"There is still no mention of an 1/8 of a turn on one or any of the steps."
Look at the diagram and you will clearly see it. In Ballroom Dancing the text description does not break down the turn per step for this figure; in other volumes such as the ISTD book it is broken down and that same 1/8 turn seen in the diagram in Ballroom Dancing is explicitly stated in the text.
"Where you are making a mistake is you are taking the line of the feet as being the alignment of the body."
No, I am taking the alignment of the feet as being the alignment of the FEET. The alignment of the body is not necessarily the same as that, but it is also not relevant to the fact that turn exists, because "TURN" IS MEASURED BETWEEN THE FOOT ALIGNMENTS, NOT IN THE BODY.
"Once again. The turn of the feet the 1/8 which you are concerned with is not mentioned"
Wrong, it is mentioned. There is officially 1/8 turn on that step, precisely because of the 45 degree change in foot alignment.
"because there is no turn of the body on that step."
Body alignment is not a factor in "turn".
"It is the body that we have to be concerned with and Alex in his infinite wisdom didn't think anybody would think otherwise."
You could not be more wrong. The book is written largely about the foot postions, and NOT ABOUT THE BODY. To quote from the explanation of the amounts of turn:
"It should be noted that the amount of turn is measured from the positions of the feet, which is a little disconcerting at first. It would appear to be easier to take the amount of turn from where the body is facing, but in practice this becomes even more complicated".
There you have it - turn is measured in the feet, NOT THE BODY, and it's refusal to grasp this that is behind so many of your mistaken comments.