Suppose at time t some number of particles all have position r within element d 3 r and momentum p within d 3 p . If a force F instantly acts on each particle, then at time t + Δ t their position will be r + Δ Δ r = r + p m Δ Δ t and momentum p + Δ p = p + F Δ t. Then, in the absence of collisions, f must satisfy