RMC,
Could be any of may 8MM. First to come to mind is the 8X72r.
When you say a straight case do you mean a "straight tapered case"?

Is it possible to get good clear pictures of the markings on the bottom side of the barrel??? Also who made the Drilling?

Finally the "best" way to determine the caliber is to do a chamber cast or have one done by a competent gunsmith. There are a lot of these old guns that were chambered in proprietary cartridges designed by the gunsmith that built the gun. Johann Peterlongo was one that comes to mind. I ended up with one of his guns in a caliber that ammo was only available from him and not manufactured by anyone else. Wasn't hard to make up but without a chamber cast it would have been impossible to recreate..

Like I said if you can get some pics it may help answering your question..

But a chamber cast is the "Gold Standard"..

WBLDon