Ian,
Here is the hub image from the 1924 edition Handbook of the 2-3/4hp.
Not much text to go with it, but here it is:
"The hub and lock ring should always be fitted to the left-hand side of the forks, seen from the saddle, as in this position the motion of the wheel tends to tighten the cup. On no account fail to observe this, otherwise the hub may come adrift."
"All Douglas hubs since 1913 contain 5/16" balls and the adjusting cups and lock rings are left hand thread."
So it looks like the right-hand cup is screwed in fully and the left-hand one is adjusted for the proper bearing clearance. Presumably the 'washer locking axle to fork' engages the square or flats on the axle you refer to. It would then go on the opposite end from the adjustable cup, or the right-hand side of the machine.
-Doug