That's a beautiful gun. Is that the original stock? Do you have the stock the letter states was made for Matheson?

So this gun was ordered, then presumably manufactured,then used in an Exposition the previous year?

Beautiful Gun , Congratulations ! I would enjoy seeing some close up pictures of the Receiver engraving ,especially the Quail ! Thanks for posting ! Russ

As the letter doesn't state that it was rebarreled by Parker, it may have been after they kept order book information, or it could have been done at Remington. Do the flats have any stamping to indicate Remington? Does it have a Parker Brother legend on the top rib? If so, it could have been done in Meriden after they ceased order book entries. Where is the number 2 stamped? On the fore end lug?

CH flats & stamps
 

Edgar,

Is this stamping and are these the lugs you were inquiring about?
I'm using my camera phone to take the pictures, so if the clarity of the photos isn't helping answer your question just let me know.

Very cool. Looks like it was made for promotional purposes. While it went to expos, I'm sure it was also used elsewhere by Parker to promote it's guns. Probably was maintained at the factory. When it's use as promotional gun was complete, it was sold to dealer in Boston. Interestingly, at full price. Many time these promotional guns were sold at a discount hater use. Then the dealer sold it to a baseball great! Can't get much better then that! I hope you can find the barrels but if not maybe any set of Bernard barrels would do.

Yes, and good pics. Certainly appears to be a factory fitted 2nd set of barrels. It would lead me to believe that the original barrels were with the gun when it had the 2nd set fitted, but I could be wrong. I'm also speculating that the work was done in Meriden, even if Remington owned Parker at that point. If it was a set of Meriden barrels that went to Ilion, then I'd expect to see Remington stamping on the flats.
Very nice gun! I'm sure you'll get plenty of use out of it, and perhaps more so because of the Titanic barrels. I guess it's the rarity of Bernard barrels that gets some wound up, but personally, I find damascus patterns more pleasing to look at.

Can anyone tell me if the history and provenance gives the gun more value or is it just a neat thing to have and know about the gun? Many athletes and actors owned Parkers, but I'm guessing it's the condition of the gun that gives it value. Unless of course it was owned by a Czar....

Generally speaking, provenance adds interest and history to the firearm. It can also add value if one of the previous owners was a famous (not just wealthy) person such as a top tier actor (Clark Gable etc.), political figure (past president etc.) or a noted competitor or exhibition shooter (Annie Oakley etc.) or noted sports personality. :)
After seeing the pictures it appears your barrels are Vulcan, not Titanic. The circled V on the right barrel flat indicates Vulcan steel.
My BHE 20ga (originally Damascus ) was fitted with Vulcan steel barrels sometime in the mid 30's, probably by Remington/Parker as evidenced by Remington codes on the barrel flats.
Could you take another picture of the flat of the left barrel? That is where the repair codes are usually stamped.

Here are the close up photos that you requested. Excuse the lack of focus, I'm using a camera phone right now until I can find my wife's digital camera.