That post was this:
I just disagree. Since the inverse square law of charge attraction is analogous to gravity, consider the following comparison. We have a ball of metal of a certain mass that is suspended above the earth at a certain distance (between the earth's centre of gravity and the ball's centre of gravity). Knowing the distance and the mass of the ball we can calculate the force of gravity acting on the metal ball. Now say that ball broken into a number of different sized pieces, and each piece is suspended above the earth at the same distance as the original ball. What is the total force of gravity acting on the pieces? It will be the same as the the force acting on the singular ball. Similarly if the metal ball was flattened into tinfoil thickness and spread across a large area. The force of gravity acting on it will be the same. So, I don't see a problem in what Mills is doing there.
Although I see why you believe the change density should be uniform, you have to consider that this is charge on the move, so things are different. If I recall the product of the charge density function and the velocity function, which yields current density, has to be uniform.
If you're invoking the hairy ball theorem, I'm doubtful that it applies here, because each point has multiple velocity components, that is, current overlap in different directions.
The whole things requires some serious thought and rigour which I can't provide. If you are not satisfied by Mill's reasoning and rigour (which I assume you have seen in chapter 1), I won't be able to change your mind. But at least you tried and have come to a considered opinion.