The Collaborative International Dictionary of English v.0.48:

Medium \Me"di*um\, n.; pl. L. Media, E. Mediums. [L.
   medium the middle, fr. medius middle. See Mid, and cf.
   Medius.]
   1. That which lies in the middle, or between other things;
      intervening body or quantity. Hence, specifically:
      (a) Middle place or degree; mean.
          [1913 Webster]

                The just medium . . . lies between pride and
                abjection.                        --L'Estrange.
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      (b) (Math.) See Mean.
      (c) (Logic) The mean or middle term of a syllogism; that
          by which the extremes are brought into connection.
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   2. A substance through which an effect is transmitted from
      one thing to another; as, air is the common medium of
      sound. Hence: The condition upon which any event or action
      occurs; necessary means of motion or action; that through
      or by which anything is accomplished, conveyed, or carried
      on; specifically, in animal magnetism, spiritualism, etc.,
      a person through whom the action of another being is said
      to be manifested and transmitted.
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            Whether any other liquors, being made mediums, cause
            a diversity of sound from water, it may be tried.
                                                  --Bacon.
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            I must bring together
            All these extremes; and must remove all mediums.
                                                  --Denham.
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   3. An average. [R.]
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            A medium of six years of war, and six years of
            peace.                                --Burke.
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   4. A trade name for printing and writing paper of certain
      sizes. See Paper.
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   5. (Paint.) The liquid vehicle with which dry colors are
      ground and prepared for application.
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   6. (Microbiology) A source of nutrients in which a
      microorganism is placed to permit its growth, cause it to
      produce substances, or observe its activity under defined
      conditions; also called culture medium or growth
      medium. The medium is usually a solution of nutrients in
      water, or a similar solution solidified with gelatin or
      agar.
      [PJC]

   7. A means of transmission of news, advertising, or other
      messages from an information source to the public, also
      called a news medium, such as a newspaper or radio; used
      mostly in the plural form, i. e. news media or media.
      See 1st media[2].
      [PJC]

   Circulating medium, a current medium of exchange, whether
      coin, bank notes, or government notes.

   Ethereal medium (Physics), the ether.

   Medium of exchange, that which is used for effecting an
      exchange of commodities -- money or current
      representatives of money.
      [1913 Webster]

WordNet (r) 3.0 (2006):

medium of exchange
    n 1: anything that is generally accepted as a standard of value
         and a measure of wealth in a particular country or region
         [syn: medium of exchange, monetary system]

Moby Thesaurus II by Grady Ward, 1.0:

34 Moby Thesaurus words for "medium of exchange":
   and pence, cash, circulating medium, coinage, coined liberty,
   cold cash, currency, dollars, emergency money, filthy lucre,
   fractional currency, gold, hard cash, hard currency, legal tender,
   lucre, mammon, managed currency, mintage, money, necessity money,
   pelf, postage currency, postal currency, pounds, scrip, shillings,
   silver, soft currency, specie, sterling, the almighty dollar,
   the wherewith, the wherewithal