  We consider the motion of a finite though large number $N$ of hard spheres in
the whole space $\mathbb{R}^n$. Particles move freely until they experience
elastic collisions. We use our recent theory of Compensated Integrability in
order to estimate how much the particles are deviated by collisions. Our
result, which is expressed in terms of hodographs, tells us that only $O(N^2)$
collisions are significant.
