  We have observed five sulphur-bearing molecules in foreground diffuse
molecular clouds lying along the sight-lines to five bright continuum sources.
We have used the GREAT instrument on SOFIA to observe the 1383 GHz $^2\Pi_{3/2}
J=5/2-3/2$ transitions of SH towards the star-forming regions W31C,
G29.96-0.02, G34.3+0.1, W49N and W51, detecting foreground absorption towards
all five sources; and the EMIR receivers on the IRAM 30m telescope at Pico
Veleta to detect the H$_2$S 1(10)-1(01), CS J=2-1 and SO 3(2)-2(1) transitions.
In nine foreground absorption components detected towards these sources, the
inferred column densities of the four detected molecules showed relatively
constant ratios, with N(SH)/N(H$_2$S) in the range 1.1 - 3.0, N(CS)/N(H$_2$S)
in the range 0.32 - 0.61, and N(SO)/N(H$_2$S) in the range 0.08 - 0.30. The
observed SH/H$_2$ ratios - in the range (0.5-2.6) $\times 10^{-8}$ - indicate
that SH (and other sulphur-bearing molecules) account for << 1% of the
gas-phase sulphur nuclei. The observed abundances of sulphur-bearing molecules,
however, greatly exceed those predicted by standard models of cold diffuse
molecular clouds, providing further evidence for the enhancement of endothermic
reaction rates by elevated temperatures or ion-neutral drift. We have
considered the observed abundance ratios in the context of shock and turbulent
dissipation region (TDR) models. Using the TDR model, we find that the
turbulent energy available at large scale in the diffuse ISM is sufficient to
explain the observed column densities of SH and CS. Standard shock and TDR
models, however, fail to reproduce the column densities of H$_2$S and SO by a
factor of about 10; more elaborate shock models - in which account is taken of
the velocity drift, relative to H$_2$, of SH molecules produced by the
dissociative recombination of H$_3$S$^+$ - reduce this discrepancy to a factor
~ 3.
