  We present a study of {\it finite} $a$ and {\it volume} effects of the
leptonic decay constant $f$ of heavy pseudoscalar mesons in the static
approximation. This study is performed on a number of lattices at $\beta=$
5.74,~6.0 and 6.26 covering sizes from about 0.7~$fm$ to 2~$fm$. We confirm
that beyond 1.5~$fm$ the volume dependence is negligible. By carefully
analysing results obtained using different trial wave functions for the heavy
meson we find no dependence on the smearing. We also give results for the mass
difference of the scalar - pseudoscalar and the $\Lambda _{b}$ - pseudoscalar.
Using the mass of the pseudoscalar meson we estimate the distance of string
breaking in the static quark potential.
