according to this, it's part of a cufflink https://www.etsy.com/listing/385360152/eagle-snake-antique-button-cuff-links?ref=market
Cool! That does look like it .. Must be GIGANTIC cufflinks! Thanks.
I'm only riding the coat tails of Bramblefind's good work, but here is one that essentially confirms the size question, in that it is slightly larger, but that would be because the button is complete, with ring around the outside: 3227 I ? The Eagle The Snake 1800?s Brass Button | eBay