See quotation. Carlyle (1837) has “thoughts which he must button close up.”—‘French Revolution,’ ii. 136 (N.E.D.).

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1841.  As soon as the whole class of small speculators perceived they had been “stuck,” aware of the injury the little credit they possessed would sustain, they all shut their mouths, except, that each one pitied his neighbor; and strange as it may seem, not a man could be found in Wall-street, who confessed the ownership of a share; where three weeks before there were thousands. This is called “buttoning up.”—F. Jackson, ‘A Week in Wall Street,’ p. 47 (N.Y.).

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