Definition of "potentially"

Nevertheless, it is clear that the global energy demand for air-conditioning will grow substantially as nations become more affluent, with the consequences of climate change potentially accelerating the demand.

2013 September-October, Michael Sivak, “Will AC Put a Chill on the Global Energy Supply?”, in American Scientist

I freely assert, that the cosmopolite philosopher cannot, for his life, point out one single peaceful influence, which within the last sixty years has operated more potentially upon the whole broad world, taken in one aggregate, than the high and mighty business of whaling.

1851 November 14, Herman Melville, Moby-Dick; or, The Whale, 1st American edition, New York, N.Y.: Harper & Brothers; London: Richard Bentley