§ 23. Intensity, Extent and Duration as Attributes of Sen- sation. — Every sensation quality possesses a certain strength or intensity, and lasts for a certain lejtgth of time. The qualities of colour, brightness, pressure and tempera- ture have always, in addition to duration and intensity, a certain extent, i.e., are spread over a certain amount of space within the field of vision or of touch.
It is evident that sensations may differ very widely in ail three respects. We can hear the faint sound made by the fall of a pin upon the floor, and we can hear the roar of thunder (intensity); we can see as long as daylight lasts, and we can see a momentary flash in the dark (duration); we can appreciate the heat of a hot needle- point, or the cold of water in which the whole body is immersed (extent). Not only, then, can each of the forty thousand sensation qualities combine with other qualities, to form a perception or an idea, but each quality can combine at various intensities, for different lengths of time, and, in the four cases mentioned, in varying extent.
In § 7 we analysed the idea of a book into sensations of sight, sound, smell, pressure and strain. These qualities are present in the idea of every book. But the smell of the leather binding may be faint or strong; the pressure of the volume on the hand may 68 § 23. Intensity, Extent and Duratio7i as Attributes 69 be light or heavy; the strain of holding it great or small. The component sensations, i.e., may differ widely in intensity. Again: the scent, pressure and strain are less important elements of the total idea than are the qualities of sight. When we ' think of ' the book, we shall probably recall both smell and weight; but they will not long remain as constituents of our idea. After a few seconds, perhaps, they will have entirely disappeared, and the idea of the book will be an exclusively visual idea. The visual elements persist as long as we continue to think of the book. The component sensations, then, differ widely in duration. Lastly: the yellow of the gold lettering and the red of the leather cover are both sensation qualities contained in the idea; but there is a greater extent of red than of yellow.
It is clear, then, that a few qualities may give rise to a large number of different ideas, in consequence of differences in inten- sity, duration and extent. My ideas of two books may be very different, although the qualities of sensation which they contain are the same.
Three questions might be asked in connection with these three attributes of sensation. We might enquire: (i) What are the least intensity, extent and duration which a sensation may possess and still be a sensation? (2) What are the greatest intensity, extent and duration which a sensation quality can reach } And (3), just as we asked how many qualities of sensation could be ascribed to the eye, the ear, the skin, etc., so we might now ask: How many different intensities of sensation lie between the faint sound that we can barely hear and the loud sound that is almost loud enough to stun us 1 How many different sizes of black or red can we distinguish, from the tiny dot which is just visible, up to the expanse which fills the whole field of vision.'' How many durations of tem- perature sensation can we obtain, from the heat which flashes in consciousness for an instant, and then dis- /o Intensity, Extent, Duration of Sensation appears, to that which persists so long that it ceases to be itself and becomes pain?
The first of these questions we can answer, at least in a large number of cases. The second we cannot answer with the same degree of certainty. Our answer to the last plainly depends upon our answer to the other two. We cannot say, e.g., how many different intensities lie between the two extremes of sensation — the weakest and the strongest — unless we know what these two ex- tremes are. As we cannot determine the upper extreme very certainly and our knowledge of it cannot therefore be very accurate, we cannot calculate the whole number of sensation intensities, and compare it with our list of sensation qualities. Fortunately, the third question may be left unanswered, as regards all the three attributes under discussion, without any loss to psychology. We shall see later (§ 26) that the attempt to answer the first two suggests another, which takes the place of our present third question, and which can be satisfactorily and profitably answered.
§ 24. The Minimal Intensity, Extent and Duration of Sen- sation. — (i) It is a familiar fact that in every department of sensation there are stimuli which are too weak to be sensed. We know that the clock of the church tower is ticking, because we see that its hands move: but the noise of the ticking is too faint to be heard from the ground. As we climb the stairs, it becomes audible.
What we have to do, in order to discover the point at which sensation begins, is to take a stimulus which is too weak to be sensed, and gradually increase it until it calls forth a sensation.
Method. — Methods of determining the least noticeable inten- sity of stimulus follow the same general principle in all sense § 24- Minimal Intensity, Extent, Duration J\ departments. It will only be necessary, therefore, to give two or three concrete illustrations.
To find the least noticeable intensity of noise, — Let the subject be seated, with closed eyes, in a large room which has no echo. Hold a watch before his face, and gradually remove it from him — taking care to hold it always directly fronting him, and to keep it at the right height above the floor {i.e., on a level with the ear) — until he ceases to hear its ticking. Measure the distance from this spot to the centre of an imaginary Hne joining his two ears. The distance will be somewhat too short: the sound has been growing fainter throughout the experiment, and he has therefore been expecting it to disappear. He has not been altogether impartial (§ lo). Now start again from a point some few feet beyond the spot at which sensation ceased, and move the watch slowly towards the subject, till he can hear the ticking. This point will probably lie on the far side of the other, as he knows that the ticking will soon be heard, and is therefore expecting it. Measure as before. Take the average of the first (too short) and second (too long) distances. The least noticeable intensity of noise is the intensity of the tick of the watch at this average distance.
The investigation of the intensity of visual sensations is pecul- iarly difficult. For {a) the eye is never wholly at rest, as the ear or the skin may be. When we close our eyes, or enter a room from which light is shut out, we still see; we see black, and black is one of the brightness qualities. This ' intrinsic ' brightness sensation, therefore, is always mixed with the brightness of the stimulus which we employ to test the eye. {li) We cannot change the intensity of a visual sensation without at the same time chang- ing its quality. If we make a grey lighter, it becomes a different grey, i.e., another sensation. In all the other sense departments it is possible to vary intensity independently of quality.
All that we can do, then, is to enquire what amount of light is necessary to give a sensation of brightness just different from (brighter or stronger than) the ' intrinsic ' black of which we have spoken. For the purpose of this enquiry, the subject is placed in a dark chamber; and, when his eyes have grown thoroughly 72 Intensity, Extent, Duration of Sensation accustomed to the dark, a metal wire is heated until it just * shim- mers.' The intensity of the just noticeable shimmer must be measured by the aid of a * photometer,' such as is employed in physical laboratories.
It is also by no means easy to ascertain the least noticeable intensity of temperature sensations. The skin has a natural warmth, as the eye has an intrinsic black; and this warmth — which differs considerably from time to time — is added to or subtracted from the temperature of the stimulus, according as it is hot or cold. The part of the skin under investigation — say, the hand — must be kept in water of a neutral temperature, until the cutaneous organs have become adapted to it. The hand is then plunged into water which is slightly warmer or colder than this, and the point noted at which an increase or decrease of temperature is sensed.
(2) A stimulus may be too small to be sensed. We know that there is a skylark somewhere above us, because we saw it rise from the grass, and can still hear it sing: but it is too small to be seen. There is, then, a certain minimal extent of visual stimuli, by which no sensation is aroused. And what holds of sight, holds also of pressure and temperature.
Method. — To find the least noticeable extent of brightness. — Two white threads are stretched vertically over a grey background, at a convenient distance from the eye. They are very slowly and gradually brought together, until they seem just to touch. This will happen when they are actually separated by some little dis- tance. The procedure is now reversed: the threads are gradu- ally separated, until they seem to the eye to be just apart. The average of the two distances between them (the first too large, because their junction was expected; the second too small, be- cause their disjunction was expected) is the least noticeable extent of grey, in the horizontal direction, at the given distance from the eye. It corresponds to a distance of about.005 mm. between the images of the two threads upon each retina.
§ 24- Minimal hitensity, Extent, Duration y^ (3) A particular sensation — a sensation of bitter, e.g. — may last for a few moments or for a considerable length of time, its quality remaining unchanged. How much time must a sensation quality be allowed, if it is to be a full and adequate sensation?
Method. — One instance of the way in which this question is answered may again suffice.
To find the least noticeable duration of pressure. — For this purpose we require a small toothed wheel of hard wood. The arm is placed comfortably upon a sloping arm-rest, in such a way that the tip of the first finger can be laid lightly upon the teeth of the wheel. When the wheel turns slowly, we have a series of dis- tinct pressure sensations, one from each tooth. But at a certain rate of rotation, we lose the distinct pressures, and have a percep- tion of roughness, like that obtained by passing the finger over velvet; while if the teeth strike at a still higher velocity, the per- ception becomes indistinguishable from that of a perfectly smooth surface, such as marble. We must ascertain the highest speed at which the wheel can be revolved, and still give a series of distinct pressures. Dividing the time of revolution by the number of teeth, we get the minimal duration of pressure sensation required.
We must note here that a sensation does not come to an end at the moment when its stimulus ceases to act. If we look at a bright light, and then close our eyes, we see on the black back- ground a coloured patch, of the same form as the light. It may persist for several minutes. If we blow out a lighted match, and wave it round while the burned end is still glowing, we see a red circle in the air; the red sensation at any point upon the circle persists until the match has returned again to that same point. This is why a disc composed of black and white sectors looks grey when it is rotated (§ 12); the sensation of black remains while the white stimulus is given, and the sensation of white per- sists while the black sector is stimulating the eye.
The after-sensations, or after-images, as they are called, are of very different duration in the different sense departments. Thus, 74 Inte7tsityy Extent^ Duration of Sensation the total duration of a loud sound or heavy pressure is consider- ably less than that of even a moderately strong visual or temper- ature sensation.
We cannot say in definite terms what is the minimal in- tensity, duration or extent of a particular sensation quality. The chief reasons for this are the following, (i) Al- though one man may be able to distinguish as many qual- ities of noise as another, it does not follow that he can hear equally faint sounds. That is to say, the stimulus which arouses sensation in one case may prove to be too weak in another, even if the two sense-organs are per- fectly normal. (2) A stimulus which is effective at one part of the sense-organ may be inefficient to call forth sensation at another. A weight which excites the sen- sation of pressure upon the finger-tips is not noticed when laid on the back of the hand (intensity); and threads which seem just separate when directly looked at appear to be a single thread if observed indirectly, from the side of the retina (extent). (3) The just notice- able intensity of stimulus depends upon its own extent and duration. A light which is too faint to be seen at once may produce a sensation if it continue for some time together; and a faint speck of light may be invisible, though an extended light of the same intensity would be easily seen.
No general table of minimal values can be made out, therefore. They must be determined afresh in every series of experiments for which a knowledge of them is required.
§ 25. The Maximal Intensity, Extent and Duration of Sen- sation.— (i) The maximal intensity of sensation is that intensity which cannot be increased by any further in- § 2 5- Maxhnal Intensity, Extent, Duration 75 crease of stimulus. It seems- probable that the greatest intensity which a sensation quality can attain is its inten- sity at the moment before it passes over into pain. For though the quality of pain does not wholly destroy the original qualities of pressure, strain, etc., it so obscures them that we do not know whether they undergo change with further increase of stimulus or not. For all practi- cal purposes, then, sensation intensity does not increase beyond the point at which a stimulus becomes painful.
Method. — To determine the maximal intensity of sweet, e.g., we must increase the intensity of a sweet stimulus by slow degrees until we reach the point at which the sweetness is ' sickly ' and * nauseating.' The amount of sweet stimulus which is just not sickly is the equivalent of the maximal sweet sensation.
There are two reasons why we cannot ascertain the maximum of sensation intensity with any great accuracy, (i) The sense- organ may be so much fatigued by a succession of very strong stimuU that it refuses to act at all. The ear may be ' deadened,' smell may be ' blunted,' before the really maximal intensity of stimulation has been reached. (2) We can work only in one direction, up towards the stimulus which produces a maximal sensation. If we began to experiment with a stronger stimulus, we might injure the organ. Now we have seen that when experi- ments are all made in one definite direction, the subject is not impartial; he expects or anticipates the result of the experi- mental series. Pain will occur, therefore, earlier than it should; and the maximal intensity obtained will, in every case, be too small. Could we reverse our procedure, and come down to the maximal stimulus, we should be able to correct the error of expectation by averaging.
(2) The maximal extent of a visual quality is produced by a stimulus which completely fills the field of vision. The maximal extent of pressure or temperature sensa- tion is produced by a stimulus which affects the entire 'j^ Intensity, Extent, Duration of Sensation surface of the skin, or the whole extent of the internal organ from which the sensation proceeds (muscle, joint, etc.).
Method. — If we immerse the body in cold water, we obtain a cold sensation of maximal extent; if we plunge into water of a neutral temperature, a maximally extended pressure sensation. A maximally extended black is obtained when we look straight before us in a dark chamber; a maximally extended blue, when we look directly at the sky under such conditions that there is nothing to 'break the view,' — e.g., as we he on our back on a hill-top.
(3) The maximal duration of the various sensations has not been investigated. Many qualities, if long con- tinued, pass over into pain; e.g., shrill tones. Others, it would seem, might be prolonged indefinitely; e.g., black, a moderate warmth.
§ 26. The Relation of Intensity, Extent and Duration to ftuality of Sensation. — The foregoing Sections have brought out several differences between quality and the other attributes of sensation. One difference, a differ- ence in the importance of the attributes to sensation as an elementary conscious process, we have emphasised previously by saying that intensity, duration and extent are always the intensity, duration and extent of some quality (§ 8). Quality is the most important attribute. The further distinctions which we are now able to draw are four in number, (i) Knowledge of the number of qualities helps us in our analysis of consciousness; know- ledge of the number of intensities, etc., does not. (2) Knowledge of the number of qualities helps us to ascer- tain the bodily conditions of sensation; knowledge of the number of intensities, etc., does not. (3) Quality is ab- § 26. Their Relation to Quality of Sensation jy solute; the other sensation attributes are only relative or comparative. (4) Quality is individual; the other three attributes are common or general.
(i) Two sensations which differ in quaHty are two different sen- sations. But a sensation may differ widely in intensity/ extent or duration, and yet remain the same sensation. Since the first task of the psychologist is to analyse consciousness into its elements, he is obhged to count up the total number of sensation qualities. Ignorance of any one of them would mean that his analysis was incomplete, and his final account of mind so far wrong. But he is in no way assisted by a list of the possible intensities, etc. These are not new conscious elements, but only degrees or amounts of elements already known. (2) We laid it down in our definition of sensation that the mental process is always con- nected with a bodily process in a definite bodily organ. It fol- lows that every sensation quality is connected with a different kind of bodily process. Hence it is necessary for us to know the number of sensation quahties, if we are to give a complete descrip- tion of the bodily processes connected with sensations. Our view of the way in which the ear works, e.g., depends upon the number of sensations obtainable from it. There is no similar reason for knowing the number of sensation intensities, etc.; for it is clear that one and the same kind of bodily process may last for a longer or shorter time (duration of sensation), be more or less widely diffused within the bodily organ(extentof sensation), and be more or less well-marked (intensity of sensation) in different instances. (3) There is nothing absolute about an intensity, etc., as there is about a quality; we estimate intensity always by comparison with other intensities. Our use of terms indicates this. ' Blue ' means something fixed and absolute; but * large ' is altogether relative or comparative: a ' large ' beetle, a '■ large ' table, and a '■ large ' village refer to objects of very different absolute sizes. If we had our full Hst, therefore, we could do nothing with it; its terms would lose all definite meaning as soon as they were taken out 1 With the single exception of visual sensations: cf. §§ 12, 24.
'/S Intensity^ Extent^ Duration of Sensation of the list, i.e., as soon as it became impossible to compare them with the other terms. (4) No two elementary processes have the same quality. They may have the same intensity, extent and duration; for intensity and duration are universal attributes, common to all sensation processes alike, while extent is common to all sensations from eye and skin. Not only, then, is quality absolute, and intensity, etc., relative; quality is an individual at- tribute, while intensity, etc., are common characteristics of differ- ent elements.
Now an individual fact requires individual explanation: we found it necessary to give one account of the action of light on the eye, another of the action of sound on the ear, etc. But a common or universal aspect of all sensations should receive a general explanation. May we not be able, then, instead of dealing with each organ separately, to give a single account of what goes on in all the bodily organs when a sensation changes in intensity, etc.?
This is the question which was referred to in § 23 as growing out of the discussion of the first two questions propounded in the present chapter. The third question there raised, and judged unanswerable, we have found to be not worth answering. The new question, on the other hand, is one of the most important in the whole sphere of sensation psychology. Very many experi- ments have been made upon our estimation of intensities (Weber's law), extents (eye measurement) and durations (time sense): we must briefly review these before we can answer it.
§ 27. Weber's Law. — We have seen that some stimuli are too weak to produce a sensation. Every one must have noticed the further fact that a stimulus may be of considerable intensity, and yet not strong enough to add to the intensity of a sensation already existing. If a candle is lighted in the room in which we are sitting on a dull winter's afternoon, the room becomes quite noticeably brighter; but if the same candle is lighted in the same room on a sunny morning, it makes no appreciable difference in the general illumination. If we dissolve an extra spoonful of sugar in a cup of coffee, we make it very perceptibly sweeter; but if we stir the same amount of sugar into a cup of honey, we do not find that there is any difference in the taste. Let us see what follows from this fact in a particular series of experiments.
Suppose that we are investigating the intensity of noise. We shall begin with a stimulus of moderate intensity: say, the noise made by the fall of an ivory ball upon a wood plate from a height of 90 cm. We will call the intensity of this sensation i. If we gradually increase the height of fall, we shall reach a point at which the noise of the fall is just noticeably greater than the original noise. We may call the intensity of this second sensa- tion 2. If we further increase the height of fall, we shall presently get a noise, 3, which is just noticeably louder than 2; and so on. Now what are the different heights of fall — i.e.y intensities of stimulus — necessary to arouse sensations of the intensities 2, 3, 4, etc. } The stimulus required for a sensation of the intensity i was a fall of 90 cm. That required for intensity 2 was a fall, let us say, of 120 cm.; we were obliged to add 30 cm. to the original 90 cm. Will the stimulus required for the sensation in- tensity 3 be a fall of 150 (120 -f 30) cm.; that for intensity 4, a fall of 180 (150 + 30) cm., and so on } However natural it may seem to reply to this question in the affirmative, the facts stated just now show that the answer would be incorrect. Dull daylight + candle-light gives a stronger sensation than dull daylight; but bright sunlight + candle-light is not stronger than bright sunlight. On the same principle, a fall of 90 + 30 cm. gives a louder sound than a fall of 90 cm.; but a fall of 120 -|- 30 need 8o Intensity, Extent, Duration of Sensation not give a more intensive sensation than a fall of 120. The stronger the stimulus already is, the greater must be the addition made to it if the sensation which it arouses is to increase in intensity. An addition of 30 cm. suffices to raise the intensity of sensation from i to 2; but if we are affected by the stronger stimulus 120 cm,, we must add more than 30 to it to change intensity 2 to intensity 3. In other words: change in the intensity of sensations does not keep even pace with change in the intensity of the stimuli which occasion them.
Experiment enables us to replace this general state- ment of the relation of sensation intensity to stimulus intensity by a definite scientific law. If sensations are to increase in intensity by equal amounts, their stimuli must increase by relatively equal amounts. If the increase of 90 cm. to 120 {i.e., increase by \) raises the intensity of sound from i to 2, then 120 must be increased by \ of itself, i.e., by 40 cm., if the sensation intensity is to rise from 2 to 3; and 160 must again be increased by \ of itself, i.e., by 53 cm., if the intensity of noise is to rise from 3 to 4. In the same way, a stimulus of 30 cm. must in- crease to 40, and a stimulus of 60 cm. to 80, if we are to obtain equal differences in the intensity of the sensations corresponding to them. This law — that equal differences in the intensity of sensation are produced by relatively equal differences in the intensity of stimulus — is known as Weber's law.^ It has been found to hold good for 1 Ernst Heinrich Weber (b. 1795, d. 1878) held successively the chairs of comparative anatomy, human anatomy and physiology in the University of Leipsic (from 1818 until his death). The first statement of his law is to be found in a paper De tactu (" Upon Touch"), published in 1834. It runs as follows: In observando discrimine reriim inter se comparatartim non differ- entiani rerum, sed rationem differ entice ad magnitudinein rertcm inter se stimuli and sensations of widely different intensities in several sense departments, — indeed, in all those which have been thoroughly investigated. It is of especial im- portance as the first law, in the scientific meaning of the word, discovered by psychology.
The numerical expression of the law (z>., the exact ratio in which stimuli must increase to produce equal differences of sensa- tion intensity) is different in the different sense departments, (i) Weights laid upon the finger-tips must increase by one- twentieth to produce a noticeable difference in the intensity of pressure-, (2) noise stimuli must increase, as in our illustration, by one-third; (3) brightness stimuli by one-hundredth; (4) strain stimuli — lifted weights — by one-fortieth. There are indications that (5) intensities of tone and (6) of taste (salt and bitter) obey Weber's law, but no exact statement can be made with regard to them. Whether the law holds for the temperature sense is an open question. No investigation has been made of smell, or of any organic sensation other than strain.
The law may be phrased mathematically as follows: If sensation intensities are to increase in arithmetical progression, stimulus intensities must increase in geometrical; or, more shortly: Sensa- tion increases as the logarithm of stimulus.
Method. — To find the numerical expression of Weber's law for noise. — An ivory ball is let fall, from two different heights, upon a hard-wood plate. The difference of intensity between the two sounds {i.e., the difference between the two heights of fall) must be slight. The two sounds are given in irregular order in different experiments (to avoid the influence of expectation), and the subject is required to say, in each case, whether the second is louder or weaker than the first. In 100 experiments, he will give a certain number of right answers, and a certain number of wrong.
comparataruvi percipimus. (" In observing the difference between com- pared objects, we perceive not the [absolute] difference between the objects, but the proportion which the difference bears to their magnitude.")
G 82 Intensity^ Extenty Duration of Sensation The method assumes that if the two sounds are just noticeably- different in intensity, the subject will give about 80% right and 20% wrong answers. This proportion is calculated by what mathematicians call the ' law of probability.' Now suppose that a certain difference gave 70 right and 30 wrong answers in 100 experiments. We could calculate, by aid of the integral calculus, how much larger the difference must have been to give 80 right and 20 wrong, — i.e., to be just noticeable. The calculated dif- ference (difference of height of fall) is the numerator, and the original intensity (original height of fall) of the weaker sound, the denominator, of the fraction which expresses Weber's law.
§ 28. Eye Measurement. — We have found a general law governing the relation of sensation intensity to stimulus. Is there any similar lav^ governing the relations of stimu- lus and sensation extent? Nothing can be said by way of answer to this question in the spheres of pressure (whether from skin or joint) and temperature. Many experiments have been made, however, upon what is termed * eye measurement '; that is, upon the accuracy of our estima- tion of visual extents (lines).
If a horizontal line, of moderate length, is bisected, and one of the halves gradually lengthened, the eye will find a difference between the two parts when the larger becomes one-fiftieth longer than the smaller. This rule holds good for stimuli of widely different absolute extent (lines of widely different length).
Extent is one of the necessary attributes of visual sensations; whenever we see, we see something extended. But it does not follow from this that extents are compared or estimated as ex- tents, i.e., that we can make a direct judgment of the relative lengths of two lines, without calling in the aid of other attributes of sensation. The rule given above — that equal additions to the extent of sensation mean relatively equal additions to the extent