I should have mentioned, the photo on the right shows an excavated specimen's front. The photo on the left shows a non-excavated ("non-dug") specimen's back. I included the non-exacavted back view to show the CORRECT original brass wire attachment-loops. The loops were held onto the insignia with a spot of solder. The attachment-loops are usually missing on excavated specimens.
The reason I said "CORRECT" attachment is that many non-exacavated Originals, and most Reproductions, have a straight wire as the attachment method. When you see one of these US 1851-to-1871 Enlisted-man's hat insignia with straight wire instead of a loop, it means the Enlisted-man's hat insignia is either Post-Civil-War or a Reproduction. Here is a photo of some specimens sold by Bannerman's Surplus, long after the Civil War ended, with the straight wires. Please do NOT pay a civil war relic price for these with straight wire. It should be a brass wire LOOP, with both ends of the wire loop embedded in the solder-spot, as you see in the photo I posted previously.