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In Figure 7, we show the distribution of RV member- ship probabilities, displaying a clean separation between the cluster members and field stars. In the following analysis, we use a probability cutoff of P$_{RV}$ ≥ 50 % to define our cluster member sample. Using the 344 single cluster members and binary cluster members with orbital solutions, we find a mean cluster RV of -8.16 ± 0.05 km s − $^{1}$. From the area under the fit to the cluster and field distributions, we estimate a field contamination of 6% within our cluster member sample (P$_{RV}$ ≥ 50%). Though this estimate is derived excluding the RV variables that do not have orbital solutions, the percent contamination should be valid for the cluster as a whole. 

Our RV membership probabilities agree well with the proper-motion memberships of Cudworth (1971) and McNamara & Sekiguchi (1986a). We note that our stel- lar sample covers only the faintest portion of either proper-motion study. There are 24 Cudworth (1971) 

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proper-motion members within our observed stellar sam- ple, of which we find 14 (58%) to also have ≥ 50% RV membership probabilities. Cudworth (1971) note that for V > 13 they begin to find significant errors in their photometry and expect many field stars to con- taminate their proper-motion member sample; this can likely explain the 10 discrepant stars. There are 70 McNamara & Sekiguchi (1986a) proper-motion members within our observed stellar sample, of which we find 64 (91%) to also have ≥ 50% RV membership probabilities. McNamara & Sekiguchi (1986a) expects up to 15 field stars contaminating their cluster member sample from 13 < V < 15, which can easily account for the 6 dis- crepant stars. 

We also note that NGC 2158 is only ∼ 28 arcminutes away from the center of M35, at α = 6 $^{h}$07$^{m}$25 s and δ = +24 $^{◦}$05$^{′}$48′′ (J2000), and thus is within the spatial region that we have surveyed. Scott et al. (1995) find a mean RV for NGC 2158 of 28 ± 4 km s − $^{1}$. There are five stars within our sample that lie within the cluster radius of 2.5 arcminutes Carraro et al. (2002) from the center of NGC 2158 and have RVs within three times the standard error (12 km s − $^{1}$) of the mean RV : 125044, 39017, 111050, 57037, 54048. Two of these stars (125044 and 57037) have less than three observations; the remaining three have ≥ 3 observations and appear to be non-RV-variables. 

RV-variable stars are distinguishable by the larger standard deviations of their RV measurements. Here, we assume that such velocity variability is the result of a binary companion, or perhaps multiple companions. Specifically, we consider a star to be a RV variable if the ratio of the standard deviation of its RV measurements to the single-measurement RV precision 7 ( e/i ) for that star is greater than four (Geller et al. 2008). We provide the e/i value for each single-lined star in Table 3; we label double-lined systems as RV variables directly, and include the comment of SB2 in Table 3. 

Monte Carlo analysis has shown that, for similar obser- vations of solar-type stars in NGC 188, Geller & Mathieu (in preparation) can detect the majority of binaries with periods less than 10 4 days and a negligible fraction of longer-period binaries. Though the slightly poorer preci- sion for the M35 data will effect the specific completeness numbers, we can assume a similarly high completeness in detected binaries with periods less than 10 4 days and a corresponding drop in completeness for longer-period bi- naries. Some of the undetected systems are evident from their separation from the main sequence (see Figure 8). We have currently identified 55 RV-variable members of M35, and have derived orbital solutions for 71% (39/55) of this sample. In following papers we will pro- vide the orbital solutions for these systems, including all derived parameters. We will then perform a detailed analysis of the distributions of these orbital parameters as well as the binary frequency of the cluster. 

## 4.2. Radial-Velocity Variability 

