haustion varies directly as the power of sustaining an afterimpression, and if this latter varies directly as the power of ideal revival or recollection, one must expect to find among those classes of sensations least susceptible of this revival the least capacity for sustained and unbroken feeling. Thus for example, tastes ought, on this supposition, to fade away much more rapidly, and to require a change of stimulation much sooner, than sensations of colour of equal intensity. Whether this is so, may well be left to the individual reader to decide from his own experience.

We may now pass to the consideration of another class of investigations into what may be called the dimensions of a sensation, namely the numerous attempts recently made to measure the intensive and extensive magnitude of sensation. By intensive magnitude is meant the strength of a sensation; by extensive magnitude, its volume, which roughly speaking corresponds to the area of the sentient surface and the number of nervous elements acted upon. Professor E. H. Weber led the way to these investigations in his famous discoveries respecting the various degrees of tactile and muscular sensibility resident in different parts of the bodily surface. Others have carried similar modes of inquiry into the region of visual sensations. Finally the results of these many experiments have been collected and formulated into a general law by Weber's colleague Professor G. T. Fechner. In giving an account of these investigations I shall be able to quote almost entirely from this author's works.*

It is clear that the intensity of a sensation, as distinguished from that of its external stimulus, is entirely a matter of subjective feeling. At the same time, as I have already hinted, mere subjective feeling would tell us very little about the general quantitative relations of our sensations. In order to reduce these scattered and isolated subjective appreciations to something like a general law, it is necessary to study them in conjunction with certain definite variations in the objective cause. By this means one may learn how the feeling of magnitude varies with changes in the absolute magnitude of the object, and so reach a more precise and scientific statement of this particular aspect of the coexistence between body

Fechner has several statements of his general theory in the Abhandlungen der sächsischen Gesellschaft der Wissenschaften. His most systematic exposition is to be found in his Elemente der Psychophysik, and from this work I have mainly quoted.

and mind. This is Weber's method, as it has been enlarged and rendered more precise by Fechner.

By the mere introspection of our sensations we know first of all the fact of their equality, and secondly the bare fact of their inequality as greater or less. As a general rule it is impossible to say that one sensation is twice or three times as intense as another. We do, no doubt, speak of a light being twice as bright as another, or a sound twice as powerful; but such numerical judgments are generally very indefinite, and involve for the most part a reference to some objective measure; as for example that the sound twice as powerful would produce the same force of sensation as the other at twice its distance. Further, it may be added that when the sensations are of different orders any estimation of their relative intensities is very inexact. Thus it is often impossible to say that one sensation of tone is more intense than another of colour. In cases where our judgment is very unwavering, it will be found that we compare the sensations mediately, by means of the average strength of either class. Thus when an impression of light rises in intensity far above the common level of light-impressions, and another sensation of sound sinks far below the level of its class, we do not hesitate to pronounce one more intense than the other. Another mediate mode of measurement is to reckon the distance of each feeling from the limits of distinct sensation. Thus it is clear that two impressions of sound and light, each of which approached very closely the minimum sensibile, would be reckoned as about equal. Yet this method, again, is only very faintly and imperfectly employed in individual and subjective judgments. In proportion as the heterogeneous sensations have any element in common besides mere force, as a pleasurable or painful quality, they are of course much better susceptible of this direct measurement.*

* Still even here one may see the impossibility of reaching exact appreciations of equality or inequality between heterogeneous feelings. A pleasure of light or of colour can be much more precisely measured with another pleasure of the same sense than with one of another sense, and nobody probably would attempt to determine the exact equivalent of a sensuous enjoyment in the sphere of imagination. Hence perhaps the habit of setting one class of pleasures above another because of an average superiority, even though the intensest of the inferior class are much greater than the feeblest of the other. I think it might be shown that it is this practical device, of great value where exact measurement is precluded, which has led to the supposition that pleasures excel one another, not only by virtue of strength and duration, but also by virtue of their qualitative differences.

The methods, then, of estimating the force of sensation by objective experiment need to recognise both these limitations: first of all, that exact immediate comparison is confined to sensations of the same genus, and secondly, that it can only make known their equality, or their inequality as greater or less. Acting on this knowledge, Fechner has sought to construct a standard of sensuous quantity for the various parts of an organ, and for different states of the same part. His statement is as follows: The sensibility of an organ at a particular time, or of a particular part of an organ, is reciprocally proportional to the magnitude of the stimulus requisite, then and there, to produce a sensation equal in intensity to a given sensation. Thus if weights of five and six pounds are required to produce equal degrees of muscular feeling on the same part of the surface at different times, or on different parts of the surface at the same time, we may say that the sensibility in the first case is to that in the second as 6: 5.

There is one circumstance that greatly favours the employment of this method of measuring sensibility. It is a well known fact that every stimulus must be of a certain force before it can produce any sensation at all. Objective light may actually impinge on the retina, and yet be of such feeble nature as to be unnoticed. Similarly, sounds, when travelling from any considerable distance, enter the ear without having any appreciable conscious effect on the auditory nerve. Now if we can estimate the objective force of two external stimuli which are just adequate to produce sensation on two occasions, or at different parts of an organ, we have in their ratio a very precise measure of the respective degrees of sensibility.

This measurement of the force of an external stimulus is capable of being made very exact in some instances, by employing the principle of the conservation of force, and by means of the excellent apparatus of physical science. Thus for example, Schafhäutl sought to determine the precise value of the physical impetus requisite to produce a sensation of sound. He calculated that a piece of cork, weighing 1 milligram, falling through 1 millimetre on a glass plate, produces the faintest observable sound, the observer being 91 millimetres from the plate. In the case of the eye's sensibility to light, it is impossible to determine the exact degree of physical light requisite to produce a sensation in a perfectly dormant nerve, since even when all external light is excluded from the eye, the nerve is known to undergo a certain amount of "subjective stimulation" resulting in what Helmholtz very aptly terms the eye's Eigenlicht, or

own proper light. In the case of weights, estimated by sense of pressure, it is very difficult to determine the minimum pressure perceptible, since other tactile sensations, such as the feeling of smooth and rough surface and the sense of temperature, are pretty certain to co-operate with, and so to disguise, the particular feeling tested. Finally, in the case of the so-called chemical senses, taste and smell, we have as yet no method of reckoning the degree of the physical force which constitutes the stimulus.

The immense value of this physical method consists in its applicability to the sensibilities of different individuals. It is obvious that we cannot, in one subjective judgment, directly compare the sensations of two or more persons, as we can those of two organs of the same individual. Still we may roughly assume that the least perceivable sensation of every mind is an invariable quantity, and in this manner we can reach a measure of the relative sensibilities of different persons. These will clearly be in the inverse ratio of the physical stimuli needed to produce the faintest recognisable

sensation.

From sensibility to stimuli, or absolute sensibility, Fechner distinguishes sensibility to differences in stimuli, or discriminative sensibility. While the former may be measured by the magnitude of the stimulus fitted to produce a sensation equal in intensity to a given sensation, the latter is to be estimated by the magnitude of the difference of two stimuli needed to produce a certain change of feeling. In both these cases, the greater the objective cause required, the less must the subjective sensibility be supposed to be. Thus if, in order to effect a certain difference of sensation, a greater change of light-intensity is needed at the circumference of the retina than at the centre, we may conclude that the latter part possesses the greater discriminative sensibility.

Here again we have the all-important fact that a certain amount of change in the objective force of a stimulus is possible without any variation in the feeling produced. That is to say, there is a certain limit below which our several sensibilities are unable to discriminate. This boundary, which we have found to belong to both absolute and discriminative sensibility, Fechner calls the "threshold" (die Schwelle). Its existence in the case of discriminative sensibility is very easily proved. Objective light, sound, and pressure may all be made to vary within very small limits without the subject, upon whom the experiment is made, detecting any change. Further, this threshold offers, as in the case of ab

solute sensibility, the best means of measuring two or more discriminative sensibilities. If we compare two parts of the retina, or two regions of tactile surface, we find it very difficult to pronounce a change of impression at one part to be exactly equal to a change at another. But the fact that there exists a least-noticeable difference of stimulation makes this rough method of estimation unnecessary. Thus if, in comparing the discriminative sensibility to pressure at the palms and backs of the hands, we are able to discover in each instance the exact amount of objective change required to produce the faintest sense of difference, we may conclude that the ratio of the two sensibilities will be inversely as that of the amounts of change. Similarly, this method is perfectly applicable to an estimate of the relative degrees of discriminative sensibity of different individuals. The smaller the amount of variation in the stimulus perceptible, the greater must be the person's delicacy of sensibility. In this manner the ear's sensibility to the pitch of tones is found to be of very unequal degrees of delicacy in different persons. It might also be shown, perhaps, that very wide differences in the eye's discrimination of colours exist in different individuals.

Hitherto we have been considering discriminative sensibility without any reference to the absolute magnitude of the sensations distinguished. It has been assumed provisionally that the eye, for example, recognises quite as fine shades of difference when the compared impressions of light are very powerful as it does when they are very feeble. But a very little reflection shows that this assumption is incorrect. Everybody is aware that he is unable to recognise slight differences in weight when the weights compared are very heavy, though these same amounts of objective difference are very apparent when the factors of the comparison are small. So, too, it is demonstrable that the eye, when looking at a very bright object, as the sun, is unaware of differences of lightintensity which, if they existed between feebler constituents, would afford a striking constrast of sensation. Hence the question arises what is the relation of the discriminative power of a sense to the absolute magnitude or force of the sensations to be distinguished ?

With the view of solving this problem Fechner has conducted a large series of experiments, varying in every possible manner the absolute magnitude of the stimuli to be distinguished, and always carefully noting the ratio of the amount of difference of the stimuli