_Stereoscopic Angles._--I am concerned that my definition and
solution of stereoscopic angles (a misnomer, for it should be
_space_) in "N. & Q.," with subsequent illustrations, have not
satisfied MR. SHADBOLT, as I am thus obliged to once more request
room in your pages, and this time for a rather long letter. When I
asserted that my method is the only correct one, it behoved me to be
prepared to prove it, which I am, and will now do.
It seems that MR. SHADBOLT has not a knowledge of perspective, or,
with a little reflection and trifling pains in linear demonstration
on paper, he might have convinced himself of the accuracy of my
method. It were well, then, to inform MR. SHADBOLT, that in
perspective, planes parallel to the plane of delineation (in this
case, the glass at back of camera) have no vanishing points; that
planes at right angles to plane of delineation have but one; and that
planes oblique have but one vanishing point, to the right or left, as
it may be, of the observer's eye. This premised, let the subject be a
wall 300 feet in length, with two abutments of one foot in front and
five feet in projection, and each placed five feet from the central
point of the wall, which is to have a plinth at its base, and a stone
coping at top. On a pedestal four feet high, two feet wide, and six
feet long, exactly midway betwixt the abutments, let an ass be
placed, a boy astride him, a bag drawn before the boy, who holds up a
long stick in line with the ass, &c., that is, facing the observer.
The right distance for the observer's place is 450 feet. If the
cameras be placed two inches and a half apart, on one line parallel
to the wall, the stereographs will be in true perspective for the
_two_ eyes, that is, all the planes at right angles to the plane of
delineation will have _two_ vanishing points, which, being merely two
inches and a half apart, will, in the stereoscope, flow easily into
one opposite the eye; whilst the plinth, coping, and all lines
parallel to them, will be perfectly horizontal; and the two pictures
would create in the mind just such a conception as the same objects
would if seen by the eyes naturally. This would be stereoscopic, true
to nature, true to art, and, I affirm, correct.
Now, let the same subject be treated by Professor Wheatstone's
method, when the cameras would be eighteen feet apart. Situated thus,
if placed on one line, and that parallel to the wall, the extreme end
at the right could not be seen by the camera at the left, and _vice
versâ_; so that they {420} must radiate from the centre when the
glass at back of camera would be oblique to the wall, and the plinth,
coping, top and bottom of pedestal, would have _two_ vanishing
points, at opposite sides of the centre, or observer's eye; both
sides of the ass, both the legs of boy, and two heads to the drum
would be visible; whilst the two sides of pedestals would have each a
vanishing point, serving for all lines parallel to them. But these
vanishing points would be so far apart that they could not, in the
stereoscope, flow into one: the result would be, that the buttresses
would be wider at back than in front, as would also the pedestal,
while the stick held by the boy would appear like _two_ sticks united
in front. This would be untrue to nature, false to art,
preposterously absurd, and I pronounce it to be altogether erroneous.
This being the case with a long distance, so must it be with shorter
distances, modified in exact proportion to the diminution of space
between the cameras, &c. For, let the object be a piece of wood three
feet long, four inches wide, and six inches deep, with a small square
piece one inch and six inches high, placed upright exactly on a line
from end to end of the three feet (that is, one at each end) and
midway between the sides. Let this arrangement be placed across
another piece of wood three or four feet long, which will thus be at
right angles to the piece at top. By my method all will be
correct--true to nature and to art, and perfectly stereoscopic:
whilst by the radial method (recommended by MR. SHADBOLT), with two
feet space for cameras, there would be the top piece divided at the
farther end, where there would be two small upright pieces instead of
one; and this because the two vanishing points could not, in
stereoscope, flow into one: whilst the lower piece of wood would have
two vanishing points at opposite sides. This, then, being untrue to
nature, untrue in art, in short, a most absurd misrepresentation, I
pronounce to be utterly wrong. I have made the space two feet between
cameras in order to show how ridiculous those pictures might become
where there is an absence of taste, as, by such a person, two or ten
feet are as likely to be taken as any less offensively incorrect.
As regards range of vision, I apologise to MR. SHADBOLT for having
misconceived his exact meaning, and say that I perfectly agree with
him.
With respect to the "trifling exaggeration" I spoke of, allow me to
explain. For the sake of clearness, I denominate the angle formed
from the focal point of lens, and the glass at back of camera, the
angle of delineation; the said glass the plane of delineation and the
angle formed by the stereograph to the eye, the stereoscopic angle.
It must be borne in mind that the stereoscopic angle is that
subtended by one stereograph and the eye. I find by experiments that
the angle of delineation is very often larger than the stereoscopic
angle, so that the apparent enlargement spoken of by MR. SHADBOLT
does not often exist; but if it did, as my vision (though excellent)
is not acute enough to discover the discrepancy, I was content. I
doubt not, however, under such circumstances, MR. SHADBOLT would
prefer the deformities and errors proved to be present, since he has
admitted that he has such preference. I leave little doubt that, if
desirable, the stereoscopic angle, and that of delineation, could be
generally made to agree.
As to the means by which persons with two eyes, or with only one eye,
judge of distance, I say not one word, that being irrelevant to this
subject. But that the axes of the eyes approximate when we view
objects nearer and nearer cannot be doubted, and I expressed no
doubt; and it appears to me very probable that on this fact MR.
SHADBOLT founds his conclusion that the cameras should radiate. This,
however, ought not to be done for the reasons I have assigned. It
will not do to treat the cameras as two eyes, and make them radiate
because our eyes do; for it must be remembered that light entering
the eyes is received on curved--whilst when it enters the cameras it
falls on flat surfaces, occasioning very different results. And if
this be maturely considered by MR. SHADBOLT, I believe his opinion
will be greatly altered.
As to the model-like appearance, I cannot yet understand exactly why
it should exist; but of this I am certain, the eyes naturally do not
perceive at one view three sides of a cake (that is, two sides and
the front), nor two heads to a drum, nor any other like absurdity; so
that I perceive no analogy between this model-like appearance and
natural vision, as stated to be the case by MR. SHADBOLT.
To confirm, practically, the truth of my illustrative proofs, I will
send you next week some glass stereographs, to be placed at MR.
SHADBOLT'S disposal, if he likes, and you will be so kind as to take
charge of them.