With the advent of synchrotron radiation sources, the issue of beam lifetime becomes increasingly important. Users of these machines need to perform experiments which seldom last 15 minutes, but require hours for their completion. Therefore, the beam should circulate stably for hours. The beam of the Advanced Photon Source (APS) storage ring at Argonne National Laboratory is assumed to circulate stably for a minimum of 10 hours. The main contributions to the total beam lifetime (which is the inverse of the loss rate) come from residual gas scattering and Touschek scattering. The residual gas scattering is comprised of single Coulomb scattering and bremsstrahlung. The single-Coulomb scattering involves elastic collisions, while bremsstrahlung involves inelastic collisions, between the bunch and the surrounding residual gas. In the calculation the authors take the gas to be nitrogen at a pressure of 1 nTorr. Touschek scattering involves scattering of particles within the bunch, transferring energy among themselves. Such an energy transfer, if large enough, may eject the particle out of the bunch, thus causing it to be lost. Let us not forget the residual-gas lifetime. As pointed out, the calculation of this lifetime is done for the very low pressure of 1 nTorr. If the pressure is higher, the residual-gas lifetime will be smaller. This will further reduce the total beam lifetime, causing it to slip deeper below the minimum lifetime for stable storage ring operation. They begin this article by reviewing the Touschek integral and the associated limits of integration. The program ZAP has been altered to take into account the possible loss due to induced betatron oscillations. At each lattice position the energy loss required to produce, by coupling, a vertical oscillation that exceeds the vertical aperture is calculated. When this energy loss is less than the rf bucket half-height, it replaces the rf bucket half-height in the Touschek integral.