For those who replied to my questions on the Atomic radii of Isotopes and those who claim the vacuum force is fictictious. I have just overlaid a graph of atomic radii with a graph of the vacuum force using a group of 18 isotopes. There is only a small dissagreement between the two plots. This error can reasonably be attributed to the fact that I have to start with radii that are average figures, without knowing how this average is achieved. It will be several weeks before I can complete work on most of the isotopes listed in Emsley's Table Of Elements but I know think a good case can be made for claiming that the vacuum force does exist and it determines the atomic radii. This means that I now have a very tentative beginning of a mathematical theory that supports my concept of a single force universe. This would not have been possible without 'Physicsforums' and I am very grateful to those who answered my request for help.