Hi JHG
Within the fluid power industry such a fitting is known as a JIC fitting (say the letters "Jay-Eye-See" or pronounce it as a word to rhyme with "quick"). You can also call it a "37 degree flare", and some fittings manufacturers refer to it as "AN flare". I think AN stands for "American National".
JIC stands for Joint Industry Council (sometimes Committee, sometimes Conference - it doesn't matter because the group is defunct anyway). The standard SAE J514 covers this arrangement and has been mirrored as ISO 8434-2 but, IMHO, these numbers aren't spoken aloud as often as "JIC".
By the way - this is NOT a "JIS" fitting. In this context JIS stands for "Japanese Industrial Standard". Some JIS fittings are similar to JIC fittings but they have a 30 degree external flare and use metric or BSP threads.
I hope not to offend anyone, but I once heard that "J.I.C" actually stands for "Jesus, I'm Confused!". Maybe that should be raised to the status of the Pipefitter's Prayer?
DOL