colloquial for "sleep," 1899, from shut (v.) + eye (n.). Hans Christian Andersen's "Ole Shut-eye," about a being who makes children sleepy, came out 1842; "The Shut-Eye Train" popular children's poem by Eugene Field, is from 1896.
To tell someone to be quiet and stop talking • Very often a command: ''Shush!'' he shouted, uselessly, to the large noisy hound
[1905+; the dated form is spelled sush]