Found a 7.8 x 57 R (yes, that's what it says)beneath 16 ga. barrels. German, I think, got a horn trigger guard, etc.

Is this the 7.92 JR (8mm JR) or another caliber I've never heard of? Gun is about 98%, asking price is $2400 or so. I can't afford it, just asking.

It could be the forerunner of the 8x57 Mauser. That's about all I could find on it in Cartridges of the World. I could be wrong.

Rimmed 8mm Mauser with .318 bullet.

Get some Cerosafe, and make a chamber casting. Let it rest for one hour, then mike the dimensions.

Yup, that's the only real solution, since there are about 8 trillion old German rimmed 8mm rounds. It's probably some version of the 8x57R, but you want to make sure, both about the chamber and the bore dimensions.

I'm not an expert, but own two, and have handled a bunch more. I've also spent a lot of time researching drillings and O/U guns.
One has to be bit careful with drillings. Price depends on condition, manufacturer, model, proofs and marks, calibers, etc. Like bolt rifles,drillings made by different makers vary in price. The type of action of the same manufacturer can change value.
A couple things you need to look at for a shooter: is it on face, that is, is the barrel tight to the action? What caliber and guage is it. You might need to do a chamber cast and slug the bore. For instance, there are two primary diameters for 8 mm, .318 and .323. There are variations in between. Numbers on the barrel may be diameter at lands, not bore diameter. What kind of shape is it really in. They are like girls with a lot of make up. You need to look at them in good light and you need to have your hormones under control, before you take them home. You can spend a lot of money on one that you won't like in the morning.
There are people on a couple other forums that are really experts on these guns and can provide much better information than I.
If you're thinking about buying a drilling, or if you just want to learn about them, The Drilling Gun by Klups is a great read.
Hope this helps
Bfly

There can also be a wide variation in bore diameters. I have seen older German guns supposedly chambered for the 9.3x72R will all sorts of dimensions. My wife has an O/U combination gun that the previous owner was so certain was a 9.3x72R (under a 16-gauge barrel) that he bought a box of RWS ammo and fired half of it through the gun. The ammo was part of the deal.

But when I got home and made some measurements I found the bore was actually .350 across the lands and .358 across the grooves, a perfect .35 caliber. Luckily, the ammo was loaded with very soft bullets and caused no problems, and the bore size makes loading for the old gun a LOT easier. But you just never know....

I had one once that was a 9X57R. Had the barrel slugged and it came out as a .358 grove diameter. I bought Norma 8X57 JRS cases, necked them up in a set of 9X57 dies and loaded them about like a .35 Remington. Worked fine, BTW.
What hasn't been mentioned is that the 16 ga. shot shell chambers were for 2 1/2 inch shells, not 2 3/4 inch shells. I had mine opened up to take the standard 2 3/4 inch ammo.
I'm really sorry I sold it. It's only flaw was the Greener side safety which was not very easy to push to the off position. Otherwise, it worked well. E

Sounds interesting, do the chamber cast, but I would bet dollars to doughnuts it will be an easy round to find or make. Then make an honest gun of it and take it hunting.

Well, someone else will have to hunt it! It's out of my price range.

One thing I noticed in handling it is that the weight is much less than I thought it would be. Partly, I guess, because it's a 16 g. as opposed to a 12 ga. It's not ballerina, but it's not bulky, either.