite sides of a street are not! But, since all observation fails to find any evidence of this want of parallelism which theory demands, the idea must be renounced as being absurd and in opposition to all well-known facts. This is a proof that the Earth is not a globe.