Wither is a verb meaning (1) to shrivel or (2) to cause to shrivel. It’s often used metaphorically, especially in the participial adjective withering, which means devastating or overwhelming. It’s also used in the phrasal verb wither away, which is more emphatic than wither, connoting death or disappearance.
Whither is an adverb and conjunction meaning to what place. Though the word has an archaic ring, it’s often used in phrases such as Whither capitalism? and Whither the Hippocratic Oath?, which mean, basically, where has [named thing] gone?, or what happened to [named thing]?, or even what will happen to [named thing]? We can’t explain why whither takes no verb in constructions like these. If you know where this comes from, please comment.
They worry that if e-books are priced too low, the public will devalue their worth, and the publishers might wither away. [New York Times]
Whither the idea of policing as something holistic, and often qualitative rather than quantitative? [Guardian]
When Woods gave into his injury on the 12th tee, the tournament hardly withered. [The Australian]
The question that hangs over each day is whither the horse — will she pull the wagon today, will she eat, will she drink, will she die? [Los Angeles Times]
Goldman Sachs faced an unprecedented assault from one of its own on Wednesday after a banker published a withering resignation letter in the New York Times, calling the Wall Street titan a “toxic” place. [Independent]