Chas.
The No. 2 is not often found in 44-40. I have no idea how many were made...
I have a No. 2 22 That has TP & B on the bottom of the barrel. The TS or TP might indicate tang peep sight. I don't know for sure.
There should be a serial # on the bottom tang. That would help date the rifle. If it has E. Remington & Sons on the barrel, it is pre-1888. If it says Remington Arms Co, it is post...
John Gyde