"in difficulties," especially "short of money," 1821, slang; it was earlier a nautical expression, in reference to steering.
also egg-shell, "the shell or outside covering of an egg, especially the hard, brittle, calcareous covering of birds' eggs," early 15c., from egg (n.) + shell (n.). It displaced ay-schelle (Middle English ei-shel, also a measure of quantity, Old English ægscill), from the native word for "egg." As a color term, from 1894. Emblematic of "thin and delicate" from 1835; the figure of tread on eggshells "move cautiously" is attested by 1734.
"egg-shaped," 1760, from Latin ovatus "egg-shaped," from ovum "egg" (see ovary).
also egg-head, 1907, "bald person," from egg (n.) + head (n.). Sense of "intellectual" is attested from 1918, among Chicago newspapermen; popularized by U.S. syndicated columnist Stewart Alsop in 1952 in reference to Adlai Stevenson's presidential campaign.
Adlai Stevenson once told what it was like to be the rare intellectual in politics. "Via ovicapitum dura est," he said, the way of the egghead is hard. [New York Times, Oct. 28, 1982]
"an egg," in a broad biological sense; "the proper product of an ovary," 1706, from Latin ōvum "egg," cognate with Greek ōon, Old Norse egg, Old English æg, from PIE *ōwyo‑, *ōyyo‑ "egg," which is perhaps a derivative of the root *awi- "bird." The proper plural is ova.