[photo-3d] Brewster and Wheatstone on the stereo base 4/5

[Abram Klooswyk <abram.klooswyk@xxxxxx>]

In his book "The Stereoscope, etc." David Brewster never 
bypasses an opportunity to argue against Charles Wheatstone, 
and certainly not on the stereo base issue. After his own 
table, based on a formula in which the camera angle depends on 
the fixed eye base of 2.5 inches and the variable photography 
distance, he writes: "Mr. Wheatstone has given quite a 
different rule. He makes the angle to depend not on the 
distance of the sitter from the camera, but _on the distance 
of the binocular picture in the stereoscope from the eyes of 
the observer_ !"  (Italics by Brewster, p 149.)

Then he quotes from Wheatstone's 1852 reading for the Royal 
Society (his second on stereoscopy, Charles Wheatstone: 
"Contributions to the physiology of vision - Part the second. 
On some remarkable, and hitherto unobserved, Phenomena of 
Binocular Vision", Philosophical Transactions of the Royal 
Society, 1852, vol 142, pp 1-17. As his first reading of 
1838 it has been reprinted in: Nicholas J. Wade: Brewster and 
Wheatstone on Vision, Academic Press, London 1983 - 
unfortunately out of print, but in many libraries).

"We will suppose that the binocular pictures are required to 
be seen in the stereoscope at a distance of 8 inches before 
the eyes, in which case the convergence of the optic axes is 
about 18°. To obtain the proper projections for this distance, 
the camera must be placed, with its lens accurately directed 
towards the object, successively in two points of the 
circumference of a circle of which the object is the centre, 
and the points at which the camera is so placed must have the 
angular distance of 18° from each other, exactly that of the 
optic axes in the stereoscope. The distance of the camera from 
the object may be taken arbitrarily, for, so long as the same 
angle is employed, whatever that distance may be, the pictures 
will exhibit in the stereoscope the same relief, and be seen 
at the same distance of 8 inches, only the magnitude of the 
picture will appear different. Miniature stereoscopic 
representations of buildings and full-sized statues are 
therefore obtained merely by taking the two projections of the 
object from a considerable distance, but at the same angle as 
if the object were only 8 inches distant, that is, at an angle 
of 18°."

Brewster comments: "According to the rule which I have 
demonstrated, the angle of convergency for a distance of 
six feet must be 1° 59', whereas in a stereoscope of any kind, 
with the pictures six inches from the eyes, Mr. Wheatstone 
makes it 23° 32' ! As such a difference is a scandal to 
science, we must endeavour to place the subject in its true 
light, and it will be interesting to observe how the problem 
has been dealt with by the professional photographer." 

Interrupting Brewster here, we must note that Wheatstone did 
not mean "a stereoscope of any kind", but a mirror 
stereoscope. In the paragraph preceding the one from which the 
quote comes he said, after mentioning different types of 
stereoscope, including those by Brewster and Dove: "... but 
there is no form of the instrument which has so many 
advantages for investigating the phenomena of binocular vision 
as the original reflecting stereoscope. Pictures of any size 
can be placed in it, and it admits any kind of adjustment." 
(Maybe a hint for debaters on the 35mm / MF / LF issue ? :-))

The adjustment possibility is the clue to resolving the 
"scandal to science". In a Brewster stereoscope, and in most 
modern stereoscopes, viewing convergence is limited. 
The 1-in-30 rule, and the 5P mounting system (laid down in 
Standards) supposes a maximal viewing convergence of two 
degrees, which can be increased to 4 or maybe 6 degrees in 
special cases (handviewer mounts, "double depth" mounting). 
The viewing convergence in Brewster stereoscopes is similar.

However, when viewing convergences of some twenty degrees are 
possible, indeed the same taking convergences can be used. And 
Wheatstone did not say "proper projections for this distance" 
accidentally. He was acquainted with the newest developments 
in projective geometry, indeed his 1838 stereo drawings were 
based on that knowledge.

Abram Klooswyk