Lawrence Shelton just published a book, "J.P. Claybrough Birmingham Gunmaker". I bought a copy from him at the Antique Arms Show.
Looking through the book, I see several guns with a 3 on the barrels. It may be a vendor/barrel maker code.
There are some serial number tables in the book. The proof marks are pre-1887.
There was an early model hammer gun with high hammers and a newer low hammer model. A serial number or photo of the action would help.
Does it have the "Duck and Quail Gun" butt plate? Seems like there must have be some whopping big quail in CA back then to need a 10 (or lousy bird dogs).
You should be able to Google the book if you want a copy.
Joe
