This paper is concerned with some aspects of determining the evolution of the size distribution of a finite number of mutually colliding and fragmenting particles such as the asteroids or interplanetary dust. If n(m, t) is the number of particles per unit volume per mass interval at time t, then n = dn/dt is the rate at which that number changes with time. This rate can be calculated if the laws are known according to which the colliding bodies erode one another and fragment and if the influence of collisions on the motion of the particles is known. To reduce the complexity of the problem, one assumes that the speed of approach between the bodies is always the same vcoll and that they, as well as the debris, occupy a fixed volume (“particles in a box”). Only collisions between two bodies are considered, and the way in which erosion and fragmentation occurs at a given value of vcoll depends only on their masses. The particles are assumed to be spherical.