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pyramids or cones rise out of quadrangular or conical hollows. All these figures may be drawn by the hand, and will produce solid forms sufficiently striking to illustrate the properties of the stereoscope, though not accurate representations of any actual solid seen by binocular vision.

If one of the binocular pictures is not equal to the other in its base or summit, and if the lines of the one are made crooked, it is curious to observe how the appearance of the resulting solid is still maintained and varied.

The following method of drawing upon a plane the dissimilar representations of solids, will give results in the stereoscope that are perfectly correct :

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Let L, R, Fig. 43, be the left and right eye, and a the middle point between them. Let MN be the plane on

which an object or solid whose height is CB is to be drawn. Through B draw LB, meeting MN in c; then if the object is a solid, with its apex at B, Cc will be the distance of its apex from the centre c of its base, as seen by the left eye. When seen by the right eye R, cc will be its distance, c' lying on the left side of c. Hence if the figure is a cone, the dissimilar pictures of it will be two circles, in one of which its apex is placed at the distance cc from its centre, and in the other at the distance cc' on the other side of the centre. When these two plane figures are placed in the stereoscope, they will, when combined, represent a raised cone when the points c, c' are nearer one another than the centres of the circles representing the cone's base, and a hollow cone when the figures are interchanged.

If we call E the distance between the two eyes, and

h the height of the solid, we shall have AB:h

hE
2 AB'

E

= : Cc, or which will give us the results in

5 h
4 A B'

and cc =
the following table, E being 21, and AC 8 inches:-

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If we now converge the optic axes to a point b, and wish to ascertain the value of cc, which will give dif

ferent depths, d, of the hollow solids corresponding to different values of cb, we shall have ab:

=

d E
2 A B'

E

=

d: cc',

2

and

cc', which, making AC= 8 inches, as before, will

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The values of h and d when cc, cc' are known, will be

found from the formulæ h =

2 AB Cc
E "

and d

=

2 A B C c' E

As cc is always equal to cc' in each pair of figures or dissimilar pictures, the depth of the hollow cone will always appear much greater than the height of the raised one. When cc = cc = 0.75, h: d 3:12. When cc cc 2:4, and when cc = cc

=

0.4166, h:d

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=

0.139,

When the solids of which we wish to have binocular pictures are symmetrical, the one picture is the reflected image of the other, or its reverse, so that when we have drawn the solid as seen by one eye, we may obtain the other

by copying its reflected image, or by simply taking a copy of it as seen through the paper.

When the geometrical solids are not symmetrical, their dissimilar pictures must be taken photographically from models, in the same manner as the dissimilar pictures of other solids.

Portraits of Living Persons or Animals.

Although it is possible for a clever artist to take two portraits, the one as seen by his right, and the other as seen by his left eye, yet, owing to the impossibility of fixing the sitter, it would be a very difficult task. A bust or statue would be more easily taken by fixing two apertures 2 inches distant, as the two points of sight, but even in this case the result would be imperfect. The photographic camera is the only means by which living persons and statues can be represented by means of two plane pictures to be combined by the stereoscope; and but for the art of photography, this instrument would have had a very limited application.

It is generally supposed that photographic pictures, whether in Daguerreotype or Talbotype, are accurate representations of the human face and form, when the sitter sits steadily, and the artist knows the resources of his art. Quis solem esse falsum dicere audeat ? says the photographer, in rapture with his art. Solem esse falsum dicere audeo, replies the man of science, in reference to the hideous representations of humanity which proceed from the studio of the photographer. The sun never errs in the part which he has to perform. The sitter may sometimes contribute his share to the hideousness of his portrait by involuntary nervous motion, but it is upon the artist or his art that the blame must be laid.

If the single portrait of an individual is a misrepresentation of his form and expression, the combination of two such pictures into a solid must be more hideous still, not merely because the error in form and expression is retained or doubled, but because the source of error in the single portrait is incompatible with the application of the stereoscopic principle in giving relief to the plane pictures. The art of stereoscopic portraiture is in its infancy, and we shall therefore devote some space to the development of its true principles and practice.

In treating of the images of objects formed by lenses and mirrors with spherical surfaces, optical writers have satisfied themselves by shewing that the images of straight lines so formed are conic sections, elliptical, parabolic, or hyperbolic. I am not aware that any writer has treated of the images of solid bodies, and of their shape as affected by the size of the lenses or mirrors by which they are formed, or has even attempted to shew how a perfect image of any object can be obtained. We shall endeavour to supply this defect.

In a previous chapter we have explained the manner in which images are formed by a small aperture, H, in the side, MN, of a camera, or in the window-shutter of a dark room. The rectangles br, b'r', and b"r", are images of the object RB, according as they are received at the same distance from the lens as the object, or at a less or a greater distance, the size of the image being to that of the object as their respective distances from the hole H. Pictures thus taken are accurate representations of the object, whether it be lineal, superficial, or solid, as seen from or through the hole H; and if we could throw sufficient light upon the object, or make the material which receives the image very sensi

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