Dąbrowski has an unidentified “American Masonic Symbols”, see below.
I know a “Masonic handkerchief” from “the 1800’s” which has the symbol not within another circle. See below, at the bottom left of the All Seeing Eye.
And here follows the answer:
It is a protractor, the symbol of the Grand Inspector of Works.
First two: Dąbrowski P. 186. Year and designer unknown. Feddersen (E/114, p. 264) calls it a silk cloth from 1850.
Third: found on online auctionwebsite, supposedly from “the 1800s”
Bottom: general officer jewel design