The cartridge was introduced in 1962, and like the other long Weatherbys, is based on the .375 H&H case, necked down, given a Venturi shoulder, and de-tapered. It holds gobs and gobs of powder, and with a 24-inch barrel produces 200 fps to 250 fps more than the .338. Weatherby has always used a 26-inch barrel for this round, and I have always rushed to the gunsmith to have 2 inches lopped off, but it will give you even more velocity. A twenty-two inch barrel, which does very well for the .338, is mere foolishness with the .340.
The .340 occupies several niches: One is as a delivery system of Major Wallop at long range. You can crank a 210-grain bullet (much better than the 200) up to nearly 3,000 fps in a 24-inch barrel and it will pound the daylights out of whatever you want to pound way, way out there. Another niche is inside of 300 yards, as a general overwhelmer of whatever poops, where it's at its best with 250-grain bullets, which I was able to get moving at 2,850 fps.