"On the basis of Lorentz's theory, if we limit ourselves to a single spectral line, it suffices to assume that each atom (or molecule) contains a single moving electron"

Pieter Zeeman's quote is referring to the Lorentz theory, which specifies that the spectral lines of an atom or particle are brought on by the motion of electrons. Zeeman is suggesting that if we focus on a single spectral line, then it is reasonable to assume that each atom or molecule contains a single electron in movement. This is since the motion of the electron is what causes the spectral line. This theory was advanced at the time, as it supplied a description for the spectral lines that had actually been observed in the past. It likewise provided a way to understand the behavior of atoms and molecules, which was previously unknown. Zeeman's quote is a testament to the importance of the Lorentz theory and its implications for the study of atoms and particles.