More Yiddish: “Es Lauft die Jauch, die Millech brennt..."

Question

This couplet by Peretz (from "The Ballad of Monisch") describes how the Rabbi's wife has neglected to pay attention to her cooking on the stove:

“Es Lauft die Jauch, die Millech brennt

Un sie sitzt, verlegt die Händt.”

We have "broth" for Jauch, but my German dictionary gives me something disgusting that you wouldn't be cooking on top of your stove. I wonder if anyone would like to comment on the possible evolution of this term?

EDIT: I forgot to include a phonetic transcription for the Yiddish: we would have,

"es loyft di yoych, di millech brennt, un sie sitzt, farleygt di hent."

Answer 1

Im Grimm steht alles, auch das hier über Jauche:

trübe flüssigkeit, flüssiger dünger. das wort gehört zu denen, die ihren ursprünglichen begriff verschlechtert haben; es bedeutet im 15. jahrh., wo es sich zuerst landschaftlich, mitteldeutsch und niederdeutsch, nachweisen läszt, sowie im 16., nur brühe, suppe: jus juche

This translates that regionally up to the 16th century the meaning indeed was broth or soup. Only later the meaning of "Jauche" diminished.

Interestingly for the synonym "Brühe" we do have both meanings still:

1. aus Fleisch, Knochen, Gemüse u. a. gekochte klare Suppe
   (landschaftlich) Gemüsebrühe
2. (umgangssprachlich abwertend) dünner Kaffee, Tee o. Ä.
3. (abwertend) verschmutztes Wasser, schmutzige Flüssigkeit
4. (umgangssprachlich) Schweiß

^Duden

Answer 2

I guess the disgusting thing is Jauche. Etymologically it comes from the Sorbian word "jucha" which means "Brühe". And "Brühe" is the English "broth".

Jauche and broth are both liquids, so I wouldn't be surprised about that change of the meaning. If you mess up your broth and it does not taste, then people may say, it smells like (liquid) manure. That could be the origin in the change of meaning.