Martin (1992: 198):
Both manner (whereby, thereby) and consequence (/ ^ so that /) have realisations which apparently make the Effect dependent, but which do not allow the beta-clause to be realised first in the clause complex:
MANNER[4:76] We prepared wellthereby managing to win.
CONSEQUENCE[4:77] We prepared well/ ^ so that / in the end we won.
 The logical relation of manner does not involve an effect of a cause. The conjunction thereby, however can realise both manner and cause: reason/result.
 In both SFL theory and formal logic, the term 'consequence' is used with condition (if P then Q), not with cause: reason/result (because P so result Q).