"The weight is not over that foot untill after it is in position."

You mistake is in the misunderstanding of the words "over" and "weight".

What is weight?

Answer, it is a FORCE. And force is VECTOR quantity, not a scalar. That means that WEIGHT MUST HAVE A DIRECTION.

And what is the DIRECTION of the weight (force) when it first transfers from the old standing foot to the new? The answer is that it is AT AN ANGLE to the vertical. This ANGLED FORCE passes from the body center through the toe of the receving foot.

And it's what means that you can immediately remove all body weight from the back foot. You'll even see the back knee starting to immediatley flex. You should not whip the feet closed - do by all means let that departed foot trail behind. But it no longer has any weight, because the direction of the weight force is now aimed at the moving foot - there is zero role for a support point left behind you, which is what the departed foot is.

The net result is that the body is instantly "OVER" the foot with respect to the force, long before the body mass arrives over the foot with respect to gravity.

"They then go to this incredible 45 degree bend of the leg."

Oh I'm scared, that must take a lifetime to develop. Not.

At the extent of the stride we have two straight legs. Heel of the front foot. Toe of the rear foot. Weight right in the middle moving. Go look at your tapes frame by frame if you like and tell me it is not so. Or a look at the technique book will do.

"At the extent of the stride we have two straight legs. Heel of the front foot. Toe of the rear foot. Weight right in the middle moving. Go look at your tapes frame by frame if you like and tell me it is not so. Or a look at the technique book will do."

You are accurately describing the visual position, yes, but it is impossible for the weight to be split when the figure is fully danced. In an exercise, yes. But not in full dancing. The reason is that skilled dancers do not let the third step land until it is no longer possible for them to support their body with the departing foot. Achieving split weight would require cutting their action short - and they don't do that.

In tango perhaps - but NEVER in foxtort.

You've lost me again. How did the third step get into this. One step, a heel lead. Every book ever written has said at the extent of the stride the weight should be equally divided between the heel of the front foot and the toe of the back foot. Man or lady, going forward or backward. After this the moving foot will come into a position that is under the body. If it is Foxtrot or Waltz the action is the same. In the Waltz as the foot comes under the body and the supporting knee is bent we turn. If its a Natural this will be over the RF. If it is a Foxtrot the Turn will be over the RF for a Natural and the LF for a Reverse. But don't take the books word for it. Get your DVD's out and watch frame by frame what our best dancers are doing. Look at those feet only.

"How did the third step get into this."

Simple: going into an action like the third step of a feather is the only sort of place where you will actually ACHIEVE the "two straight legs" you mentioned.

You might think you achieve then going into a heel lead, but in fact you don't. Nobody does...and it would be a real mistake to try to literally accomplish it there, as it would only be possible by overstriding.

That third step, if you look frame by frame, is very interesting.The weight is over the LF. The right knee is bent untill the toe of the RF is in place, then it straightens As the weight is passed onto the RF the knee starts to bend. Then watch for that LF coming under the body into a neutral position. Neutral also means a balanced position, or if you like how we started in the first place which was , with our feet under our body.
Here it is. Both knees are bent. The moving leg which is the left leg will have to straighten to a straight leg as well as the standing leg which is as the technique book says.

"That third step, if you look frame by frame, is very interesting.The weight is over the LF."

Actually, it is not. The weight is located well past the left foot, while it is still resting only on the left foot. You can plainly see this on any top quality couple - they have overbalanced past their standing foot, at a point when it is obviously still the only standing foot.

"The right knee is bent untill the toe of the RF is in place, then it straightens As the weight is passed onto the RF the knee starts to bend."

Actually it is straight shortly before it is placed. The weight transfer (when actually DANCING the feather, as opposed to doing various training exercises is INSTANTANEOUS - it has to be, as the right foot doesn't stop moving and prepare to take weight until it is no longer possible for the left foot to support the body)

"Neutral also means a balanced position, or if you like how we started in the first place which was , with our feet under our body."

Nope, having the moving left foot under the body says NOTHING about the position of the body weight relative to the standing foot. For most top-ranked dancers, the moving leg won't move under the body until the body has already overbalanced slightly beyond the standing foot.

"The moving leg which is the left leg will have to straighten to a straight leg as well as the standing leg which is as the technique book says."

Nowhere in the description of a figure is a "straight leg" called for!

Again, you mistake the description of a walking exercise for any actual dance figure. IT IS AN EXERCISE, NOT A FIGURE!!! It is NOT DANCING, but rather EXERCISING.

Page 10. Under Knees. " The knees are only straight at the full extent of the stride , not rigid ".( step three also the same ).
As your partner comes towards you to take up their dancing position. Your legs are under your body.
You do not have a leg either stuck out to the side or in front of the body. You should be in a balanced position which can be called neutral if we wish to refer back to that position.
Also page 10 Under the distribution of Weight. The reason for the book saying that . " From a stationary position always feel that the body commences to move slightly before the foot. Remember the speed of the foot is always greater than the speed of the body. If the foot is moved before the body the weight will be kept too far back and a sitting down effect will be made " .
Just my thoughts. Each of those two moves cancel each other out. 1 divided by 1 = 0. So at first the leg doesn't go by itself.
And lastly. We do not overbalance and then catch our weight. Which would happen if the body is overbalanced. In Latin in the Rumba Walks Yes. But in Modern NO.
Hold a pencil on a piece of paper keeping it verticle and move it forward. Now lean the pencil forward of itself and move it. Is that how you suggest we dance a forward step.
Victor Silvester. Page 56.
Generally speaking the knees are at their straightest - but not stiff - at the full extent of the stride and relaxed slightly as the weight is taken on the foot ".

"Page 10. Under Knees. " The knees are only straight at the full extent of the stride , not rigid ".( step three also the same )."

And what figure is that describing?

Answer: it is not describing a FIGURE, instead it is describing a TRAINING EXERCISE.

You still don't understand the difference between an EXERCISE and DANCING.

It is a Basic Technique which if not learned correctly will always result in a major fault not only in the Foxtrot but also the Waltz. The technique quoted is not a training excercise as you claim. If it were why would it be spoken about in the basic technique section. Use a bit of logic here. The figure being descibed is a simple step forward. The very first step we take.
There are none so blind that will not see. Never was a truer word spoken.