Bruce, you may be correct about the finishing of lamps at Parkers, as opposed to B&H. Parker didn't acquire B&H until the '40s, but there was a long association between the companies.
Dean, I also have a Rayo lamp, which was one of B&H's named for their different line of lamps. Actually, I have a Rayo, Parker, and 2 B&H lamps. They are so close in detail it's amazing.
http://www.thelampworks.com/lw_companies_parker.htm