Geller et al. 4 over the roughly 11 years since our survey began. 22 were not observed, 15 of which are farther than 20 arcminutes in radius from the cluster center. The difference in completeness between bright stars ob- served ≥ 1 and ≥ 3 times is also a result of an increas- ing population of rapidly rotating stars towards bluer ( B − V ) color. For many of these stars, we have multi- ple observations of which only a few, and sometimes one, exceed this cutoff value of CCF peak height > 0.4 and therefore are included in our database. For purposes of future research we also include seven rapid rotators in Table 3 for which we have been unable to derive RVs from our spectra. For a thorough description of our data reduction pro- cess, see Geller et al. (2008). In short, we perform a stan- dard bias and flat-field correction to the images using the overscan strip and the flat-field images, respectively. The flat-field spectra are used to trace each aperture in a given pointing and thereby extract the science spec- tra. Wavelength solutions derived from the emission- lamp spectra are applied, followed by sky-subtraction using sky fibers from each pointing. The three sets of spectra (one set from each integration in a given con- figuration) are then combined via a median filter to re- move cosmic ray signals and improve S/N. These reduced spectra are cross-correlated with a high S/N solar spec- trum, obtained using a dusk sky exposure taken on the WIYN 3.5m with the same instrument setup as the given pointing. A Gaussian fit to the cross-correlation func- tion (CCF) yields a RV and a full width at half maxi- mum (FWHM, in km s − $^{1}$) for each stellar observation. The mean UT time is used to find and correct each RV measurement for the Earth’s heliocentric velocity. Fi- nally we apply the unique fiber-to-fiber RV offsets de- rived by Geller et al. (2008) for the WIYN-Hydra data to these RVs. As in Geller et al. (2008), to ensure a sufficient quality of measurement, we incorporate into our database only those spectra with a CCF peak height higher than 0.4. Additionally, we examine the distri- bution of RVs for each individual star and visually in- spect any measurements that are outliers in the distri- bution. Occasionally we remove a measurement whose CCF, though having a peak height above 0.4, clearly provides a spurious measurement (e.g., inadequate sky subtraction). Because of its youth, M35 provides a sample of late-type stars with a range of rotational periods (Meibom et al. 2009); some of these stars have projected rotational velocities that exceed our spectral resolution. As such, the cluster presents an opportunity to explore empirically the dependence of our measurement precision on increasing v sin i , where i is the inclination angle of the stellar rotation axis to our line of sight. 2.3. Data Reduction 3. EFFECTS OF STELLAR ROTATION ON MEASUREMENT PRECISION 3.1. Observed Rotation 2.4. Completeness of Spectroscopic Observations Fig. 3.— FWHM as a function of v sin i for observations in the 512.5 nm region. FWHM values are measured from the CCF peaks derived from a series of artificially broadened templates, of known v sin i , correlated against the original narrow-lined spectrum. We also show a polynomial fit to the data, which we then use to derive v sin i values for observed stars in M35. Additionally we plot a dashed line at v sin i = 10 km s − $^{1}$, below which the curve flattens out due to our spectral resolution. We impose a floor in v sin i at this value as we are unable to reliably measure slower rotation. We have at least one observation for 1144 of the 1344 stars in our stellar sample, for a completeness of 85% across our entire sample. 60% of the stars in our stellar sample have sufficient observations for their RVs to be considered final (813/1344). For these stars, we ei- ther have ≥ 3 RV measurements that show no variation, or, if we do see RV variability, we have found a binary orbital solution. (These 813 stars comprise the SM, SN, BM and BN classes; see Section 4.1). Of those stars not finalized, 231 have only one or two observations, and an- other 100 stars are variable but do not yet have definitive orbital solutions. The measured FWHM of the CCF for a given star is directly related to the v sin i (Rhode et al. 2001). Thus in order to derive a v sin i value, we first measure the FWHM of the CCF peak. To do so, we fit a Gaussian function to the peak, forcing the baseline of the Gaus- sian to start at the background level of the CCF. Specif- ically, we subtract from the CCF a polynomial fit to this background level, and then fit the Gaussian to the subse- quent “continuum subtracted” CCF. We only use spec- tra from the 512.5 nm region to measure the FWHM, as the FWHM is dependent on the setup (i.e., the disper- sion, etc.), and most of our observations were taken in the 512.5 nm region. We then use a similar technique as Rhode et al. (2001), to convert this FWHM to a v sin i . In Figure 2, we show the completeness of our observa- tions as functions of V magnitude (left) and projected radius (right). We plot the completeness in stars ob- served ≥ 3 times with the dashed line and stars observed ≥ 1 time with the solid line. Our prioritization of stars by distance from the cluster center is evident by our de- creasing completeness with cluster radius. The decreas- ing completeness towards fainter stars reflects the need for dark skies with minimal sky contamination in order to obtain sufficient S/N in our spectra to derive reliable RVs for faint stars. There are 37 stars with V < 15 in our stellar sample that do not have RV measurements, one of which is a proper-motion member. 15 were observed but did not yield reliable RVs, mostly due to rapid rotation.