This was questioned in an earlier thread. ‘Accurate’ is relative, of course. There is accuracy down to the molecular level, and there is accuracy for the purpose of everyday measurement.

With the help of my late father-in-law’s theodolite, which I am just beginning to understand, I can determine this. The first picture below shows the whole instrument. It was made by Clarkson and co Holborn, and the case says it was inspected 17th April 1962. Incidentally, my father-in-law worked for the British government, travelling to distant places to check the amount of land the government owned or controlled. I don’t know if he was in on the conspiracy, he never mentioned it.

You should just be able to see the bubble in the spirit level, which I set level before the photo was taken. This was done by turning the dial in the second picture. The idea is that when the bubble is in the centre, the optical tube is absolutely level, i.e. on a line perpendicular to the force of gravity, and any object appearing in the horizontal crosshair

*will lie on that line*. It follows that if the horizon appears below the horizontal crosshair, it does not lie on that line. Rowbotham claimed that there were ‘collimation’ distortions in such instruments, but haven’t seen any evidence so far.

The instrument says that each division on the spirit level corresponds to 30''. I looked this up and this means 30 arcseconds, i.e. 0.3 of an arcminute, where an arcminute is 1/60 of a degree. If you think back to schooldays, one degree is pretty small, and 1/60 of a degree much smaller than that. I now need to work out how much difference that division would correspond to over 30 miles.

More schooldays. 30 arcseconds is 0.000145444 radians, 30 miles is 5,280 feet. Therefore to work out how much the 30 arcsecond division on the theodolite corresponds to, I use the tan function to convert the angle in radians to get the opposite/adjacent ratio. Then I multiply this ratio by the adjacent amount (30 miles in feet) to get the error in height. This works out to 23 feet. The question is whether we could live with that. Of course this is not a super high precision instrument. That said, when I levelled it, even a small pressure on the desk, even changing position in the room, caused a noticeable movement in the bubble.

Later on I plan to take the instrument to the

North Kent coast where the wind farm and the Shivering Sand fort are a known distance from the coast.