  The magnon thermal conductivity $\kappa_{\mathrm{mag}}$ of the spin ladders
in $\rm Sr_{14}Cu_{24-x}Zn_xO_{41}$ has been investigated at low doping levels
$x=0$, 0.125, 0.25, 0.5 and 0.75. The Zn-impurities generate nonmagnetic
defects which define an upper limit for $l_{\mathrm{mag}}$ and therefore allow
a clear-cut relation between $l_{\mathrm{mag}}$ and $\kappa_{\mathrm{mag}}$ to
be established independently of any model. Over a large temperature range we
observe a progressive suppression of $\kappa_{\mathrm{mag}}$ with increasing
Zn-content and find in particular that with respect to pure $\rm
Sr_{14}Cu_{24}O_{41}$ $\kappa_{\mathrm{mag}}$ is strongly suppressed even in
the case of tiny impurity densities where $l_{\mathrm{mag}}\lesssim 374$~{\AA}.
This shows unambiguously that large $l_{\mathrm{mag}}\approx 3000$~{\AA} which
have been reported for $\rm Sr_{14}Cu_{24}O_{41}$ and $\rm
La_{5}Ca_9Cu_{24}O_{41}$ on basis of a kinetic model are in the correct order
of magnitude.
