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Webster 1913 Edition

Adj.

[Gr. [GREEK][GREEK][GREEK][GREEK] club-shaped; fr. [GREEK][GREEK][GREEK] a club: cf. F.

rhopalique

(Pros.)

Applied to a line or verse in which each successive word has one more syllable than the preceding.

rhopalic ‎(comparative more rhopalic, superlative most rhopalic)

(poetry, rhetoric) Having each successive word longer by a letter or syllable.
- 1986 October 26, Alan Truscott, “Talking About Behavior”, in The New York Times:
  Soapy fired off a rhopalic sentence, that is, one in which each word is one letter longer than the word that precedes it: "I am the only dummy player, perhaps, planning maneuvers calculated brilliantly, nevertheless outstandingly pachydermatous, notwithstanding unconstitutional unprofessionalism."

increasing

rhopalic ‎(plural rhopalics)