The population of Apollo, Amor and Mars crossing asteroids is studied. With the 18-inch Schmidt camera of the Hale Observatories at Mt. Palomar, four new planet crossing asteroids were discovered.
A formal theory relating the probability of discovery of asteroid of a given orbital class to condition of search has been developed.
From the estimated populations the flux of the Apollo objects to magnitude 18 near the Earth is of the order of (0.4 ± 0.2) 10-14 km-2 yr-1. During 3.3 b.y. this flux produces an estimated 60 ± 20 craters of 10 km in diameter and larger per 106 km2 on the Moon. This number seems to be consistent with the observed crater densities on 3. 3 b.y. old mare surfaces in the eastern Oceanus Procellarum and Mare lmbrium.