The Collaborative International Dictionary of English v.0.48:
Middlings \Mid"dlings\, n. pl.
1. A combination of the coarser parts of ground wheat the
finest bran, separated from the fine flour and coarse bran
in bolting; -- formerly regarded as valuable only for
feed; but now, after separation of the bran, used for
making the best quality of flour. Middlings contain a
large proportion of gluten.
2. In the southern and western parts of the United States,
the portion of the hog between the ham and the shoulder;
bacon; -- called also middles. --Bartlett.