I can see that bound electrons are treated as spherical surfaces (with non-uniform charge and mass density, characterised by spherical multipoles defined on the associated Legendre polynomials) in the Introduction (I.63 to I.65). (By the way, these expressions are the ones that Rathke shows are not solutions to the wave equation - don't forget to give us a link or reference to Mills's rebuttal).
However in Chapter 10, the chapter where Mills ostensibly works out the orbital radius and ionisation potential of atoms with electrons numbering from three to 20, he treats the electron as a point particle:
- Take for example 10.12, his expression for the radius of the outer electron of the lithium atom, in which he sets the central centrifugal force on the electron equal to the electrical and magnetic forces on it - mv^2/r is the centrifugal force on a point rotating with velocity v at radius r.
- He repeats the use of expressions which relate to points throughout this long, tedious and numerological chapter, in many cases explicitly stating that the forces are central forces, which are not consistent with an extended spherical body centred on the nucleus. For a very small sample see 10.2, 10.29, 10.36, 10.56, 10.98 etc etc ad nauseam. And in fact the assumption of the electron as a point charge and mass is implicit in almost every expression in Chapter 10.
Given that one foundation of his hypothesis is that the electron exists as an infinite series of multipoles on a sphere, and that in this chapter, in which he performs the trumpeted task of predicting the ionisation potentials of a vast number of multi-electron atoms up to 20 electrons, he treats the electron as a point mass and charge (in other words, as a point particle), then there seems to be a rather disturbing inconsistency in his hypothesis. Since his predictions are plainly based on conditions which are grossly inconsistent with his foundational idea, then aren't we justified in raising our eyebrows?