The word influence actually comes from the latin word influentia which was used about stellar (astrological) effects on humans, caused by the stars. Nowadays, it is used for any general cases where distant effects of some sort may be manifest.
... on the west coast, and Tertiary conglomerates, sandstones, marls and clays, folded by subsequent upheavals, in many parts of the island. The clays, which contain layers ...