= Solution
Treat the quoted solar spectrum as irradiance normal to the beam, approximately constant over the narrow band. The incident band irradiance is $F_\perp=19\,\mathrm{W\,m^{-2}}$ and the horizontal value is $F_0=F_\perp\sin30^\circ=9.5\,\mathrm{W\,m^{-2}}$. The cloud's vertical <optical depth> is $25(0.4)=10$; including the clear atmosphere gives $\tau_v=10.07$. The slant optical depth is $\tau_s=\tau_v/\sin30^\circ=20.14$. Thus the <Beer-Lambert law> gives
$$
\boxed{t_{\rm dir}=e^{-20.14}=1.792\times10^{-9},\qquad F_{\rm surface,dir}=1.702\times10^{-8}\,\mathrm{W\,m^{-2}}.}
$$
The removed fraction is $1-t_{\rm dir}=0.9999999982$, almost the full incident horizontal $9.5\,\mathrm{W\,m^{-2}}$. Beam-normal surface irradiance is twice the horizontal value. These are \b[direct-beam] quantities, not the total diffuse-plus-direct surface flux. If the supplied irradiance were already horizontal, the projection factor would instead be omitted.
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