Question: What is the meaning of eager, in "like eager droppings into
milk," and in "a nipping and an eager air"?
Answer: "Eager" from French aigre. Anything sour dropped
into milk will make it curd, coagulate. "In eager and nipping air" the derivation of eager is the same French aigre,
and means keen, sharp, bitter.
Mertins, Emma. Shakespeare Examinations. Ed. William Taylor Thom, M. A. Boston: Ginn and Co., 1888. Shakespeare Online. 10 Aug. 2010. (date when you accessed the information) < http://www.shakespeare-online.com/plays/hamlet/examq/twentyfour.html >.