Welcome to Nitro Express!

The Nitro version was surely a development of the 360 2-1/4" Black Powder Express cartridge which in turn was a development of the paper case 360.
Generally, the BP 360 used 50grs of powder and usually a 155gr to 190gr lead bullet and then the full nitro version used 190gr lead (22gr cordite)up to a 300gr jacketed (30gr cordite) bullet.
Early on, Alexander Henry offered ammunition for his wonderful 360 rifles loaded with round ball and 14grs of black powder which enabled the rifle to genuinely be appropriate for rook and rabbit up to small deer. It looks like Henry started chambering his rifles for this cartridge around 1869.

What type of rifle are you shooting?