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sensations. Experience showed us what very unequal differences of sensation might come from equal differences of outward stimulus But all these experiences expressed themselves in one kind of fact, that the same difference of stimulus could in one case be felt, and in another case not felt at all—a pound felt if added to another pound, but not if added to a hundredweight. . . . We can quickest reach a result with our observations if we start with an arbitrary strength of stimulus, notice what sensation it gives us, and then see how much we can increase the stimulus without making the sensation seem to change. If we carry out such observations with stimuli of varying absolute amounts, we shall be forced to choose in an equally varying way the amounts of addition to the stimulus which are capable of giving us a just barely perceptible feeling of more. A light to be just perceptible in the twilight need not be near as bright as the starlight; it must be far brighter to be just perceived during the day. If now we institute such observations for all possible strengths of the various stimuli, and note for each strength the amount of addition of the latter required to produce a barely perceptible alteration of sensation, we shall have a series of figures in which is immediately expressed the law according to which the sensation alters when the stimulation is increased. . . .”

Observations according to this method are particularly easy to make in the spheres of light, sound, and pressure. Beginning with the latter case,

We find a surprisingly simple result. The barely sensible addition to the original weight must stand exactly in the same proportion to it, be the same fraction of it, no matter what the absolute value may be of the weights on which the experiment is made. . . . As the average of a number of experiments, this fraction is found to be about §; that is, no matter what pressure there may already be made upon the skin, an increase or a diminution of the pressure will be felt, as soon as the added or subtracted weight amounts to one third of the weight origi nally there."

Wundt then describes how differences may be observed in the muscular feelings, in the feelings of heat, in those of light, and in those of sound; and he concludes thus:

"So we have found that all the senses whose stimuli we are enabled to measure accurately, obey a uniform law. However various may be their several delicacies of discrimination, this holds true of all, that the increase of the stimulus necessary to produce an increase

of the sensation bears a constant ratio to the total stimulus. The figures which express this ratio in the several senses may be shown thus in tabular form:

"These figures are far from giving as accurate a measure as might be desired. But at least they are fit to convey a general notion of the relative discriminative susceptibility of the different senses. The important law which gives in so simple a form the relation of the sensation to the stimulus that calls it forth was first discovered by the physiologist Ernst Heinrich Weber to obtain in special cases.

Fechner's Law.-Another way of expressing Weber's law is to say that to get equal positive additions to the sensation, one must make equal relative additions to the stimulus. Professor Fechner of Leipzig founded upon Weber's law a theory of the numerical measurement of sensations, over which much metaphysical discussion has raged. Each just perceptible addition to the sensation, as we gradually let the stimulus increase, was supposed by him to be a unit of sensation, and all these units were treated by him as equal, in spite of the fact that equally perceptible increments need by no means appear equally big when they once are perceived. The many pounds which form the just perceptible addition to a hundredweight feel bigger when added than the few ounces which form the just perceptible addition to a pound. Fechner ignored this fact. He considered that if n distinct perceptible steps of increase might be passed through in gradually increasing a stimulus from the threshold-value till the intensity s was felt, then the sensation of s was composed of n units, which were of the same value all along the line.† Sensations once

* Vorlesungen über Menschen u. Thierseele, Lecture VII.

In other words, S standing for the sensation in general, and d for its noticeable increment, we have the equation dS= const. The in

represented by numbers, psychology may become, according to Fechner, an 'exact' science, susceptible of mathematical treatment. His general formula for getting at the number of units in any sensation is S = Clog R, where S stands for the sensation, R for the stimulus numerically estimated, and C for a constant that must be separately determined by experiment in each particular order of sensibility. The sensation is proportional to the logarithm of the stimulus; and the absolute values, in units, of any series of sensations might be got from the ordinates of the curve in Fig. 2, if it were a correctly drawn logarithmic curve, with the thresholds rightly plotted out from experiments.

Fechner's psycho-physic formula, as he called it, has been attacked on every hand; and as absolutely nothing practical has come of it, it need receive no farther notice here. The main outcome of his book has been to stir up experimental investigation into the validity of Weber's law (which concerns itself merely with the just perceptible increase, and says nothing about the measurement of the sensation as a whole) and to promote discussion of statistical methods. Weber's law, as will appear when we take the senses, seriatim, is only approximately verified. The discussion of statistical methods is necessitated by the extraordinary fluctuations of our sensibility from one moment to the next. It is found, namely, when the difference of two sensations approaches the limit of discernibility, that at one moment we discern it and at the next we do not. Our incessant accidental inner alterations make it impossible to tell just what the least discernible increment of the sensation is without taking the average of a large number of appreciations. These accidental errors are as likely to increase as to diminish our sensibility, and are eliminated in such an average, for those above and those below

crement of stimulus which produces dS (call it dR) meanwhile varies. Fechner calls it the differential threshold '; and as its relative value dR R

to R is always the same, we have the equation

= const.

the line then neutralize each other in the sum, and the nor mal sensibility, if there be one (that is, the sensibility due to constant causes as distinguished from these accidental ones), stands revealed. The methods of getting the average all have their difficulties and their snares, and controversy over them has become very subtle indeed. As an instance of how laborious some of the statistical methods are, and how patient German investigators can be, I may say that Fechner himself, in testing Weber's law for weights by the so-called 'method of true and false cases,' tabulated and computed no less than 24,576 separate judg

ments.

Sensations are not compounds. The fundamental objection to Fechner's whole attempt seems to be this, that although the outer causes of our sensations may have many parts, every distinguishable degree, as well as every distinguishable quality, of the sensation itself appears to be a unique fact of consciousness. Each sensation is a complete integer. "A strong one," as Dr. Münsterberg says, "is not the multiple of a weak one, or a compound of many weak ones, but rather something entirely new, and as it were incomparable, so that to seek a measurable difference between strong and weak sonorous, luminous, or thermic sensations would seem at first sight as senseless as to try to compute mathematically the difference between salt and sour, or between headache and toothache. It is clear that if in the stronger sensation of light the weaker sen. sation is not contained, it is unpsychological to say that the former differs from the latter by a certain increment."* Surely our feeling of scarlet is not a feeling of pink with a lot more pink added; it is something quite other than pink. Similarly with our sensation of an electric arc-light: it does not contain that of many smoky tallow candles in itself. Every sensation presents itself as an indivisible. unit; and it is quite impossible to read any clear meaning into the notion that they are masses of units combined.

* Beiträge zur exp. Psychol., Heft 3, p. 4.

There is no inconsistency between this statement and the fact that, starting with a weak sensation and increasing it, we feel more,' ' more,' 'more,' as the increase goes on. It is not more of the same stuff added, so to speak; but it is more and more difference, more and more distance, from the starting-point, which we feel. In the chapter on Discrimination we shall see that Difference can be perceived between simple things. We shall see, too, that differences themselves differ-there are various directions of difference; and along any one of them a series of things may be arranged so as to increase steadily in that direction. In any such series the end differs more from the beginning than the middle does. Differences of 'intensity' form one such direction of possible increase-so our judgments of more intensity can be expressed without the hypothesis that more units have been added to a growing sum.

The so-called 'Law of Relativity.'-Weber's law seems only one case of the still wider law that the more we have to attend to the less capable we are of noticing any one detail. The law is obvious where the things differ in kind. How easily do we forget a bodily discomfort when conversation waxes hot; how little do we notice the noises in the room so long as our work absorbs us! Ad plura intentus minus est ad singula sensus, as the old proverb says. One might now add that the homogeneity of what we have to attend to does not alter the result; but that a mind with two strong sensations of the same sort already before it is incapacitated by their amount from noticing the detail of a difference between them which it would immediately be struck by, were the sensations themselves weaker and consequently endowed with less distracting power.

This particular idea may be taken for what it is worth.* Meanwhile it is an undoubted general fact that the psychi

*I borrow it from Ziehen: Leitfaden d. Physiologischen Psychologie, 1891, p. 36, who quotes Hering's version of it.