Definition of "by degrees"

"She came to us snappish and suspicious, but when she found what sort of place ours was, it all went off by degrees.

1877, Anna Sewell, “Chapter 22”, in Black Beauty: […], London: Jarrold and Sons, […]

By degrees the libraries which were unendowed fell behind the age, and were consequently neglected.

1880, William Blades, The Enemies of Books, page 36