I recently acquired this official business cover with a 32mm double circle Washington, DC Feb 19, 1863 postmark. The cover has been authenticated by Assistant Adjutant General Sam G. Peck.
The addressee, G(eorge) W. Childs, was a prominent publisher in Philadelphia at this time.
One of the works Childs published in 1863 was titled "The military laws of the United States: relating to the army, volunteers, militia, and to bounty lands and pensions: from the foundation of the government to the year 1863" -- most of which would have been under the purview of the Adjutant General.
Unfortunately there was no content so I'm making an educated guess that the correspondence carried by this cover likely had something to do with that publication.
