The Galileo probe mass spectrometer determined the composition of the Jovian atmosphere for species with masses between 2 and 150 amu from 0.5 to 21.1 bars. This paper presents the results of analysis of some of the constituents detected: H2, He, Ne, Ar, Kr, Xe, CH4, NH3, H2O, H2S, C2 and C3 nonmethane hydrocarbons, and possibly PH3 and Cl. 4He/H2 in the Jovian atmosphere was measured to be 0.157 +/- 0.030. 13C/C12 was found to be 0.0108 +/- 0.0005, and D/H and 3He/4He were measured. Ne was depleted, < or = 0.13 times solar, Ar < or = 1.7 solar, Kr < or = 5 solar, and Xe < or = 5 solar. CH4 has a constant mixing ratio of (2.1 +/- 0.4) x 10(-3) (12C, 2.9 solar), where the mixing ratio is relative to H2. Upper limits to the H2O mixing ratio rose from 8 x 10(-7) at pressures <3.8 bars to (5.6 +/- 2.5) x 10(-5) (16O, 0.033 +/- 0.015 solar) at 11.7 bars and, provisionally, about an order of magnitude larger at 18.7 bars. The mixing ratio of H2S was <10(-6) at pressures less than 3.8 bars but rose from about 0.7 x 10(-5) at 8.7 bars to about 7.7 x 10(-5) (32S, 2.5 solar) above 15 bars. Only very large upper limits to the NH3 mixing ratio have been set at present. If PH3 and Cl were present, their mixing ratios also increased with pressure. Species were detected at mass peaks appropriate for C2 and C3 hydrocarbons. It is not yet clear which of these were atmospheric constituents and which were instrumentally generated. These measurements imply (1) fractionation of 4He, (2) a local, altitude-dependent depletion of condensables, probably because the probe entered the descending arm of a circulation cell, (3) that icy planetesimals made significant contributions to the volatile inventory, and (4) a moderate decrease in D/H but no detectable change in (D + 3He)/H in this part of the galaxy during the past 4.6 Gyr.