Etymology
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batch (n.)
late 15c., probably from a survival of an unrecorded Old English *bæcce "something baked" (compare Old English gebæc) from bacan "bake" (see bake (v.)). Generalized sense of "an aggregation of similar articles" is from 1590s. Batch is to bake as watch (n.) is to wake and match (n.2) "one of a pair" is to make. Extended 1713 to "any quantity produced at one operation."
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clutch (n.3)

"a brood, the number of eggs incubated at any one time," in reference to chickens, 1721, a southern England dialectal variant of cletch (1690s), noun from cleck (v.), which is from Middle English clekken "to hatch, give birth to" (c. 1400), which is probably from a Scandinavian source (such as Old Norse klekja "to hatch"), perhaps of imitative origin (compare cluck (v.)). Compare batch/bake.

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mail (n.1)

"post, letters," c. 1200, "a traveling bag, sack for keeping small articles of personal property," a sense now obsolete, from Old French male "wallet, bag, bundle," from Frankish *malha or some other Germanic source, from Proto-Germanic *malho- (source also of Old High German malaha "wallet, bag," Middle Dutch male "bag"), from PIE *molko- "skin, bag."

The sense was extended to "bag full of letters" (1650s; perhaps via phrases such as a mail of letters, 1654) and "person or vehicle that carries postal matter" (1650s). From thence, to "letters and parcels" generally (1680s) and "the system of transmission by public post" (1690s).

As a newspaper name, by 1789. In 19c. England, mail was letters going abroad, while home dispatches were post. Sense of "a personal batch of letters" is from 1844, originally American English. Mail slot "narrow opening in an exterior door of a building to receive mail delivery" is by 1893, American English. OED defines it as a "letter-slit."

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