"Touche", Tim.
This is a duck hunting model #10R which was made in 1903, 1904 and 1905.
The SN indicates 1904.
Note the reinforcing straps on the sides which were only used on the heaviest proved guns such as double rifles and Paradox.
The S powder was used for proving because it gave higher pressure than T.
4.29 gram of S powder and 45 grams of lead is quite a load.
The service load is 4.0 grams of J and also 45 grams of lead.
In 1910 ( my closest catalog), the 10C/R was sold for 380FF and was designer to "resist indefinitely to the violent strain induced by the smokeless powders". It had 80cm barrels, like this one.
There was no loaded ammunition available from the factory. Only empty shells were available in 75mm hulls (which this gun was also chambered for, I think...).
Considering that the gun was supposed to be used in adverse environment, I would say that it is quite a find as few were made and even less survived.
Best regards,
WC-