If it helps you understand better, imagine a compass with its four points laid out as a cross.Some thing tied upright would follow a South to North plane, up and down.
Horizontally would imply being tied East to West as per the Horizon.
Any good to you?,
Pedro.

 

Without reading it I couldn’t say for certain but as someone who was really into tying classic flies the number one mistake I see from folk wishing to tie as they did, was putting the wings on upside down.
Left fibres go on the right and vice versa and there’s many a good reason for that as you’re not working against the flow of the materials.

 

I can’t click on the link but re the different ways of “building” traditional flies there’s a few different ways.
1/Feather wing ie the Durham Ranger using whole feathers, tippets and crests to build a fly.
2/ mixed wing ie to take bunches of swan, parrot ect in single strands and mixed or rolled together.
3/ Built wing to build a fly by marrying the left fibres to make the right wing and right fibres to make the left or nearside wing. Same applies to the white tip and the wood duck ect.

Study the book you mentioned and look at antique examples as so many modern makers of these flies do the opposite which results in a hump in the wing which is why they have to fight the materials like tippets ect just to sit right?

 

I had no idea what the answer was when I first saw your question about half an hour ago, but I thought it was interesting.

I found an on line copy of the book (which I've not read before but will do so now that my curiosity has been aroused) https://archive.org/details/howtodresssalmon00prycrich/page/128/mode/2up

I think the answer to your question is in this extract from page 128:
"Strip-wings may be tied in so as to lie entirely on the top of the shank i.e., with a vertical inclination or they may be tied so as to encircle the shank partly i.e., with a sloping or horizontal inclination."

Looking at the illustrations in Plate XII, i and ii are upright ie tied on top of the hook and iii and iv are horizontal. The different wing shape between i and ii (and between iii and iv for that matter) are because of where from the feather the wing slips are taken from as described in (a) and (b) at the bottom of page 128.

It seems to me that i(a), i(b), ii(a) and ii(b) on page 128 refer to i, ii iii and iv in Plate XII

The top of page 132 may also shed some light on the "horizontal" wing.

Hope this is helpful, I don't mean to try to teach my grandmother to suck eggs!!

 

Course this is helpful as you'd be amazed how even really good classic fly builders get this wrong.
Most of this stuff suddenly becomes clear when you have a go at tying in hand as for some reason the materials do seem to naturally end up as the description?
There's another important thing that many folk get wrong and that's the size of materials and fly? So basically anything with the description of small fibres such as duck and parrot will dictate the size of fly one makes. For show purposes I suppose it becomes natural to tie on 4/0s ect but as soon as you approach it from a fishing perspective as they did it's far more in keeping with the time as oppose to just making a show fly in my humble opinion of course.