For practical considerations one may assume a proton at the orbital center since the effect is quite small (the proton is 1836 times more massive). However, for purposes of calculation (to 1 part in 50,000,000) it must be accounted for. The velocity of the electron in the ground state must be modified by recalculating the radius of centripetal force, i.e. the electron is at one end of a dumbell balanced at a point between the electron and proton. Namely, 1836.1527... / 1837.1527... of radius=h/aB . Since h=1 in our previous calculation, the new radius is (1836.../1837...) / (aB) = .99945568 x 251619.002 = 251482.0407 The velocity of the electron must therefore be somewhat slower because it traverses a shorter circumference in the same time. Then, a_{r} = a / (1  [ a/(1+B) ]^2 )^1/2 From Eq.#2 sec.19 ... a_{r} = a / (1  a^2)^1/2 Replacing the right side of Eq.#2 with the right side of the equation given here above ... into the final equation in sec.19 a_{r} = [ 3/2^1/3 {B_{r} ^4 / (2/3^2/3)}^1/2 ]^1/3
yields a new general equation relating the e/P mass ratio and FSC with due consideration for the electron gfactor.
Unfortunately, this "fix" only affects the eighth digit (1836.1517...) yielding a final value of 1836.15195...Whereas we are looking for 1836.1527... a "shortfall" of .0008 , i.e. 1836.1519 + .0008 = 1836.1527.I am here accepting that the seventh digit, 2, is "secure" meaning that the past history of Codata type evaluations indicates that this digit is very unlikely to change with further refining experimentation. I consider this shortfall to be caused by some gross error in my approach rather than something trivial. Addendum: 3282000 New Codata estimates (1998) favor me slightly. If evaluated with the new numbers my "shortfall" would be about .0005 instead of .0008. I don't consider this enough to get me on the right track though. I wouldn't want to be off by more than .0002 at this juncture.
Addendum: 12142004 codata 2002 7.297 352 568(24) x 103 = FSC 1836.152 672 61(85) = e/P mass ratio Evaluated to ~12 digits (in my shorthand for eq. parts): 1:54 AM 12/13/2004 a....6.23373009138 x104 =alpha^1.5 b....2/3 ^1/3 = .873580464736 c....[1alpha^2] = .9999467486455 .... ^1.75 = .9999068119905 axb= .00054456648302665 axb/c = .000544617234822705 1/[axb/c] = 1836.151954 and figure another .0002 for gfactor correction still gives a .0005 shortfall .... 1836.1521
Note:
[ 11/137.0359895^{2} ]^1/2 = .99997337397
A large shift in velocity (in the 5th significant digit) produced a change in the Bohr magneton generating output in only the 8th digit (and a smallish change at that). The robustness of gfactor calculations (about which scientists sometimes seem overly proud) are byproducts of the forms of the equations rather than from experimental "technique".
