8.4 Completeness of Survey
The frequency function of apparent diameters for the DDO dwarfs is as follows:
 | 16' | 8' | 4' | 3' | 2' | 1'.5 | 1'.0 |
| n | 1 | 6 | 8 | 12 | 29 | 46 | 120 |
N =  n
| 1 | 7 | 15 | 27 | 56 | 102 | 222 |
A plot of log N versus log
approximates closely the N 
-3
distribution expected for a statistically uniform space density in the
range 11' < < 20', but falls off
rapidly for < 10'. Either
incompleteness begins at = 10' or
there is a local excess of dwarfs
associated with the Local Group. The seven largest DDO dwarfs
( 
8'.0) are listed in Table 9: six (DDO 008, DDO 074, DDO 199, DDO 208,
DDO 209, DDO 221) are in the Local Group and one (DDO 081) is in the M81 group.
| DDO |
|  (Mpc)
| (kpc)
|
| DDO 008 = IC 1613 | 15'.0 | 0.66 | 3.1 |
| DDO 074 = Leo I | 8'.5 | 0.23 | 0.6 |
| DDO 081 = IC 2574 | 11'.5 | 2.5 | 8.5 |
| DDO 199 = UMi | 20'.0 | 0.08 | 0.5 |
| DDO 208 = Draco | 8'.0 | 0.06 | 0.14 |
| DDO 209 = NGC 6822 | 12'.5 | 0.50 | 1.8 |
| DDO 221 = WLM | 11'.0 | 0.87 | 2.8 |
If the smallest DDO dwarfs ( =
1'.0) have the same mean linear
diameter 
= 2.5 kpc as the
seven above, the limiting range of the
survey is
8.5 Mpc on the average; half
the total (
1'.5) is within
an average range of 5.5 Mpc. However, the range of linear diameters is
large (8.5-0.14 kpc or a 60-1 ratio in the first seven), and the range
of the survey in depth is necessarily indefinite.
For a survey of dwarf galaxies in the Virgo cluster, see Reaves (1956).