or two points of a compass, simultaneously act on the sentient surface, it is found that there is a certain minimum interval of distance by which they must be separated in order that two distinct sensations may follow. This fact has been made use of by Weber in his now famous researches into the relative degrees of tactile sensibility at various points of the bodily surface. It has also been employed to estimate the fineness of the eye's local sensibility in different regions of the retina. Weber and Helmholtz found that at the centre of the retina two points of light are recognised as two, when the centres of their retinal images are from 0046 to 0052 millimetres apart. Aubert and Förster, again, discovered that this delicacy of local sensibility disappears very rapidly from the centre towards the periphery of the retina, this decrease being most rapid towards the upper and lower parts, least rapid towards the outer regions. It has been supposed that this mode of local sensibility is related to the area occupied by an elementary nervous fibre. Weber conceives that two points applied to the skin, must, in order to be distinguished at all, lie within the circles of two different nervous extremities. Helmholtz interprets the facts in another way, reasoning that two points of light can be distinguished only when the distance of their retinal images from one another is greater than the diameter of a nervous element. Otherwise, it is clear, they would fall either on the same elementary nervous fibre, or on two contiguous fibres. In the first case they would obviously produce but one sensation. In the second they would produce a double sensation; but these would not, he argues, be recognised as the effect of two points, since they might equally well follow from a single point projecting its image exactly on the boundary of two contiguous elements.

There are other modes of visual sensibility recently examined by physiologists, which are closely connected with this sensibility to distinct points. I refer especially to the feeling accompanying the convergence of the two axes, and to the sense of dissimilarity in the two retinal pictures. The appreciation of distance by one eye alone through the feeling of muscular tension in accommodation has recently been measured by Wundt.* In these experiments the local sensibility of the different nervous elements of the retina was

He made the observer look with one eye at a vertical black thread through a split in a screen. This source of judgment was found to be very vague. At a distance of 250 centimetres nothing less than an approach or removal of the thread by 12 cent. was observable.

not tested. On the other hand, in an experimental inquiry made by Helmholtz into the precise degree of the visual discrimination of the two retinal pictures, the basis of the judgment was the discriminative local sensibility just spoken of. Helmholtz used for this purpose three vertical nails, attached to the ends of three small pieces of wood at right angles to the same, at distances of 12 millimetres from one another and 340 millimetres from the observer's eye. He then stood with his eyes slightly below the other extremities of the laths, so that the line of attachment of the nails and wood was invisible. Under these circumstances, his only means of judging whether the three nails were in the same vertical plane was the comparison of the two vertical pictures. In so far as they were not, it is clear that the image of one retina would have a different local arrangement from that of the other. Helmholtz found, as the result of his experiment, that a slight deviation of the nails from a plane, such as would cause a local disparity of the two retinal images of 0044 millimetres, was at once detected. And thus we see, as might antecedently have been conjectured, that the delicacy of the feeling of extension as applied to the coincidence or non-coincidence of the two retinal images is precisely the same as that of the sensibility exercised in the single eye's discrimination of points.*

At a

Of scarcely less interest than the foregoing, are some researches of Wundt into the visual estimation of distance by help of the variations in the convergence of the two eyes. He used for this purpose a black vertical thread, viewed by both eyes through a horizontal slit, and movable to and from the observer. distance of 180 centimetres a change of distance of 3.5 to 5 centimetres was observable. An approach of the thread at this distance by 3.5 cent. implies a movement of each retinal image through 72 seconds angular measure, and this corresponds pretty exactly to the minimum interval of distinguishable retinal points. Thus, it would

* This feeling of local disparity between the images of the two retinas, which subserves stereoscopic vision or the perception of solidity, has another limit. In order that any part of an object viewed with both eyes may be seen single, its two images must fall within retinal areas circumscribed with respect to each other. That is to say, there is a circle of oscillation within which one image may move while the corresponding image on the other retina has a given locus. This boundary has also been determined by Volkmann. It appears to vary with different persons, and is clearly determined less by any original organic condition, such as accounts for the discrimination of points by a single eye, than by the effects of experience and disciplined attention.

appear that this mode of estimating distance is confined to the sentient nerves, and is not assisted by any feeling accompanying involuntary movements of the eyes. Indeed it may reasonably be regarded as a particular case of the discriminative local sensibility as tested by Helmholtz in the experiment just described.

These facts are highly curious as serving to show the exquisite delicacy of local sensibility, especially that of the retina, and they must be fully recognised in any attempts to establish the derivative character of the visual perceptions of space. The question, however, which at present interests us is whether they illustrate and confirm the psycho-physical law of Weber and Fechner. Does the discrimination of two extensive quantities depend, like that of two intensities, on their absolute magnitudes, so that the greater the magnitudes the larger the minimum amount of difference noticeable? In order to answer this question, Fechner, assisted by Volkmann, conducted a series of experiments with sight and touch. In the case of sight they both proceeded according to the method of average errors. Fechner employed two pairs of compasses, of which the tips only were visible to the observer. One of the pairs was kept fixed, and the legs of the other were gradually brought together or removed from one another till the observer deemed them to be just as far apart as those of the fixed pair. Volkmann used three vertical threads, stretched by weights, and movable to and from one another, and made the two extremes apparently equidistant from the centre according to the judgment of the observer. As the result of both these sets of experiments it appears that the discrimination of extension depends, like that of force, on the absolute value of the magnitudes employed. Thus Fechner found that the magnitude of the average error was about

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nd of the sum of the magnitudes compared, and Volkmann calculated that it was from th to st of the same. In other words, we see that the amount of error varies directly, and therefore, the degree of discrimination, inversely, as the absolute magnitude of the extensions compared. Here again it has been assumed that the comparison of two lateral distances by the eye is effected solely by means of the local sensibility of the retinal elements. Probably in these exact measurements this is so, though it is no less true that the amount and duration of the eye's movement in passing along the given distance afford through the muscular feelings another, even if a less delicate, instrument of visual measurement.

While these experiments appear to bear out the applicability of

Weber's law to our various feelings of extension, Fechner and Volkmann both found that with respect to touch no discoverable relation exists between the minimum amount of difference observable and the absolute magnitude of the extensions compared. Fechner hesitates therefore to assign to his law any universal validity for discriminative local sensibility.

One other point deserves mentioning before leaving the subject of quantity in sensibility. We have dwelt on an absolute and a discriminative sensibility to stimuli. The one is measured by the amount of objective force needed to produce a sensation of given intensity, say one barely recognisable; the other by the amount of change required to produce a sense of difference of a given quantity, say one barely recognisable too. Is there any connection between these two sensibilities, thus measured? Does sensibility to difference run parallel to absolute sensibility, so that when the latter is diminished by ill health or exhaustion the former falls to a lower fraction? It is proved, says Fechner, that this is not the case, but that on the contrary any variation of absolute sensibility which intensifies or weakens in the same proportion the effects of two stimuli leaves the feeling of their difference unaffected. Similarly with respect to the sensibilities of different parts of an organ. Weber's experiments with weights showed that there is no correspondence between the absolute sensibility of a part and its discriminative sensibility. Two parts of the bodily surface, to which very unequal weights appeared to be alike, were, in spite of this difference of absolute sensibility, pretty equal in their power of discrimination. The fact that the eye loses with exhaustion a measure of discriminative sensibility is explained by Fechner by supposing that the subjective stimulation already referred to interferes in this case with the estimation of differences in external light.

After the increased precision given to the estimation of quantity in sensation, the next important result of a general character furnished by these experiments is to be found, perhaps, in the nicer determination of the ultimate elements in sensation. Our mature sensations, the only ones we are able to examine immediately, are for the most part compounded of numerous elements. Thus, the visual impression received from an external object is made up of a number of sensations of light, colour, and form. Up to a certain point subjective reflection is able to analyse these into their constituent parts. In many cases where a given element occurs apart from the other factors, whether alone or in other combinations, it is

possible to make a mental separation of it. Yet even here the fusion of the elements may be so complete and the resulting feeling so unlike its factors, that notwithstanding a distinct knowledge of the elements it contains, the mind fails to detect their existence in the compound. Still less possible is it to make this dissection, if two elements in a sensation never both occur apart from the other. Hence we can never be certain by mere subjective knowledge that any apparently simple sensation is not compounded of other and more elementary feelings. The only other fairly safe way, yet arrived at, of determining this point, is by studying the nervous processes. Assuming, as seems legitimate, that every separate nervous fibre tends, at least, to produce some peculiar mode of feeling, the physiologist may by an exact study of these nervous elements afford important suggestions as to the ultimate elements of sensation.

The physiologist who has reached by far the most brilliant results in this objective analysis of sensation, is Professor Helmholtz. His now famous doctrine of upper-tones is a signal instance of this method of research. And he has followed a very similar line of inquiry in revising and elaborating the theory of Thomas Young, that all sensations of colour are compounded out of three elementary modes of feeling, those of red, green, and violet.† The phenomena of colour-blindness and a large number of other facts, both anatomical and optical, favour the hypothesis that three classes of optic fibres, answering to these varieties of impression, are distributed pretty equally over the surface of the retina. On this supposition our common sensations of colour are never, strictly speaking, elementary feelings, since even the purest coloured light of the spectrum is conceived as exciting, in some faint measure at least, more than one order of fibres. Thus rays of red light, though they stimulate most powerfully the fibres sensitive to red, are supposed to affect in a weaker degree the other two classes of fibres also. Hence, in order to produce a pure elementary sensation, it is necessary to incapacitate for a brief interval these other two classes of fibres. This may be done by first allowing the eye to rest awhile on a mass of the complementary colour, in perceiving which the fibres to be temporarily blunted are most actively employed. They

* See the following essay on The Basis of Musical Sensation.

+ Professor Maxwell supposes the third elementary sensation to be blue rather than violet.