Let B denote a ball centered at the origin with radius R=(4pi-1/pi). Gravitational forces from a singularity generate rotation about an axis. Internal rotational forces form a vacuous prolate ellipsoid, with major axis (4pi-1/pi) and minor axes {1/pi, 1/pi}. The ball B ejects a volume (4pi/3)(pi^(-2))(4pi-1/pi). This is the volume of the circumscribed prolate ellipsoid. It is also the volume of an elliptical wedge with curved surface area 4/pi and the elliptical sector with curved surface area 4/pi. It is not unreasonable to suppose that the electron is a ball of unit radius. The volume of the electron is V_e = (4pi/3). The ratio of the volume of ball B to the volume of the electron is given by V_B/V_e = (4pi-1/pi)^3 = 1837.392727.... Let V_w be the volume of the wedge of ejecta. (V_B-V_w)/(V_e) = (4pi-1/pi)^3-(pi^(-2)(4pi-1/pi) = 1836.15 Look at V_w. V_w/V_e = (pi^(-2))(4pi-1/pi) = 1.24098801$. This ejecta easily supports a charged unit ball, whereas the original ball only had the property of gravitational attraction. At this point we have the basic two stable particles, namely the proton and the electron. We then look at the mass ratio of the proton to the electron. V_p/V_e = (V_B-V_w)/(V_e) = 1836.15 There are several expressions that yield the same numerical value as the previous equation. First among equals is (4pi)(4pi-1/pi)(4pi-2/pi) = 1836.15 Moreover, 64pi^3-48pi+8/pi = 1836.15 The above equation is the original estimate. harry.watson@att.net