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N.b., the second way is strongly connected to St. Thomas' argumentation in ST.I.Q104.A1-2. Thus, it is recommended that one read this before proceeding onto reading the second way. Especially focus on the distinction between being and becoming.
Efficient Causation: In this article, it refers to the conservation of some thing in being, not merely the becoming of a certain thing, but the do whereby some thing effects the continuity of a thing. An example can be given in the relationship between the sun and the light of air. The sun not only illumines the air into becoming light, but the air has a continuous relationship with the sun in its being light. It is not merely the movement from potency to act as before, but the conservation in act.
Efficient Cause: "THAT WHICH BY ACTING EXERCISES INFLUENCE UNTO THE BE OF A THING DEPENDENT IN REGARD TO BE." (Woodbury)
Efficiently caused thing: That thing which's being has its raison d'etre in the influence of another thing.
Caused cause: Something which has its being in another and, in turn, communicates being to another.