A pioneer researcher in the field of radioactivity and isotopes, Kasimir Fajans discovered the radioactive displacement law simultaneously with Frederick Soddy of the United Kingdom. The Polish-born physicist taught at the University of Michigan for more than 20 years; and in this concise and systematic study, he surveys groundbreaking research in the study of radioactivity and isotopy.The first part explores radioelements and isotopes, particularly the origin of the actinium series and the stability of isotopes. The second part examines chemical forces and optical properties, starting with an outline of atomic and crystal structures and the ideal ionic linkage. General remarks on the deformability of ions follow, with discussions of the change of the refractivities of ions in molecules and crystals, the transitions between ideal ionic linkage and non-polar linkage, adsorption of ions on salt-like crystals with applications to volumetric analysis, and photochemical applications of ion adsorption.