To give out; to be exhausted.

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1854.  He ‘hoped this ’spectable meeting war n’t going to Peter-out.’—H. H. Riley, ‘Puddleford,’ p. 84 (N.Y.).

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a. 1865.  The store in which he clerked was “petering out”—to use his own expression.—I. M. Tarbell, ‘Abraham Lincoln,’ McClure’s Mag., vi. 127 (Jan., 1896). (N.E.D.)

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1876.  [He advised him] to sell out at any sacrifice, as the mines were petered out.Boston Post, May 5. (Bartlett.)

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1888.  The Boston Herald thinks the Hill boom is petering out. When the time comes for Mr. Hill to have a boom, it will not peter.Missouri Republican, Feb. 15. (Farmer.)

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