When Gidget is in the library and a thought hits her while she's reading a book, the sound effect signaling her idea is the same one used when Jeannie on "I Dream of Jeannie" uses her magic.
The passage Professor Lawrence quotes in his letter to Helpful Hannah, i.e. Gidget, is, as he correctly attributes it, from Washington Irving. It can be found in the work "Philip of Pokanoket: An Indian Memoir" that is contained in a collection of stories and essays entitled "The Sketchbook of Geoffrey Crayon, Gent" and first published in 1820.
Two early American men of letters are given some airtime in this episode: Benjamin Franklin makes an appearance in the picture Gidget inadvertently lobs a dart; and Washington Irving is quoted by Professor Lawrence.