white dwarfs that emerged from stable mass transfer is 5 . 0 × 10 − $^{3}$. Table 1 shows a representative sample of the results. In this section we focus on the totals listed in column 6. These totals are normalized to the case in which transits can be detected in 135 , 000 monitored stars The first two rows correspond to a single simulation, labeled “1”. Simulation 1 is the one used to produce Figure 3. ( α = 10 , δ < 0 . 1 , the only criterion imposed on the Kepler target stars is that their masses are between 0 . 9 M ⊙ and 2 . 9 M ⊙ . ) If this case applies, more than 1100 transiting systems would be discovered by Kepler . In the next 4 rows, also labeled “1”, we alter only the value of α, the common envelope ejection efficiency. We find that, as the ejection efficiency declines, significantly more mergers occur. For example when α declines from 10 to unity, the numbers of mergers increase by 50% and the common-envelope survivors are found in closer orbits than those shown in Figure 3. The transit probability declines by only 15%, however, because transits are more likely for closer orbits. The value of α must decline to ∼ 0 . 1 in order for common envelope survivors to produce fewer than 100 transits per year. Thus, the result that a large number of white dwarfs should produce transits is robust with respect to changes in the common-envelope efficiency factor. In any realistic population, the efficiency of envelope ejection will be different for different systems. To determine the numbers of transits expected from common envelope survivors, we should therefore average over a range of efficiencies. We also tested the effect of changing the rule used to compute the final core mass for the donor stars that contribute mass during stable mass transfer. We used three prescriptions: (1) the maximum value of δ is 10%; (2) the maximum value of δ is 20%; (3) the value of δ can be as large as half the difference between the white dwarf mass expected for a star with initial mass M 1 (0) and the core mass M$_{c}$ at the start of mass transfer. Changing these rules doesn’t change the numbers of stable mass-transfer binaries, but it does affect the transit probability; the larger the core mass at the time of depletion, the wider the orbit, and the smaller the transit probability. With prescription 2, the numbers of transits by white dwarfs that are the end states of stable mass transfer decreased by ∼ 13% . With prescription 3, the numbers of transits by the end states of stable mass transfer decreased by roughly 70% . No single rule for selecting a final core mass can apply to all binaries. Once mass transfer begins, the donor’s envelope is depleted through mass loss, and the envelope is also contributing mass to the growing stellar core. The final core mass depends on the time scales for these two competing processes. These time scales depend on the state of the system and on the evolution of the orbital angular momentum, for example on the amount of angular momentum carried off in winds. For donors that fill their Roche lobes when their core masses are small ( ∼ 0 . 1 − 0 . 2 M ⊙ ), mass transfer may deplete the envelope at a faster rate than the nuclear evolution of the core. Values of δ may be modest. For donors that fill their – 13 –