Short-period comets with P I 15 yr represent one of the most complete comet samples. The magnitude distribution of these comets was analysed using a maximum likelihood method. The brightness (magnitude) index for the comets with H,, 5 11 mag was estimated together with the large sample errors and found to be 0.62 f 0.09. It was clear that inany faint comets with H,, > 11 mag remain to be discovered. Some of the faint, smaller comets have probably been removed from the distribution altogether.
Observational selection wasialso apparent for the sample of comets with perihelia q < 1.5 AU. It was found that comets satisfying the combined criteria Ps 15 yr, H,, I 11 mag, q< 1.5 AU probably represent the most complete set of comets available. The brightness index of this sample estimated by maximum likelihood was 0.69 + 0.14. This translates into a mass distribution index s of 1.69 * 0.14 indicating that most of the mass is contained in a few of the larger comets rather than spread throughout the smaller ones. This distribution, although modified by mass loss, is most likely to have been produced by a process of particle accretion.