  We study the relation of the middle convolution to the $\ell$-adic Fourier
transformation in the \'etale context. Using Katz' work and Laumon's theory of
local Fourier transformations we obtain a detailed description of the local
monodromy and the determinant of Katz' middle convolution functor $\MC_\chi$ in
the tame case. The theory of local $\epsilon$-constants then implies that the
property of an \'etale sheaf of having an at most quadratic determinant is
often preserved under $\MC_\chi$ if $\chi$ is quadratic.
