Great explanation, JT. I look forward to your instructional sessions at
HTL VI.
By the way, did you know that "umbra" is the Italian word for "shadow"? It's also the basis of our word "umbrella" -- a device that casts a shadow. (Okay, we use one mostly to "cast" a dry spot when it's raining, but its original use was to protect the user from the sun.) The prefix "pen" means "next to," so "penumbra" literally means "next to the shadow." I once was given directions in London and told to "get off [the subway] at the penultimate stop." (I think he knew that most "yanks" don't know the true meaning of "penultimate"!) --Randy