  A scaling form for the local susceptibility, derived from renormalization
group arguments, is proposed. The scale over which the uniform part of this
scaling form varies can be viewed as a definition of the Kondo ``screening
cloud" $\sim \xi_K$. The proposed scaling form interpolates between
Ruderman-Kittel-Kasuya-Yosida (RKKY) results in the high temperature limit,
$T\gg T_K$, and Fermi liquid results in the low temperature, long-distance
limit, $T\ll T_K$, $r\gg \xi_K$. The predicted form of the Knight shift is
longer range at low temperatures where the screening cloud has formed, than at
high temperatures where it has not. Using weak and strong coupling perturbation
theory combined with large scale density matrix renormalization group (DMRG)
results we study the validity of the finite size version of the scaling form at
$T=0$. We explicitly extract a length scale proportional to the Kondo length
scale, $\xi_K$. The numerical results are in good agreement with the proposed
scaling form and confirm the existence of the Kondo screening cloud.
