Steve is correct that the .360 no.2 a great cartridge.
Graeme Wright, author of the book "SHOOTING THE BRITISH DOUBLE RIFLE" says: "A very much overlooked cartridge. With the 320 grain bullet it is up there with the .375 Flanged H&H Magnum in effectiveness. It shares the same bullet diameter as the 9.3 so a wide variety of bullets are available." Wright lists a number of loads for the cartridge in his book.
On another note, I have a copy of the UK book: "Rules of Proof 1954" which includes the proof loads that the London and Birmingham proof authorities used then to proof rifles and guns. The .360 No. 2 shows that it was proofed with 64 grains of Cordite with a 320 grain bullet and greased cloth wadding. The length of the cartridge with this proof load was 3.875 inches.
The same "rules of proof 1954" shows the proof load for the .375 H&H Flanged Magnum was 1 grain less of Cordite than the .360 No. 2 with a 300 grain bullet; while the .375 H&H Belted Magnum was proofed with 1 grain more of Cordite than the .360 No. 2 with a 300 grain bullet--both .375 H&H cartridges were 3.700" long.
I do not advocate that you re-proof your rifle, just giving you what I discovered.