
NB  the mathematical symbols used for PePax are not the same as in the rest of the stereo mathematics section. This is a very old section and will/might be updated shortly...
Herbert C McKay wrote a book on stereoscopic photography. His word "parastereoscopy" referred to photographs not following the rules of orthostereoscopy. He claimed a parastereoscopic image could not be distinguished from orthostereoscopy as long as his "PePax principle" was followed. (PePax was a word he invented, of dubious etymology, probably perspective / parallax.) orthostereoscopy etymology
PePax states the stereo base and the focal length of the taking lens must remain in proportion.
PePax: if you double the focal length from standard,

McKay recognised there was different perspective in telephoto parastereoscopy, and he stated it in an interesting way (telephoto lenses pack more matter into the same space...) However, the people he tried PePax out on were unable to tell the difference between true orthostereoscopy and parastereoscopy.
The modern use of this effect is taking stereo with two cameras on a bar, each equipped with a zoom lens (e.g. Sony cameras used with the Lanc Shepherd controller). If you do not change the stereo base, then zooming the lenses in to telephoto reduces 3D parallax. Often the stereo base is too big, because the camers will not sit close together on the bar. Do not worry, just operate them telephoto and move back a bit. The problem will be when you want to take a wide angle view from nearby.
Note that PePax is answering a different question to the Bercovitz formula.
PePax is designed to make things look sensible. (Not actually orthostereoscopic though).
Bercovitz formula is designed to make stereographs that are possible to view without strain, using a standard stereo window, despite showing amazing stereo depth.
There is only one problem with the PePax principle, according to some people writing on the internet, it is wrong! 

Telephoto lens versus standard lens.
The effect on stereo parallax is to change from p1 to p2
But this is not the conditions of the PePax principle, where the magnification is fixed. McKay wants to make a distant object the same size and stereo depth as if it were photographed from nearby with a standard stereo camera using short focal length lenses.

Consider a stereo pair taken with everything the same, except the focal length of the lenses (F) is changed. Let us assume F1 is the standard focal length for the camera format and F2 is a telephoto lens. MacKay was correct: magnification = F2/F1 MacKay was "wrong": BUT the linear parallax on the film is magnified, just the same as everything else in the picture is enlarged by F2/F1. SO the telephoto lens (F2) has a bigger parallax on the image. It has already magnified the stereo depth.
Doing nothing but change from short focus to telephoto lens gives hyperstereoscopy. Those who prefer orthostereoscopy will have to reduce the stereo base (B) when shooting telephoto.

The PePax principle quotes the special case where the magnification is the same despite changing from a standard to a telephoto lens. Dropping the magnification in telephotography (with a fixed focus lens) can only be done by moving further away from the subject. To get the same magnification changing from F1 to F2
Now consider the parallax between front and distant objects. If you doodle on the back of an envelope, using similar triangles and the above diagram, the parallax as you get further away from the subject is found to be:
The surprising consequence of this parallax equation is:
So PePax is right: you must do two things to regain "proper" stereo depth when photographing a distant object:
Then the stereo parallax is back to "normal". In other words we must use a quadratic (square) function for the stereo depth but a linear function for the magnification. Stereo depth perception decreases by the square of the distance: a stereoscopic inverse square law. Just as McKay said  only he put it differently and confused everybody ever since! PePax is still not orthostereoscopy, as the attractive purple column to the right explains. 
The reason perspective decreases with telephotography comes from the change in magnification with distance. Magnification on the film changes with focal length in a linear fashion: For a subject with fixed depth, d: So the difference in magnification between the near object (n) and the distant object (m) We say the perspective has decreased in a telephoto picture, because we are losing the size cue of distant objects looking smaller than closer objects.
Variation in stereo base and focal length is shown very nicely by Tony Alderson {here} 
Derivation of the parallax formula(according to nonmathematician John Wattie) q is the real relative parallax between (In "stereoplotter talk", q is the measured relative parallax on the two photographs corrected for photographic magnification). BY SIMILAR TRIANGLES: q / p = n / F (1) q / (mn) = B / m (2) CROSS MULTIPLY q = pn / F (1) q = B(mn) / m (2) OR since q = q, combine (1) and (2): pn/f = B(mn) / m (3) CROSS MULTIPLY equation (3): pnm = Bf(mn) DIVIDE RIGHT AND LEFT BY nm
IF d = depth of the object, d = mn SO
nm is the square of the geometric mean distance from the camera to n and m because 
