The values of neutrino masses and mixing angles which are required by the Mikheyev-Smirnov-Wolfenstein (MSW) solution to the solar-neutrino problem are found from analytic solutions to the neutrino propagation equations in the Sun. They coincide with those obtained through extensive numerical computations by Rosen and Gelb. They divide into three classes of oscillation parameters that can solve the solar-neutrino problem. The gallium solar-neutrino experiment will be able to test only two alternatives. However, the third alternative yields sizable oscillations of atmospheric neutrinos in Earth which can be detected by the massive deep-underground proton-decay detectors and neutrino telescopes. Finally, some solutions yield a sizable amplification of neutrino oscillations in Earth which change both the flavor and the spectrum of solar neutrinos that reach terrestrial detectors at night. The day-night modulation of the flux of solar neutrinos perhaps can be used to establish their solar origin in the radiochemical detectors and the MSW solution to the solar-neutrino problem.