As skeptical scientist pointed out the results of the experiment failed when unbaised people attended the experiments.
If you are planning on reading through the experiments I will save you some time.
There are basically four types of explanations he uses to say the earth isn't round. I say explanations because sometimes (due to his rambling style of writing) the "experiments" contain a couple of explanations that aren't connected to the "experiment". You will also note that his "experiments" are mostly vague and sometimes don't actually really say anything (e.g. EXP 10, it's really just an introduction to EXP 11).
1. A "lack" of obstructed vision.This is basically denying that ships disapear over the horizon. From what I've seen his maths is correct but the results have been falsified. Conducting similar experiments yourself should demonstrate this.
2. A "lack" of curvature to the horizon.This is basically denying that the horizon curves, saying that because we can't see it with our eye when we are close to sea-level it doesn't exist.
3. A "lack" of a dip to the horizon.These are probably the funniest experiments because the results confirm what you would expect on a round earth and Rowbotham then goes on to suggest that a naked eye is more accurate than the equipment he used. He's basically saying that because (when viewed without equipment) the horizon appears at eye level it must mean it hasn't descended at all.
4. Altitude over distance.These are also close to being the funniest. With these Rowbotham basically takes two points a fair distance apart (e.g. London & Liverpool) and says that because they're at the same altitude that they must be level with each other. He then creates an imaginary line that goes through the earth and shows how much higher a point in between would be "if" the earth was round. The funny thing is he's quite accurate, if you drilled a tunnel between the two points the point referred to in between would be that much higher than the tunnel.
Of course my favourite "experiment" is this one...
EXPERIMENT 3.A good theodolite was placed on the northern bank of the canal, midway between
Welney Bridge and the
Old Bedford Bridge, which are fully six miles apart, as shown in diagram, fig. 7. The line of sight from the
"levelled" theodolite fell
FIG. 7.
upon the points B, B, at an altitude,
making allowance for refraction, equal to that of the observer at T. Now the points B, B, being three miles from T, would have been the square of three, or nine times 8 inches, or 6 feet below the line of sight, C, T, C, as seen in the following diagram, fig. 8.
FIG. 8.
I highlighted the part where he tampers with his results. Depending on how high the theodolite was depends on how high up the bridge it would land. The "6 feet below the line of sight" refers to how much lower the ground is at 3 miles, so if the bridges were taller than 6 feet it is likely that they were visible at 3 miles - and that's assuming you were on the ground, if you aren't a worm yourself they wouldn't even need to be 6 feet tall.