"Anonymous. To save starting another bit of writting. Foxtrot step three has no CBM."

Nobody said it did!

"The third step if the Natural is coming after a half a turn over steps 1-3 cannot be compared to the Reverse Turn."

Sure it can. It's not an exact mirror image, but there are qualities that are mirrored between the two. Notably the quality you overlooked in this case: in both figures, the body will be underturned at the step 2- step 3 transition, meaning that the third step (to go direclty down LOD) would have to fall somewhat across the body, which is not actually rotated to back LOD. But of course that does not mean the third step is in CBMP.

This is an example of a step which falls across the body, BUT NOT ACROSS THE STANDING FOOT, and thus is not in CBMP.

"If you are following the book the Natural Turn starts facing the LOD."

Yes, but it's much more commonly danced in accordance with the note directly underneath the chart, which tells you how to commence it DW.

"The third step is still straight. I am looking at the chart now. The step is as straight as a bullet in both cases"

Yes, the step is straight, but the body is not yet pointed in the direction of the step, hence the step is somewhat across the body. But not across the foot, so not in CBMP.

In those bygone days and as first taught in a Medal. The Feather Step was always followed by a Three Step and then a Natural Turn straight down the LOD. The one in the book and the description of the steps have the half a turn on that alignment. The ladies usually enjoy that half a turn on their Heel Turn. It's good training also for later steps.

"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.