The number 137 expresses the translation component n of the path s of the electron on Bohr orbit .
The two-sided distribution ranges from the translation n = -[infinity] to n = 137 on Bohr orbit and further from there to n = [infinity].
z] rapidly lessen in the negative as well as positive direction from the zero numbered position z on Bohr orbit so the enough accurate value of the constant can be calculated numerically on the appropriate finite interval, for instance n = [104,170]:
Such special distribution of the frequencies of the path of the electron is considered on the zero position and zero sides on Bohr orbit.
According to the double surface model  where the characteristic values for the path and its translation component on Bohr orbit are s = 137.
elliptic] = [infinity] The infinite elliptic radius allows the electron to move uniformly on Bohr orbit.
Its destiny is to be in some way glued on Bohr orbit in the Hydrogen atom.