OK 1864 the light house was 59 feet tall. Not really sure how high the rock that it was constructed on was above sea level, so I will assume it was between 5 and 10 feet. Making the light house about 65-70 feet above sea level.
http://en.wikipedia.org/wiki/Eddystone_Lighthouse#Smeaton.27s_lighthouseI will now do some number crunching using Rowbotham's own chart.
[url]http://www.sacred-texts.com/earth/za/za05.htm[url]
Now, we don't know how high above sea level the telescope was placed. I will assume around 6 feet as I am 6 foot tall.
A height of 6 feet above sea level causes the horizon to be about 3 miles out.
So now the light house is 11 miles further past the horizon.
As 11 miles is not on his chart, I must use his calculation to determine the drop.
So 11^2 = 121
121*8=968
968/12=80
So there is only a drop of 80 feet. A difference of 10-15 feet.
IMO, since I made quite a few assumptions about the problem, mainly how high the rocks are, and how high the telescope was set up, I believe that it is well within possibility that they did see the light house. You change those two factors, and the light house would easily be visible.
So now jroa, please show your number crunching that shows the light house should have been 40-60 feet lower. Or at least a source where the numbers are calculated.
BTW, remember, I used Rowbotham's own numbers and showed that it is very possible that the light house is visible.