I came across this thought experiment, and I even think I have a solution for it, but my book insists that I am wrong. Consider a completely airtight shere, filled with air. Applying any sort of pressure outside the sphere surely cannot increase the airpressure inside the sphere? (assuming that the volume of the sphere is constant). As I see it, only a change of volume, amount of substance or temperature can change the pressure of the air. I believe that the book incorporates the method of simply adding pressures together. This works fine when asking for a total pressure at a certain depth at sea (total pressure equals the airpressure and the hydrostatic pressure), but surely it cannot work for the "sphere problem" Thoughts?