A 19th century ordnance or artillery award?

[A26Blackhawk]

538 uniform buttons.jpg (71.19 KiB) Viewed 716 times

538 uniform buttons back.jpg (53.42 KiB) Viewed 716 times

The collar insignia on my cabinet portrait is a prominent wheel over a gun trail and cannon barrel. The domed buttons are all numbered either 538 or 638. There are no epaulettes, and the wearer resembles US army ordnance officer Adelbert Rinaldo Buffington who served 1861-1901. The face of the medal has a circular inscription around the rim but I can't make out the central design. Your information and details are apprciated.

[A26Blackhawk]

This uniform is worn by a member of the Ancient and Honorable Artillery Company chartered in 1638 which makes this unit the oldest chartered military organization in the western hemesphere. The unit still exists in Boston, Massachusetts and was identified by the historian when I emailed the portrait to him.