HH: Perhaps you had a typographical error and meant ".404 Jeffery."
The 400 Jeffery is just another name for the .450/400 Nitro Express 3". The firm of W.J. Jeffery & Co referred to it as "Jeffery's 400 bore" in their catalogs, but it seems that it was the .450/400 NE 3" everywhere else. About 15 years later (the records aren't quite clear) Jeffery introduced the .404 Rimless Nitro Express (a.k.a. "404 Jeffery") to provide similar ballistics in a cartridge suitable for use in a bolt-action magazine rifle.
As regards its suitability for dangerous game, well .......... far be it for me to argue with C. Larsen Esq., a man who has "shot 52 Elephants, 6 Rhinos, and many other game" with the cartridge.
This is from their 1905 catalog:
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