The nonmagnetic, inertial-electrostatic confinement of ionized gases in spherical geometry is discussed theoretically, and associated experiments are described. Assuming monoenergetic ion and electron distribution functions, the Poisson equation for bipolar currents is solved numerically. The results indicate spatially periodic solutions which respresent the alternate formation of virtual anodes and virtual cathodes. Particle pressures are found to vary approximately as the inverse square of the radius and extremely high electric fields are indicated. Near the center of the spherical cavity, there exists a high-density, high-energy region, which may be of controlled fusion interest.The experimental apparatus consists of a hollow spherical cathode concentrically placed within a spherical anode on which six ion guns are located. Steady, reproducible operation up to -150 kV and 60 mA yields a copious neutron emission, a part of which originates from a luminous spherical region within the cathode. After crowbar of the main power supply, approximately 1016 particles are released from within the cathode. This number is significantly greater than the 1012-1014 ions/cm-3 calculated from the fusion rate. The difference is attributed to the formation of two or more virtual anodes. A bremsstrahlung collimation study indicates a spatially periodic emission pattern, suggesting the formation of at least two virtual anodes, the outer of which is about 2.5 cm in diameter. No instabilities have been observed.