We have conducted a large-area search for the brightest members of the trans-Neptunian and Centaur/scattered-disk asteroid populations by reprocessing archival scans from the Spacewatch 0.9 m telescope at Kitt Peak. Our survey encompasses 331 scans taken from 1995 September to 1999 September and has a raw sky coverage of 1483.8 deg2. We discovered Ðve trans-Neptunians and Ðve Centaur/ scattered-disk objects using an automated motion detection code. In addition, we serendipitously found four trans-Neptunians and two Centaur/scattered-disk objects that had been previously discovered. This survey is unique in that it involves a method that has a reasonable chance to reacquire its lost objects. In this paper we develop techniques to aid our understanding of our software efficiency and survey procedures. We use this understanding to "" convolve ÏÏ our raw sky coverage with our measured detection efficiency and a model of our scan coverage to estimate what fraction of survey areas can be considered "" new.ÏÏ Our large sky coverage extends the cumulative luminosity function of the trans-Neptunians into a region previously constrained only by upper limits, and it allows a power-law Ðt to be attempted to the Centaur cumulative luminosity function. In objects per square degree brighter than R \ 21.5, we Ðnd cumulative surface densities of Centaurs to be 0.017^0.011, of trans-Neptunians to be 0.040^0.018, and scattered-disk objects to be 0.007^0.004. We extrapolate these values to estimate the number of each class in the ecliptic brighter than R \ 21.5 : 100 Centaurs, 400 trans-Neptunians, and 70 scattereddisk objects. Orbit analysis by the Minor Planet Center suggests that three of our Ðve trans-Neptunians are resonators : 1998 is in the 3 : 2, 1995 appears to be in the 5 : 3, and 1998 appears VG 44 SM 55 SN 165 to be in the 7 : 5 resonance.

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