Many students identify atomism with `the' atomic theory, and consider the truth of the latter established. Textbooks list successes of the atomic theory in classical physics and chemistry. How, then, could outstanding scientists, such as Ostwald and Mach, at the turn of the century, deny the existence of atoms? The best answer is given by these anti-atomists themselves. Their controversy with Boltzmann and Planck illustrates general points in the study of the history and philosophy of science. One argument, the irreversibility paradox, is not resolved satisfactorily to this day. This is Part II of an article, the first part of which appeared in the September issue of Physics Education.