Did you know that the "big four" cats - lions, tigers, jaguars, cougars (aka mountain lions) - can roar but they can't purr, whereas smaller cats, from ocelots down to the cat in your lap, can purr but not roar?
I didn't either, but a terrific video on BigCatRescue.org (spotted via Boston.com's intriguing Braniac blog) provides the scoop: The secret is the hyoid bone, in the back of the throat. If it's connected one way they can roar, if it's connected another they can purr. There's considerable debate about the details, however, including uncertainty whether mid-sized to big cats can semi-purr - that is, purr only when exhaling.
It's good stuff: Check it out here. They also have a video about whether lions etc. like to chase laser pointer lights.
As for whether there are mountain lions in New Hampshire, here's a story I did last year. (Answer: Certainly no breeding pairs, maybe a single individual, although probably not. (The story was written before a mountain lion was killed in Connecticut after walking here from Wisconsin.)