man's daily life, is admirably illustrated by the closer consideration of the beaker experiment. Taking a cylindrical beaker or lamp-glass, placed erect and seen as erect, or placed on its side and seen on its side, the vessel in each case seems cylindrical; but if, by a forcible self-suggestion, the observer 'sees' the erect beaker tilted away from him, the apparent near end looks narrower; or if he sees the overturned beaker as if erect, then the apparent upper diameter seems to be smaller; in each case the really cylindrical object appears to be conical. The observer having formed his false notion, makes further use of the real retinal magnitudes of the image conformably with that notion; in the first fiction the retinal image of the upper end is imagined to be more distant, and therefore appears larger; in the second fiction the further extremity is imagined to be nearer, and therefore appears smaller. The great power of this self-deceptive effort may be realised in its fullest extent by holding the beaker in front of the eye and tilting it in various directions; the movements may be 'seen' reversed at will, in spite of the muscular contractions that the observer is making.

There are reasons for thinking that the process of inference, or judgment, as known to us by introspective analysis, and characterised to be an exclusively' cerebral' function, is also represented in simpler degree in the unconscious operations of subordinate centres, and that we may receive in a supreme centre the resultant of impressions already combined and elaborated in a subordinate centre. We have no positive knowledge of the actual seat of formation of particular inferences; they may be superior and inferior cortical, or cortical and sub-cortical; but this ignorance is no bar to the essential conception that such processes may occur at different functional levels. In the case of Zöllner's illusion, the lower-level inference is so strong as to irresistibly elicit the higher-level inference; we cannot see the lines parallel, although we may know by measurement that they are so. In the series of beaker observations the lower-level inferences are formed from sensations sufficiently ambiguous to allow a higher-level inference to be formed, either rightly or wrongly, and if in that inference one of the lower-level components is misjudged, other lower-level components follow suit. With the erect beaker, seen so that the proximal edge appears to be behind the distal edge, that misjudgment of lower in higher inference carries with it misjudgment of the low-level inference from the retinal magnitude of the image. The image of the beaker-mouth is

no larger than before, but the beaker is seen tilted away; therefore the low-level inference of size is exaggerated in the high-level compound inference of position plus size.

An important means of estimating the distance of objects is afforded by our unconscious appreciation of the difference between the two pictures formed on the two retina; this factor is especially important in our perception of the third dimension of space, and consequently of the form of solid objects. Length and breadth can be judged of with one eye open as well as with two, but to get the notion of depth we are much assisted by the double sensation of two slightly different pictures. An ordinary landscape, looked at with both eyes open, appears much more extensive as regards the third dimension than when it is looked at with one eye shut. On the contrary, the painting of a landscape appears much flatter when it is looked at with the two eyes than with one only. These differences may easily be understood : the depth of a landscape is most apparent when two different retinal pictures are formed; the want of depth in a picture is most apparent when two identical retinal pictures are formed; it is especially the foreground effects that influence our judgment in the two cases.

In the more delicate discrimination of distance at closer ranges, e.g. when the hand is put out to move a piece at chess, other subjective factors connected with a sense of movement come into play, viz. the degree of convergence of the two visual axes and the amount of accommodation exerted.

FIG. 295.

The haploscope (áπλóos, single) is a device by which, with parallel visual axes, a single sensation is obtained of two separate visual fields. Whereas in ordinary binocular vision the visual axes converge to a point of fixation, and we have single vision excited by two slightly different retinal pictures, in haploscopic vision the axes are parallel, or nearly so, and we have single vision excited by two altogether different different pictures, forming with appropriate ob

To illustrate haploscopic vision. The distance between the bird and cage is here given as rather less than the distance between the two pupils, so that the haploscopic combination can be effected easily, with the visual axes somewhat convergent. The illusion is facilitated by holding a card vertically between the eyes, so as to hide the bird from the left eye and the cage from the right eye.

jects an illusory sensation. Haploscopic vision may be effected

by looking through two parallel tubes, and is approximately effected by stereoscopes; it may be simply illustrated by fig. 295, which represents a familiar trick: holding the figure close to the face, and looking beyond it, the bird will appear to slide into the cage as the visual axes become less convergent;

0 and 01 FIG. 296.-STEREOSCOPE.

Two objects, o and o1, are viewed in conjunction.

we then have in the right field of vision a bird, in the left field of vision a cage, and in consciousness a bird in a cage.

The stereoscope and the telestereoscope are instruments so constructed as to give an exaggerated notion of the third dimension. In the ordinary stereoscope two photographic pictures, taken from slightly different points of view, are looked at, each by one eye, and the visual axes are adjusted until the two pictures become identical' on the two retinæ, and therefore fused in consciousness as a single picture, in which depth' becomes. This is called a stereoscopic effect,' and in the actual instrument the convergence of the visual axes is imitated and exaggerated by two prisms with the thick edge outwards, one in front of each eye. That stereoscopic effect is not due to movements of the eyes, is proved by the fact that it is produced with pictures illuminated by the electric spark; no sensible movement of the eye is possible during the illumination thus produced.

particularly apparent.

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If, instead of placing in the stereoscope two photographs prepared ad hoc, we examine two identical pictures or prints, their two images give no stereoscopic relief, but combine into a single flat image. If there be the slightest difference between the two prints, this will at once be detected as an irregularity when they are combined by the stereoscope. Two genuine bank-notes can be thus perfectly combined; a genuine and a spurious note cannot.

The effect of the telestereoscope, as will be understood from the accompanying figure, is to exaggerate the difference between the two retinal pictures of a landscape by causing the points of view of the two eyes to be much farther apart than normal. The normal distance, lr, between the centres of the two eyes being 65 mm., is by the telestereoscope increased to the distance. r. If, for instance, this distance be 65 cm., the normal stereo

scopic effect is proportionately exaggerated, and at the same time objects in the landscape appear reduced in size, producing the effect of stage scenery.

FIG. 297.--TELESTEREOSCOPE.

Two small mirrors in front of the eyes, r; two larger mirrors arranged to reflect images of distant objects upon the smaller mirrors, and thus to the eyes. The effect is as if the eyes were placed at 1, r. (Helmholtz.)

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Contrast. Any quality, optical or other, of an object or person causes in the observer an impression that is intensified if the surroundings are of an opposite quality, weakened if they are of a similar quality. Any given quantity is over-estimated when its surroundings are unusually small, under-estimated when its surroundings are unusually large. Rest can only be enjoyed after labour; sound, to be heard clearly, must rise out of silence; light is exhibited by darkness, darkness by light; and so on in all things.' Stated more generally, the value of any given constant is estimated to be + or - according as its surroundings or +. A person of average height appears taller among short people, shorter among tall people. If one finger dipped in hot water, and another finger dipped in cold water, be both simultaneously transferred to tepid water, the first finger will feel cold, the second warm; these are phenomena of successive contrast, analogous with the negative after-effects of visual excitation.

are

Formally expressed, if A: B is the personal ratio or major premise, ab the minor premise formed by an object in its surroundings, then the object a varies inversely as the surroundings b; if by the focussing of attention b is made the premise, a becomes the conclusion, and vice versâ.

The theory of contrast has long been a vexed question, and has been debated most closely in the case of simultaneous colourcontrast (p. 455). The question at issue is very similar to that stated on p. 550 with reference to the Weber-Fechner ratio between

stimulus and sensation, and as in that case, so in this, a curt, and therefore dogmatic, verdict would be of no value. Weighty names are subscribed to rival theories; Helmholtz, as the chief upholder of the psychological theory,' represents contrast effects as being due to an error of judgment; Hering, as the chief upholder of the "physiological theory,' represents contrast effects as being due to the up-and-down chemical modifications of a hypothetical retinocerebral 'vision-stuff.' In the psychological theory, a transforming factor is presumed to occur between sensificatory change and sensation. Helmholtz holds that material sensificatory data do not directly modify each other, but that in the meta-physiological process of inference sensations are modified by other sensations. within the field of perception. In the physiological theory, a direct material modification of sensificatory data by each other is presumed to occur; Hering urges that each such datum diffuses. in the retino-cerebral organ beyond its precise locus of incidence, and directly modifies contiguous sensificatory data, and the observations of Charpentier, alluded to on p. 456, are confirmatory of this mode of view. According to Hering's mode of expression, an opposite or assimilatory change (black, blue, or green) is induced in the retino-cerebral area surrounding a given spot or area in which a dissimilatory change (white, yellow, or red) is provoked-and vice versa.

One of the experiments upon which the Helmholtz-Hering debate has especially turned is that already alluded to on p. 455 as Meyer's experiment.

Helmholtz's interpretation of that experiment is as follows: If the background is green, the covering-paper looks greenish. If the latter covers the grey scrap without interruption, we fancy that a grey object is seen through a greenish veil; such an object to look white must be rose-coloured.'

But, says Hering-and the statement is easily verified-a chessboard pattern of grey and green squares, covered with tissue-paper, over which a black paper with a square opening is placed, gives a similar if less pronounced effect; a person coming fresh to it sees no covering-paper, but merely a pattern composed of greenish and reddish squares. His view is that the contrast effect depends upon the fact that any excitatory disintegration of a retinal area is accompanied by a reverse alteration or integration of the surrounding neighbourhood, or vice versâ, causing a light halo round a dark patch, red round green, green round red, blue round yellow, yellow round blue.