The Collaborative International Dictionary of English v.0.48:

Influence \In"flu*ence\ ([i^]n"fl[-u]*ens), n. [F. influence,
   fr. L. influens, -entis, p. pr. See Influent, and cf.
   Influenza.]
   1. A flowing in or upon; influx. [Obs.]
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            God hath his influence into the very essence of all
            things.                               --Hooker.
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   2. Hence, in general, the bringing about of an effect,
      physical or moral, by a gradual process; controlling power
      quietly exerted; agency, force, or tendency of any kind
      which affects, modifies, or sways; as, the influence which
      the sun exerts on animal and vegetable life; the influence
      of education on the mind; the influence, according to
      astrologers, of the stars over affairs.
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            Astrologers call the evil influences of the stars,
            evil aspects.                         --Bacon.
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            Canst thou bind the sweet influences of Pleiades, or
            loose the bands of Orion?             --Job xxxviii.
                                                  31.
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            She said : "Ah, dearest lord! what evil star
            On you hath frown'd, and poured, his influence bad?"
                                                  --Spenser.
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   3. Power or authority arising from elevated station,
      excelence of character or intellect, wealth, etc.;
      reputation; acknowledged ascendency; as, he is a man of
      influence in the community.
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            Such influence hath your excellency.  --Sir P.
                                                  Sidney.
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   4. (Elec.) Induction.

   Syn: Control; persuasion; ascendency; sway; power; authority;
        supremacy; mastery; management; restraint; character;
        reputation; prestige.
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The Collaborative International Dictionary of English v.0.48:

Influence \In"flu*ence\, v. t. [imp. & p. p. Influenced
   ([i^]n"fl[-u]*enst); p. pr. & vb. n. Influencing
   ([i^]n"fl[-u]*en*s[i^]ng).]
   To control or move by power, physical or moral; to affect by
   gentle action; to exert an influence upon; to modify, bias,
   or sway; to affect; to move; to persuade; to induce.
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         These experiments succeed after the same manner in
         vacuo as in the open air, and therefore are not
         influenced by the weight or pressure of the atmosphere.
                                                  --Sir I.
                                                  Newton.
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         This standing revelation . . . is sufficient to
         influence their faith and practice, if they attend.
                                                  --Attebury.
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         The principle which influenced their obedience has lost
         its efficacy.                            --Rogers.
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WordNet (r) 3.0 (2006):

influence
    n 1: a power to affect persons or events especially power based
         on prestige etc; "used her parents' influence to get the
         job"
    2: causing something without any direct or apparent effort
    3: a cognitive factor that tends to have an effect on what you
       do; "her wishes had a great influence on his thinking"
    4: the effect of one thing (or person) on another; "the
       influence of mechanical action"
    5: one having power to influence another; "she was the most
       important influence in my life"; "he was a bad influence on
       the children"
    v 1: have and exert influence or effect; "The artist's work
         influenced the young painter"; "She worked on her friends
         to support the political candidate" [syn: influence, act
         upon, work]
    2: shape or influence; give direction to; "experience often
       determines ability"; "mold public opinion" [syn: determine,
       shape, mold, influence, regulate]
    3: induce into action by using one's charm; "She charmed him
       into giving her all his money" [syn: charm, influence,
       tempt]

The Devil's Dictionary (1881-1906):

INFLUENCE, n.  In politics, a visionary _quo_ given in exchange for a
substantial _quid_.