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.
      [1913 Webster]

   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.
      [1913 Webster]