There are many interesting facts about US military uniform buttons.
American Duchess has an awesome guide for this handy technique here.
Attching buttons that way makes sure they stay flat, flush and firm instead of flopping around.
“The shift of the eagle's aspect to right-facing from left-facing is logical from the perspective of heraldic tradition, since the right side (dexter) is the honor side of the shield and the left side (sinester) indicates dishonor or illegitimacy.” (source: the buttons in the picture, those on the left are Civil War-era, those on the right are from a WWII US Navy uniform (my father-in-law’s).
There were two primary types of US Navy buttons worn during the Civil War. They are both “an eagle resting on a horizontal anchor, three cannon balls below, with 13 stars encircling, on a lined field”.
Research led me to lots of metal detecting and mudlarking websites where I learned that these buttons are commonly dug up across the English and New England countryside. The English discovered a process for gilding buttons in the late 18th century and by the 19th century the manufacture of gilded buttons was in full swing.