The Nagaoka potential used to describe the kinetics of particles in the atom is the Coulomb potential of a geometrical point center of the atom that is given by V(r) = E/r, where r is the distance from the point center and E is a positive charge of the center.
The 1st term in the potential V is the Coulomb potential of the point center of the atom; the remaining terms come from the uniform distribution of electrons that is negligibly small compared with the 1st term.
Figure 3 provides a pictorial comparison of their models in light of the Coulomb potential that they used.
Rutherford must have read the 1904 Nagaoka paper (3) in bewilderment, while finding the Coulomb potential of the core of the atom to be the same as that which he assumed for a point center.
In view of the Coulomb potential they used, it is hardly acceptable that such a statement as Rutherford made is a fair reference to Nagaoka, though some people considered that it was proper, (33) or that Nagaoka might have been grateful for it.