To quote from the
Stanford university website:-
Challenge: How to measure the roundness of a sphere at the precision level of 1/10th of one millionth of an inch? The British instrument company, Rank, Taylor, and Hobson, created the Talyrond instrument for measuring the sphericity or roundness of GP-B gyroscope rotors using a stylus mounted on a round spindle to encircle a gyroscope rotor. However, they could not produce a spindle that was itself perfectly round, and thus the spindle introduced error into the measurement.
Solution: Combine the errors in the spindle's roundness with the errors in the sphere being measured. Then, rotate the sphere to a new position and repeat the measurement.
The measurement errors in the roundness of the spindle remain constant, while the measurement errors in the sphere change with each new position. After repeating this process several times, it is possible to separate out the constant spindle error. (The spindle roundness must be checked from time to time, to ensure that it has not changed.)
Result: The spindle roundness errors were calculated and stored in a computer, so they could be reused with different spheres. For each rotor, 16 great-circle measurements were made in the perpendicular plane and one final measurement was made around its equator, tying all the vertical measurements together. The spindle errors were subtracted out of the sphericity measurements, and then the sphericity measurements were translated into contour maps.
