Severndroog Castle was part of the mapping survey of England. In 1783, the Royal Society and the Paris Observatory agreed to work together, in the name of science, to measure and map distances between London and Paris. The Castle was one of the survey points for this project. By 1788 the rest of England had been surveyed. By 1791 there was a risk of invasion from France, and more surveys were needed. Surveying was started by William Roy, and continued through the 1790s by William Mudge.
The approach they used is called triangulation. This is a surveying method based on the relationship between the angles and sides of a triangle.
This diagram explains the principle. The distance between two known points was measured and called the baseline. From each end of the measured baseline, the third point of the triangle was sighted and the angles to it measured.
Once all the lines and angles are drawn, the position of a far distant point is found where two lines of sight cross. The sides of the first triangle then become the new baselines for more triangles to be drawn using sightings of more distant points. In this way, large areas can be covered.
A vital piece of equipment was the theodolite. This was a rotating telescope to measure vertical and horizontal angles. The Great Theodolite, made by Jesse Ramsden, was placed on a wooden scaffold on the roof of Severndroog Castle. It is now in the Science Museum in London.