"The one in the book and the description of the steps have the half a turn on that alignment. "

What you overlook is that the book also has a note giving the method for accomplishing 3/8 turn, and that THIS IS THE MOST COMMONLY DANCED VERSION TODAY.

Not only that, it's the version I was actually talking about.

If you did a Natural Turn in the Foxtrot half way down the floor the amounts of turn cannot be the same as one that is at the bottom end and entering side two. I think you will find that is what the instructions are trying to tell you. It is boring but the Natural Turn taken at the bottom corner will finish acording to the book facing the new LOD (side two) to be followed by a Feather Step Three Step and another Natural Turn. On this new LOD (side three) we did a Feather and Reverse and so on. This was once all that was allowed in a Bronze Medal and with the other dances took six months to complete. This teacher had a very good reputation if it wasn't perfect it was a no go till next time.

"If you did a Natural Turn in the Foxtrot half way down the floor the amounts of turn cannot be the same as one that is at the bottom end and entering side two."

That is not actualy the distinction that the book is making.

Instead, it gives in the chart the amount of turn for commencing the natural facing LOD, such that you would be backing LOD after step three, having made 1/2 turn up to that point. (This would likely be used after a three step following a feather)

Then immediatly under the chart, it explains how to commence facing DW, make 3/8 turn, and end up backing LOD after step 3. (This would likely be used after a three step following a feather finish)

This 3/8 turn version (of steps 1-3 only) is the version I was comparing to the reverse turn, and also the waltz natural and reverse turns which share same alignments. What the foxtrot figures reveal in their foot passing is that the 3rd step moves down LOD in each case. In waltz, the 3rd step must establish a new direction of down LOD, but since the step itself is a closing in waltz this isn't as obvious as it is in the passing footwork of foxtrot.

And when the third step is a passing one, it will end up going somewhat across the yet-underturned body. But since it is not on or across the track of the standing foot, that step is not in CBMP - despite it's being across the body.

If you look at the book a little closer and read the writting underneath a description of a Natural Turn in the Foxtrot. When 4 5 6 are taken at a corner make a quarter of a turn to Face the new LOD. That is straight down the LOD on the short side of the room. Not diagnal to the centre. And there is more. Sometimes we will have a 1/4 a turn or an 1/8 on step 4 5 6. On 1 2 3 we may on the turn have 1/2 or 3/8 . Natural Turn is boring but as explained to me for beginners it is a must. They must learn how to use amounts of turn which later will prove to be priceless to their dancing. This is the part on which a poor school skip through. Tell me. Have the medal tests where you are, have they become a joke.

"When 4 5 6"

Steps 456 were never part of the discussion, which was about steps 1-3, specially how step 3 will go across the yet-underturned body, but not across the foot.

I think you rattle on sometimes without thinking
The first example in the book is for a half a turn on the first three steps of a Natural to finish backing LOD. End of story.
When taken at a corner the only change is on 4 5 6 is, make 3/8 of a turn to face diagnal to the centre. If we wish to finish facing the new LOD we will make a 1/4 of a turn
On any second quick dont forget to hit that crotchet right in the black dot with the music..
If you want to see a 1/2 turn over steps 1 2 3 of a Reverse Turn. Lasts years Foxtrot final with Timothy Howson will show how. I think most will have access to the video by now.

"The first example in the book is for a half a turn on the first three steps of a Natural to finish backing LOD. End of story. When taken at a corner the only change is on 4 5 6 is"

In jumping to your "end of story" you persist skipping over the first note in the book, which is not about changing the second half of the figure (that's the second note), but instead about MAKING 3/8 TURN ON THE FIRST HALF, WHEN COMMENCING MOVING TO DW.

That - the most common version of the figure - is what has been the subject all along, and what is comparable to the foxtrot reverse turn, and to the waltz natural and reverse turns. All feature a third step that declared an LOD direction, after a first two steps that moved on the diagonal.

"On any second quick dont forget to hit that crotchet right in the black dot with the music..

WRONG. See here:

https://www.ballroomdancers.com/Message_Board/view_messages.asp?MsgID=23818

On any second quick in the Foxtrot. dont forget to hit that crotchet right on the black spot. Spoken by Pat Thompson. You know who she is. You should if you have any Blackpool Tapes.
Exactly were are you when you go diagnal to the wall for a Natural Turn. Your not one of those who does a Reverse Turn and Three Step and heads straight across everybody coming down behind you. Heaven forbid.Try that with 20 couples on the floor. You'd get flattened. Hasn't it entered your head that why the Three Step has a curve in it with the right shoulder leading and a Sway to the left.. It is to keep with the flow.
Just to correct you again. The first note (a) There is nothing there about heading diagnal to the wall. Don't get the end mixed up with the beginning which for some reason you have.

"On any second quick in the Foxtrot. dont forget to hit that crotchet right on the black spot."

WRONG. See here:

https://www.ballroomdancers.com/Message_Board/view_messages.asp?MsgID=23818

"Exactly were are you when you go diagnal to the wall for a Natural Turn. Your not one of those who does a Reverse Turn and Three Step and heads straight across everybody coming down behind you. "

If you knew anything about the flow of the dances, you'd know they generally move on diagonals. Extended movement straight down the LOD happens near the center and near the wall, in between the movement is generally diagonal. Look at the classic figures with their 3/8 turns (or in some foxtrot cases, 1/8 change of direction) and this will become clear.

"Heaven forbid.Try that with 20 couples on the floor. You'd get flattened."

Hardly, diagonal movements are the norm, and what those behind you will be expecting if they have any real experience (and those without real experience won't be catching up to real dancers anyway)

"Hasn't it entered your head that why the Three Step has a curve in it"

Check your book: "The three step may also be danced DW. When danced in this direction it may be ended facing DW or curved to L to end LOD"

"Just to correct you again. The first note (a) There is nothing there about heading diagnal to the wall."

Oops, you really stepped in it that time. Open up your book, and you'll see that the first note says:

"Alignment. When the Natural Turn is commenced DW..."

You might also want to look here

https://www.ballroomdancers.com/Dances/breakdown.asp?Dance=FOX&StepNum=193&Part=M

and here

https://www.ballroomdancers.com/Dances/media.asp?Dance=FOX&StepNum=193

Where you will see the common version commenced moving DW with 3/8 turn on the first three steps.

Isn't it great that we have the 2006 Foxtrot Final to compare notes and to watch in particular Timothy Howson who unfortunately had to withdraw from this years due to injury.
You have read the book .A Three Step following a Reverse Turn goes into a corner. Not half way down the floor or anywhere inbetween.
On the vodeo you will not see any of them cutting across the LOD. You do know the difference in the technique between a Waltz and our present subject don't you. With Timothy did you see the sway to the left with the right shoulder leading on the Three Step., or did that go unoticed.
Sway is used on any turn or curve. The Feather Step sways to the right with the left shoulder leading
because it is supposed to curve to the right slightly. The Three Step sways to the left with the right shoulder leading and curves to the left slightly. This is how we find the LOD and consiquently a half a turn on the Natural Turn so that we do not chop the field off who are coming down the LOD. This is as said, not at a corner. The corner is on a diagonel as it is written in the book
With sway the sharper the turn ,the more sway there will be. I did ask exactly where in your routine would you would be after a Reverse Turn. You had best not say half way down the floor. Have you ever been on a floor with twenty other couples in a competition. If you had we would not be having this conversation. Once again . This is not a Waltz. And here. its a small room. But did you see a 1/2 turn there among the 3/8ths of a turn.
To go back to the beginning. This is what was written. Years ago in a Bronze Medal we had to start facing down LOD. We comenced on the outside of the ballroom with a Feather Step a Three Step and 1/2 a turn on our Natural Turn. If we needed more distance to reach the corner we would repeat. Having reached the corner we would turn to the new line of dance. Take note . We are not going into the corner from a Reverse Turn and Three Step.
If you as I suspect are one of those who starts with a Feather Reverse and a Three Step. Your only part of the way down the floor and you cut straight across the field diagonel to the wall. Try that in a competition and see where you land. It is necessary to have good Choreography, Even at a corner one has to be carefull. If you work it out. Going into a corner from the middle you are with diagonel to the wall. But you are also going against the LOD on the short side at the same time. Did you realize that one. You can put your note book away. Schools out.