The temporal use of French ‘à travers (de)’: metaphorical transfer or cancellation of the spatial sense?

The semantic changes that take place during a grammaticalization process are often described in terms of metaphorical transfer (e.g.: Sweetser 1988). For example, a spatial meaning can be projected into the time domain. However, the hypothesis of metaphorical transfer can be dispensed with if the temporal meaning is already available, i.e. inferentially derivable from the spatial one (cf. Bybee, Perkins and Pagliuca 1994). In fact, a movement in space always correlates with a movement in time. In this view, the hypothesis that a cancellation process eliminates the spatial sense would be sufficient to explain the shift from a literal use to a figurative one.
In their spatial use, the French prepositions 'à travers (de)' and 'au travers de' express the internal phase of a movement (in contrast to prepositions that express its beginning or end). In general, they introduce a moving entity (a 'figure') that runs across a reference entity (a 'ground'). One allegedly metaphorical meaning of theirs applies to a fictive movement across or through time intervals conceived of as reference entities. At a certain point in history (the first token we found dates back to 1550), this new sense emerged from the existing spatial meanings. In this paper I discuss how this exactly happened.
To this end, I will compare the earliest instances of the temporal use (taken from the 'Frantext' database) with the semantically closest examples of the spatial use during the same period (cf. Plungian 2002, Stosic 2002 and Dominicy and Martin 2005 for synchronical approaches of the expressions at hand). I will analyze the similarities and differences with a view to shedding light on the process that took place. The results may contribute to further elaborating the current models of semantic change.