Mike, that is one fine looking Reilly SxS .500 rifle. I assume this was SN 20674, the one sold at Gavin Gardner.
http://gavingardiner.com/BidCat/detail.asp?SaleRef=0049&LotRef=63A couple of observations. The SN should date to very late 1876 or very early 1877. At that time point no Reilly rifle or shotgun that I know of had steel barrels. The label is from between summer 1887 (closure of the Paris shop) and May 1897 (closure of 16 New Oxford St.). I'd bet it was rebarreled in Whitworth steel by Reilly in that time period - late 1880's or early 1890's.
Gavin's ad said it was proofed for black powder. Does it look as if it has been rebarreled? What is the address on the rib? Could we see a photo of the barrel flats and proof marks? Many thanks. Gene