Discussion of a paper by C. D. McGillem and B. P. Miller, ‘Lunar surface roughness from crater statistics’

In a recent paper McGillem and Miller [1962] arrive at crater frequencies on a scale of 1 to 100 meters by extrapolating statistical data compiled on the size distribution of craters in the range of sizes visible on lunar maps and photographs. They show that cumulative crater size distribution in the visible range of sizes may be approximated by the law N = AD−B where N is the number of craters having diameter greater than D, and A and B are constants. The coefficient A depends upon the total number of craters per unit area, varying from about 1400 for the maria to 30,000 for the highland regions when D is measured in kilometers and N is in craters per 106 km2. It is found, however, that the exponent B is reasonably independent of location on the lunar surface, having a value of 1.6.