Note there are several early large body ukes with no serial numbers. This one is unique for the screen coverplate with an extra 'diamond' under the tailpiece.It also has an early (non-spirals) 'step' cone. (see the large body style 2 ukulele page for pictures of one of these cones).
It is, I believe the only style 3 large body in existence.
NB This instrument also has a cast aluminum tailpiece, rather than the wooden one on later instruments. I suspect it has been drilled out at some point to take these new strings. It would almost certainly have had steel strings when 'new'. Please see this note on National Ukulele stringing.
I have pictures of another early painted, no serial number large body uke, which also has an ali tailpiece, with four little hooks to catch the ends of loop end strings. Look for pictures here soon.