The Collaborative International Dictionary of English v.0.48:

Amphigory \Am"phi*go*ry\, n. [F. amphigouri, of uncertain
   derivation; perh. fr. Gr. 'amfi` + ? a circle.]
   A nonsense verse; a rigmarole, with apparent meaning, which
   on further attention proves to be meaningless. [Written also
   amphigouri.]
   [1913 Webster] Amphilogism