"as the crow flies", 1757 (antedates OED 1810-)

[Joel S. Berson]

"as the crow flies":  OED 1989, s.v. "crow, n.1", sense 3.c., 1810-

Art. XIII, Mr. Keysler's travels through Germany, Bohemia, Hungary,
Switzerland. Italy, and Lorrain. 4to. 4 vols. Linde.  [Concluded.]

In _Critical Review, or, Annals of literature_, 4 (1757 July), p. 68.

This is the substance of Mr. Keysler's last volume. In our extracts
from it we shall take the same liberty as in the preceding, of
traveling with him as the crow flies, passing over many places, and
only stopping at those which seem best to deserve our reader's attention.

(Might this have been written by Tobias Smollet?  The Pickering and
Chatto reprint might say.)

Joel

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