The Collaborative International Dictionary of English v.0.48:

Thirtieth \Thir"ti*eth\, a. [From Thirty: cf. AS.
   [thorn]r[imac]tig[=o][eth]a.]
   1. Next in order after the twenty-ninth; the tenth after the
      twentieth; -- the ordinal of thirty; as, the thirtieth day
      of the month.
      [1913 Webster]

   2. Constituting or being one of thirty equal parts into which
      anything is divided.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Thirtieth \Thir"ti*eth\, n.
   The quotient of a unit divided by thirty; one of thirty equal
   parts.
   [1913 Webster]

WordNet (r) 3.0 (2006):

thirtieth
    adj 1: coming next after the twenty-ninth in position [syn:
           thirtieth, 30th]
    n 1: position 30 in a countable series of things