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The Collaborative International Dictionary
Subtileness

Subtile \Sub"tile\, a. [L. subtilis. See Subtile.]

  1. Thin; not dense or gross; rare; as, subtile air; subtile vapor; a subtile medium.

  2. Delicately constituted or constructed; nice; fine; delicate; tenuous; finely woven. ``A sotil [subtile] twine's thread.''
    --Chaucer.

    More subtile web Arachne can not spin.
    --Spenser.

    I do distinguish plain Each subtile line of her immortal face.
    --Sir J. Davies.

  3. Acute; piercing; searching.

    The slow disease and subtile pain.
    --Prior.

    5. Characterized by nicety of discrimination; discerning; delicate; refined; subtle. [In this sense now commonly written subtle.]

    The genius of the Spanish people is exquisitely subtile, without being at all acute; hence there is so much humor and so little wit in their literature. The genius of the Italians, on the contrary, is acute, profound, and sensual, but not subtile; hence what they think to be humorous, is merely witty.
    --Coleridge.

    The subtile influence of an intellect like Emerson's.
    --Hawthorne.

    5. Sly; artful; cunning; crafty; subtle; as, a subtile person; a subtile adversary; a subtile scheme. [In this sense now commonly written subtle.]

    Syn: Subtile, Acute.

    Usage: In acute the image is that of a needle's point; in subtile that of a thread spun out to fineness. The acute intellect pierces to its aim; the subtile (or subtle) intellect winds its way through obstacles. [1913 Webster] -- Sub"tile*ly, adv. -- Sub"tile*ness, n.

Wiktionary
subtileness

n. The quality of being subtile.