Arthur S. Eddington (1882–1944) certainly was one of the world’s most famous astronomers during the interwar period. For thirty years he was the director of the Cambridge Observatory and taught at Trinity College. From 1916 onwards, he endeavored to develop a series of stellar models, along with some investigation in Einstein’s theory of General Relativity. It will be showed that in both cases Eddington purposely used trial and error, which he considered “as scientific as any other method,” the important point being to obtain physical insight on the problem one intends to tackle, and to keep mathematics “as the tool and not the master in physical research.” Eddington’s final theory published in Relativity Theory of Protons and Electrons and Fundamental Theory is not different, contrary to Matt Stanley’s statement: “The method of Eddington’s unified theory was an almost complete about-face from the method of his astrophysics.” Methodological continuity is the main claim of this talk, grounded on published works and unpublished correspondence.