tones. This fact is very curious, as serving to assimilate pitch with some aspect of force of sensation. It may be added, that the phenomena of light impression do not confirm the view that rapidity of molecular vibration in the stimulus, and so, probably, in the nerve, is equivalent to force or amplitude of vibration. Just perceivable differences of coloured light do not correspond to a constant fraction of the absolute number of vibrations. In the case of the muscular appreciation of weight, Fechner has supplemented the experiments of Weber by applying the method of correct and incorrect instances of the problem. As a result of a series of trials with liftings of one hand in 1856, and with liftings of the two hands in 1857, he finds that as the weight is increased and the difference increased proportionately, being always the same fraction of the first, the fraction representing the proportion of correct to incorrect judgments is pretty constant. At the same time a deviation from this uniformity was discovered at the lower end of the series, when the weight employed was 300 grammes. Once more Fechner has tested the validity of this law in the case of sensibility to temperature, and found that within certain degrees of temperature (20° R. to bloodheat) the differences just observable were always proportional to the elevation of the particular temperature above a medium point between freezing-point and blood-beat (14.7 R.). That is to say, by reckoning the intensity of heat or cold by its distance from a middle and indifferent point, the discrimination was found within certain limits to follow Weber's law. On the other hand, from 20° down to 10° R., the sensibility to change was so great that it was impossible to give the least noticeable difference a precise value, while below 10° this minimum grew larger than was required by Weber's law.

From all this it appears that for all the senses in which the force of the objective stimulus is distinctly appreciable, Weber's law is found to have a certain measure of validity. In order to erect it into a precise general expression of sensibility, it is necessary to discover some method of estimating the force of the stimuli in the case of sensations of taste and smell, and also to account more completely for the slight deviations from this regularity beyond certain limits of intensity in the sensations.

Thus far we have been speaking of the quantity of a sensation in respect of its force or intensity only, and have not discussed

another aspect of quantity which belongs in some measure to most, if not all, of our sensations. We mean the extensive as distinguished from the intensive magnitude of a sensation. This property of our sensations is connected, as has been hinted, with the number of nervous elements involved in the sensation. To assume the existence of this aspect of sensation as an ultimate fact involves no theory of immediate perception of extension under any of its aspects. It simply implies that homogeneous sensations-say those of light

are distinguished somehow according to the nervous route along which the stimulation travels, and that there is a clear and marked contrast between a sensation produced by means of one or a few fibres, and one in which a large area of nervous elements takes part, and this contrast is in nowise confounded with that of a great and feeble intensity.

This extensive sensibility, like the intensive, may be regarded as absolute or discriminative. By absolute extensive sensibility we mean any feeling whatever of extent or volume. This, too, has its threshold or limited condition in the originating stimulus. Every stimulus must act on a certain area of the sentient surface in order that any feeling of extension or volume may arise.* For example, different pencils of rays of very unequal circumference are nevertheless both felt by the eye to be unextended points. So different points applied to the skin, though of very unequal area, are equally felt to be unextended. This mode of absolute sensibility, it may be added, is susceptible of just the same kind of comparative estimation as that of force or intensity. The hand which felt a surface with the least extent of the applied stimulus, would clearly be most sensitive to this aspect of stimuli.

It is, however, in the form of a discriminative sensibility that the feeling of extension commonly presents itself. In the distinguishing of different points and lines, in the comparison of linear and superficial magnitudes, this feeling plays a very prominent part in our knowledge of external phenomena.

The simplest exercise of this sensibility is the discrimination of two adjacent points. Whenever two stimuli, as two rays of light, two points of a compass, simultaneously operate on the sentient

In the case of visual impression it is known that some area of operation is required to produce any sensation at all. This fact, however, bears rather on the estimation of intensity than on that of extensive magnitude.

surface, it is found that they must be a means of the degree of intensity of the certain distance apart in order that two muscular feeling. On the other hand, in distinct sensations may follow. This mode an experiment made by Helmholtz, as to of determining the relative sensibility to the degree of the feeling of similarity of the extension of two parts has been made the two retinal pictures, the basis of the use of by Weber in his now famous ex- judgment is clearly a feeling of extension. periments on the tactile sensibility of va- Helmholtz used for this purpose three verrious parts of the bodily surface. It has tical nails placed at the ends of three small also been employed to estimate the fine- pieces of wood at distances of 12 millimeness of visual sensibility on various parts tres from one another and 340 millimetres of the retina. Weber and Helmholtz from his eyes. He then stood with his found that at the centre of the retina two eyes slightly below the other extremities points of light are recognized as such, of these laths, so that the line of union of whose retinal images are from 0046 to the nails and wood was invisible. Under 0052 millimetres apart. Aubert and Förs- these circumstances he could judge ter discovered that this delicacy of sensi- whether the three nails were in exactly bility to extension disappears very rapidly one vertical plane only by means of the from the centre towards the periphery of comparison of the two retinal pictures. the retina, this decrease being most rapid In so far as they were not, it is clear that towards the upper and lower parts, least their image on the one retina would have rapid towards the outer regions. All these a different local arrangement from that of facts of sensibility to points or extension the other. Helmholtz found by this means are supposed to be related to the area oc- that a slight deviation of the nails from a cupied by an elementary nervous fibre. plane, such as would cause a local dispariWeber supposes that two points applied ty of the two retinal images of 0044 milto the skin, in order to be distinguished, limetres, was at once detected, and that must lie within the circle of two dif- thus the delicacy of the feeling of extension ferent nervous extremities. Helmholtz, in the comparison of the two images of an on the other hand, conceives that two object is precisely the same as that empoints of light can only be distinguished ployed in a single eyes' discrimination of when the distance of their retinal images points.t from one another is greater than the diameter of a retinal element, for otherwise they would fall on the same or on two contiguous elements. In the first case he thinks they would produce one sensation, in the second two, but these would not be recognized as the effect of two points, since they might equally well follow from a single point whose image is projected on the boundary of two elements.

Of much the same character as this discrimination of points are other modes of visual sensibility recently examined by physiologists. We refer especially to the eyes' estimate of the degree of convergence and the amount of dissimilarity of the retinal pictures. The appreciation of distance by one eye by means of the feeling of muscular tension in accommodation has been recently measured by Wundt, but this is clearly not a case of feeling of extension, since in the experiments alluded to any change in the magnitude or position of the retinal image is excluded, and the judgment is formed solely by

Wundt made the observer look with one eye at at a vertical black thread through a slit 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.

At

Of equal interest are some experiments by Wundt, on 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 moveable to and from the observer. a 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 shifting of each retinal image through 72 seconds angular measure, and this corresponds pretty exactly to the least distinguishable distances of retinal points. It should be remarked here that one may suppose the eyes to remain fixed while the thread is moved to or from them, so that the first recognition of the change is due to the shifting of the images on the retinæ. At

It is necessary to distinguish from this percep tion of similarity or dissimilarity of the two retinal of single vision, as measured by the limits of retinal pictures for stereoscopic vision, the eye's capability surface within which any two points of the two images must lie in order that the corresponding part of the object be seen single. This appreciation has also been measured by Volkmann. It appears to be of very various degrees of delicacy in different individuals, and is clearly determined less by any origi nal mode of sensibility, such as the discrimination of points, than by the effects of experienced and disciplined attention.

the same time it is possible that the eyes at once follow the moving thread so that the feeling of change of distance is simply a mode of the muscular 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 the weakest possible; the other by the amount of change, i.e., according to the psycho-physical law, of the fraction of the absolute stimulus required to produce a feeling of change of a given amount, say the least observable. Is there any connection between these two sensibilities thus measured? Does sensibility to difference go 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 abso

It remains to inquire whether Weber'slaw is in any sense applicable to these phenomena of discriminative sensibility as applied to extension. Does the discrimination of two extensions depend on the absolute magnitude of these extensions, so that the greater the magnitude the larger the minimum amount of difference noticeable? In order to answer this question Fechner, assisted by Volkmann, has instituted experiments with sight and touch. In the case of light 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 these pairs was kept fixed and the legs of the other gradually brought togeth-lute sensibility which intensifies or weakens er, 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 moveable to and from one another, and made the two extremes 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 1-62nd of the sum of the magnitudes compared; and Volkmann found it to be from 1-88th to 1-101th of the same. In other words, the amount of error varies directly, and so 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 by means of the various local sensibility of the retinal elements. Probably in this exact measurement 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 a chief instrument of such 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 amount of difference observable and the absolute magnitude of the extensions compared. Fechner hesitates, therefore, to assign to his law any universal validity for this mode of discriminative sensibility.

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 alike 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 in the estimation of differences in externa! light.

The next important result of a general character furnished by these experiments with the senses, after the increased precision given to our estimation of quantity in sensation, is to be found perhaps in the advance made towards the determination of the ultimate elements of 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, shade, colour, and form. Up to a certain point subjective reflection is able to analyze 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 is it possible to effect this separation if two given elements of a sensation never both occur in perfect isolation. 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 way of determining this is by studying the nervous processes. Assuming, as seems legitimate, that some peculiar mode of feeling is effected by every separate nervous fibre, the physiologist may by an exact study of these nervous elements afford important suggestions as to the ultimate elements of sensation.

which fibres minister respectively to the three modes of sensation just mentioned. On this supposition our common sensations of colour are never pure elementary feelings, since even the purest coloured light of the spectrum is conceived as exciting more than one order of fibres. Thus the red rays, though they stimulate most powerfully the fibres sensitive to red, affect in a feebler degree the other two classes of fibres also. Hence, in order to produce a pure elementary sensation, it is necessary to incapacitate, temporarily, 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 the seeing of which these fibres are chiefly concerned. They then become exhausted, according to the principle already spoken of, and when the eye is turned to the required colour, an approximately pure sensation is obtained. In this way it is possible, by looking for example, at a mass of purple, to obtain a subsequent sensation of green much purer in tone, that is, less whitish than the green of the spectrum. It is needless, perhaps, to point out how impotent mere subjective observation had been to discover any combining feelings in an ordinary sensation of colour. In point of fact, every sensation of colour is, when looked at subjectively, one and indivisible. Yet, by means of physiological investigation, it becomes possible to determine certain more elementary feelings, out of which these quasi elements are built up.

The naturalist who has recently done most 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. From certain physical facts with respect to sound, he was led to infer that in such apparently simple and indivisible sensations as the tone of a violin or a vocal sound, there are many feeble elements present which go to form the peculiar quality of the sound. Since these upper tones never present themselves in isolation from the more prominent fundamental tones, the mind's attention fails to disentangle them from the composite mass of sensation. Yet they are perfectly distinct sensations, produced by means of different nervous fibres, and could easily be distinguished if they oc- It may be well to observe that this physi-' curred in less perfect simultaneity. In- ological method of analyzing sensation has deed, their discoverer asserts that, with its limits in the number of discoverable considerable discipline in attention, they nervous elements and processes involved may be detected even in this close fusion in a sensation. If it be demonstrable that of elements when once the mind is aware in mediating a given sensation, two or of their existence, and consequently able inore nervous fibres are employed, it is alto lie in wait for them, so to speak. The lowable to assume that the resulting feeleffect of this discovery is clearly to greatly ing is compound, in the sense that it is the reduce the number of elementary auditory effect of two or more stimulations, which sensations. It resolves all the sensations would apart produce distinct modes of of timbre as well as those of vowel clang sensation. But this does not warrant one into mere variations of pitch. in subdividing each separate stimulation Very similar to this discovery of Helm-into separate time-elements, and inferring holtz is his revival and amplification of that a sensation of colour, for example, is Thomas Young's theory, that all our sen- the result of an indefinite number of mosations of colour are compounded out of lecular impulses in the nervous substance, three elementary modes of feeling, namely, each of which may be conceived as producsensations of red, green and violet. The ing some rudimentary mode of feeling, phenomena of colour blindness, and a large some vague shock of consciousness. Yet number of other facts, both anatomical and this mode of analysis has recently been atoptical, favour the hypothesis, that three tempted by so eminent a thinker and natuclasses of optic fibres are distributed pret- ralist as Mr. Herbert Spencer, and also, ty equally over the surface of the retina, and apparently in complete independence, Maxwell supposes the third elementary sensaby M. Taine.* Such a hypothesis is of great tion to be blue rather than violet.

* See Spencer's "Psychology." Second Edition.