Never heard of a Brown Ballard in anything but .32, .38, .44 and .46 rimfires. John Dutcher does have a picture of one in .44-60 Sharps Bottleneck, but they were extremely rare, and the only centerfire cartridge known in a Brown.

Ray,

     I'm with Greg on this.  I am wondering if it is a .38 rf bore that you are seeing.  If it is an unaltered Brown breech block, it would be expected to be superficially pretty much like a longer Marlin block only instead of having a reversible firing pin it would have had a percussion nipple in the middle and probably a rimfire firing pin integral to the hammer nose...but this last may be variable.   

     Another giveaway that it was a higher grade sporter is the presence of a dovetail in the wrist of the receiver casting for a tang sight...NOT two threaded holes like the Marlin.  The Brown receiver I have does indeed have this last and has the same internal tang as the Marlin, so having a non-original  buttstock could be easily explained.

HTH, Froggie

Actually the old .38 rimfire used a .375" bullet, same as the .38 Colt centerfire. The later Marlin Ballards with the reversible firing pin shot both .38 RF and .38 CF longs or shorts.
Not sure why it would slug .354, especially if it has the dual ignition system of the Brown Ballards. These were the .38 rf load, and should slug to about .370".
I'm not positive, but I think if I remember right my old Brown Ballard has a slightly thinner breechblock in front to back than my Marlin Ballards. It needed to be thinner to allow the fixed firing pin on the hammer to reach the edge of the rimfire cartridge. These Brown Ballards also had a little longer hammer spur than Marlin Ballards.
The "brass ring for a forearm" is tough to picture? Do you mean there's no forearm wood, or is there a brass ring for the extractor, instead of the usual lever to extract? I've seen more than a few of these early Ballrds with extra dovetails for long scopes. Is the "pencil scope" you have, a lter scope, or an early brass scope? Full length, or short?

Got the pictures! Thanks. That explains it well.

Most palm rests used a 1/4-20 thread, but I do know that a lot of better hardware stores have an adapter to take 1/4-20 to 5/16-24, so that might work.
Jeff's Outfitters sells a palm rest complete for about $60. He has a web site, and you can contact him through it to ask the dimensions of the staff. (You need to Login or Register to view media files and links)