# Why the permutation of the right hand rotor given in Rejewski's paper is $PNP^{-1}$?

I would like to know why the permutation of the right hand rotor given in Rejewski's paper is $$PNP^{-1}$$. First of all I can't get how he added an $$P$$(alphabetic permutation) at the front of $$N$$(right hand rotor permutation) when there's no alphabetic permutation taking place before the current enters the first rotor permutation. As far as my knowledge goes I think there's only a plugboard swapping that takes place. Second I can't get how an inverse permutation takes place before the current through $$N$$(right hand rotor permutation) enters the middle hand rotor.

When ring setting is 01 (A) and indicator shown through the corresponding window is A (01) as well, the wiring core is at its home position. Suppose ring setting is $$r$$ (variable $$r$$ not letter $$\tt R$$) and indicator shown is $$s$$. Their combined effect is turning the wiring core forward (or counterclockwise when viewing from the right of the machine/rotor) by $$n$$ places, where $$n=(r-1)-(s-1)$$ (mod 26). Suppose input letter is $$x$$. Output letter $$y$$ is given by $$y=(x)P^n N P^{-n}$$. If you will allow me to be very verbose on left association, I can write $$y = \Big( \big( (x)P^n \big) N \Big) P^{-n}$$.