Rhopalic describes text in which each word contains one more letter or syllable than the one preceding it. It derives from the Greek rhopalos, for a club or cudgel which, like most of its kind, is thicker towards one end than the other.
Though the English word is first recorded only at the end of the seventeenth century, the technique is almost certainly much older. It is commonly applied to poetry whose words advance each time by one syllable, or sometimes one metric foot, but it can also apply to prose. The classic example of the latter form was created by Dmitri Borgmann:
I do not know where family doctors acquired illegibly perplexing handwriting; nevertheless, extraordinary pharmaceutical intellectuality, counterbalancing indecipherability, transcendentalises intercommunications’ incomprehensibleness.
which manages the difficult feat of reaching a word of twenty letters. (David Crystal, who quotes this in his book Language Play, remarks: “It would be ultraconscientiousness to go further”. Even overintellectualisation, perhaps.) In poetry, such wordplay has also been described as snowball verse and wedge verse.