In the Context of Sir Arthur Eddington

To All:
In the context of Sir Arthur Eddington,
http://en.wikipedia.org/wiki/Arthur_Stanley_Eddington
and more definitive universal constants available at this time,
I would like to know why the following energy correlation
between universal constants dimensionally and numerically holds:

h*H = 2*G*m^2/R

h = Planck constant 6.62607E-27 g cm^2 sec^-1
H = Hubble constant 2.31E-18 sec^-1
G = Newton constant 6.6725985E-8 cm^3 sec^-2 g^-1
m = mass (~110*electron mass) or (~.06*proton mass) 1.00E-25 g
R = radius of proton 8E-15 cm

Quantum theory is represented by 'h'
Universe expansion is represented by 'H'
Gravity is represented by 'G'
The proton which represents a substantial part of the universe mass
is represented by the proton radius 'R'
and an intermediate mass between the proton and electron
is represented by its mass 'm'.

The equation's simplicity is assumed to be indicative of reality.
It looks like something Sir Eddington would have done
in his many attempts to link proton mass to universe mass
with the Eddington constant
which he mistakenly believed to be the integer 137
but conceptually may be near the truth.

Richard D. Saam