  Following our previous work on `perpendicular' boundary conditions, we show
that transmission conditions \[ f'(0-)=\alpha(f(0+)-f(0-)), \quad
f'(0+)=\beta(f(0+)-f(0-)),\] describing so-called snapping out Brownian motions
on the real line, are in a sense complementary to the transmission conditions
\[f(0-)=-f(0+), \quad f''(0+) =\alpha f'(0-)+\beta f'(0+). \] As an application
of the analysis leading to this result, we also provide a deeper
semigroup-theoretic insight into the theorem saying that as the coefficients
$\alpha$ and $\beta$ tend to infinity but their ratio remains constant, the
snapping-out Brownian motions converge to a skew Brownian motion. In
particular, the transmission condition \[ \alpha f'(0+) = \beta f'(0-), \] that
characterizes the skew Brownian motion turns out to be complementary to \[
f(0-) = - f(0+), \beta f'(0+)=- \alpha f'(0-). \]
