  We describe a simple and efficient procedure for approximating the L\'evy
measure of a $\text{Gamma}(\alpha,1)$ random variable. We use this
approximation to derive a finite sum-representation that converges almost
surely to Ferguson's representation of the Dirichlet process based on arrivals
of a homogeneous Poisson process. We compare the efficiency of our
approximation to several other well known approximations of the Dirichlet
process and demonstrate a substantial improvement.
