quality just illustrated is, moreover, as we shall presently see, aided by an exceptionally fine discrimination of duration, which allows of a nice discrimination of sounds in rapid succession. In this way we are able through the sense of hearing to acquire a good deal of exact information, as well as a considerable amount of refined pleasure. The delight of music sums up the chief part of the latter. The former is most strikingly illustrated in the wide range of knowledge derived by way of that system of articulate sounds known as language.

As a set off against these advantages, it must be borne in mind that in the case of hearing the appreciation of extensity and distinctness of points exist in only a very faint and germinal form. The very structure of the organ and the way in which the stimulus is applied exclude a definite discrimination of extensity and number of points such as we find in the case of touch and sight. It is commonly supposed that we are able to distinguish a massive sound, such as that produced by a large area of water, from an acute one. Recent experiments, moreover, go to show that the ear possesses considerable power of distinguishing direction of sound (within certain limits). This suggests that in the case of hearing there is a germ of local discriminations, not only in relation to sounds entering different ears, but in relation to sounds of unlike direction entering the same ear.

The assertion that we distinguish degrees of volume or massiveness of sound made by Dr. Bain and others has been cautiously disputed by Stumpf, who is inclined to resolve 'massiveness' of sound into compositeness, i.e., the addition of new qualitative elements by the extension of the sounding area. At the same time he allows that sounds of low pitch have an aspect analogous to massiveness or spatial extent.1

The discrimination of the direction of sound has been elucidated by the recent experiments of Preyer, Münsterberg and others. The tendency of these experiments seems to be to connect the appreciation of direction with the action of the three semi-circular canals, in the dilatations of which (ampullae) a part of the auditory nerve is known to terminate. There is good reason to suppose that the varying pressure of the fluid contents of the canals with changing positions of the head is a factor in the sense of equilibrium. It is further argued by Münsterberg that owing to the different position or lie of the canals sounds of unlike direction would stimulate their respective fibres with different proportions of intensity. But the whole question of the precise functions of this part of the ear is still undecided." 1 See Bain, Mental and Moral Science, p. 53; and Stumpf, Tonpsychologie, i. p. 210, and ii. p. 51 ff.

* On the functions of the semi-circular canals consult Ferrier, Functions of the Brain, p. 127 ff.; Wundt, Physiol. Psychologie, ii. p. 25 ff.; and Münsterberg, Beiträge zur exper. Psychol. ii. p. 182, etc.

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SIGHT.

$25. Characteristics of Visual Sense. The sense of Sight is by common consent allowed the highest place in the scale of the senses. The stimulus, ether vibrations, greatly exceeds in point of subtlety the stimuli which (under normal circumstances) operate in the case of the other sense-organs. It is owing to the nature of this stimulus, moreover, that the sense of sight is capable of being acted upon by objects at enormous. distances, as the heavenly bodies. Conformably to this subtlety of the stimulus, we find that the structure of the eye shows a greater delicacy than is observable even in the organ of hearing. This applies both to the end-organ itself, the retina with its several layers, more especially the finely-roulded structures. known as the rods and cones in which the fibrils of the optic nerve terminate, and also to the optical apparatus, the lens, and other contents of the eye-ball, by means of which the luminous stimulus is brought to bear on these.

The eye, though under normal circumstances stimulated by light, is capable of being excited by other stimuli as well. Thus an electrical current sent through the eye gives rise to a sensation of light. Mechanical pressure produces the same effect, as is illustrated in the well-known " "phosphenes or discs of light produced by pressing a finger on a corner of the eye-ball. Lastly, the retina is susceptible to the action of certain internal stimuli, its nervous elements being for the most part in a state of 'tonic' excitation. This effect of internal stimulation is marked off by German physiologists as the eye's 'own light' (Eigenlicht).1

$26. Scale of Luminous Intensity. The scale of intensity in the case of visual sensations is obviously a very extended one. It answers to all distinguishable degrees of luminosity, from the brightest self-luminous bodies which we are capable of looking at without temporary blinding down to the objects which reflect a minimum of light, and are known as black. The eye's capability of recognising at a glance the particular nature of an object, as well as of discriminating a multitude of unlike objects in a scene, rests in part on this delicate discriminative sensibility to degrees of light.

1 For a fuller account of the structure and function of the eye, see Ladd, op. cit., pp. 171 ff. and 325 ff.

Here again careful experiments have been conducted in order to ascertain the limits of intensity. The threshold of absolute sensibility is specially difficult to determine owing to the constant presence of the Eigenlicht. With respect to discriminative sensibility, it is found that (in the median region of the scale) the eye distinguishes two stimuli having the ratio of intensity (about) 120: 121. These experiments were carried out by Bouger, Volkmann, Aubert, Masson and others, partly by means of two lights throwing a double shadow of a rod on a white screen, and partly by means of rotating discs having circles of unequal brightness. The results differed in different series of experiments. Some investigators make the fraction much less (e.g., Aubert ). This fineness of quantitative discrimination belongs only to the central area of the retina (or area of perfect vision). On the side parts of the retina it is much less. The discrimination of degree is much less

fine when, instead of white, coloured light is employed.1

It is to be added that the sensibility to light not only varies as between individual and individual, but undergoes considerable changes in the case of the same individual. There seems to be a periodic variation during the twenty-four hours. According to Hubert and C. P. Müller, an object appears only half as bright in the evening as in the morning. The eye further accommodates itself to various degrees of luminosity. Thus in first going from a softly-lit room into the sunlight there is a temporary inability to distinguish objects as brighter or less bright, but after a time the eye adjusts itself to its new surroundings.

§ 27. Colour-Sensations: (a) The Chromatic Scale. The stimulus of the eye, like that of the ear, varies according to the rapidity of its vibrations. The analysis of solar light into its constituent rays in what is known as the prismatic spectrum separates the different kinds of rays, that is to say, those of different rates of oscillation. The red rays at one end of the spectrum are the slowest, making about 456 billion of vibrations per second, whereas the violet rays at the other extremity make about 667 billions. These variations in the rapidity of the vibrations occasion (within certain limits) differences in the quality of the resulting sensations. In this way we obtain a scale of chromatic quality resembling that of pitch in the case of musical sensations. Beginning with the rays of slowest vibration, we have the series red, orange, yellow, green, blue and violet, together with intermediate hues not so commonly distinguished by separate names. The colours at the red extremity are known as the warm colours, those at the other the cold colours. It is to be added, however, that in the case of violet there seems to be a return to a warmish hue. As may be seen by a glance at the solar spectrum, these colour-sensa

1 For a fuller account of these investigations, see Ladd, op. cit., p. 374 ff.; and Wundt, Physiol. Psychologie, i. cap. viii. § 2, p. 357 ff.

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tions form, like the sensations of pitch, a perfect continuum, or series of perfectly gradual transitions. The scale of coloursensations further resembles that of tone-sensations in that the series of effects is limited at each extremity. Rays of slower vibration than the red rays, or of more rapid vibrations than the violet rays, fail to produce a proper sensation of colour.

The several colour-sensations here spoken of are only clearly distinguished by the central region of the retina (yellow spot). Towards the periphery colourdiscrimination falls off more rapidly than discrimination of intensity. These facts, taken with the anatomical fact that the (retinal) cones are most numerous in the central region and fall off relatively to the other elements (the rods) towards the periphery, suggest that the cones are the structures specially engaged in coloursensation, while the rods are concerned merely in the appreciation of the intensity of light.1

While there are these points of analogy between the scale of colour-sensations and of pitch-sensations, the two differ in important respects. To begin with, the quality of the colour-sensation does not change continuously in close correspondence with the changes of the stimulus, as in the case of tone-sensations. In some parts of the spectrum considerable changes in the rate of vibration occur without producing any appreciable effect on the sensation. Hence we cannot speak of a colour-scale in precisely the same sense as we speak of the tone-scale. Again, the series of colour impressions, instead of assuming the form of a straight line, each successive member being further removed from the starting-point than its predecessor, rather assumes the form of a bent or curved line. As already observed, the extremities red and violet seem to approach one another. This affinity between the extremities of the spectrum is seen in the fact that if the rays are combined we have an intermediate sensation, that of purple, which forms a connecting link between the terminal sensations red and violet. These and other differences show that the tone and colour scales cannot be assimilated in the way attempted by those who seek to establish quasi-musical relations, harmonious interval, etc., among different members of the chromatic scale.3

(b) Saturated Colour. The sensations occasioned by the separated homogeneous rays of the spectrum are spoken of as pure or saturated. Our ordinary colour-sensations produced by light reflected from objects are never perfectly saturated. The

1 See Ladd, op. cit., p. 182 and p. 335.

It follows that there is no constant ratio in the region of colour-discrimination, as is found (within certain limits) in the case of pitch-discrimination. Dobrowolsky has estimated the least perceptible difference at different points of the colour-scale. At the red end it is as much as from toy; whereas in the region of the yellow it falls to a.

The points of difference between the tone and colour scales are brought out by Helmholtz, Physiologische Optik, p. 236 et seq., and Fechner, Elemente der Psycho-physik, ii. p. 267 ff.; cf. Stumpf, op. cit., ii. p. 49.

opposite of a saturated colour is a whitish hue, caused by the admixture of white or mixed light. By altering the degree of saturation we obtain for each colour a special scale of purity. It is to be noted that in some cases an alteration in the degree of saturation is popularly spoken of as a change of hue. Thus a whitish modification of purple is ordinarily marked off as pink. Such whitish modifications of hue must be carefully distinguished from change of brightness or tone, due to an increase in the intensity of the light.

(c) Different Modes of Producing Colour-Sensations. The distinguishable colours of the spectrum are not the only possible colours. By combining different kinds of rays new mixed modifications of hue may be obtained. It is found further that by taking rays at a certain distance one from another and combining them in definite proportions of intensity an intermediate hue may be produced similar to that produced by unmixed or homogeneous light. Lastly, it is known that by mixing light of different kinds white may be obtained in a number of ways. Thus if we place purple between the extremes red and violet and represent the series of colours as a closed circle instead of as a straight line, it is found that any two kinds of light standing opposite to one another at the extremities of the same diameter if combined in certain proportions occasion the sensation of whiteness. All such pairs of colours are known as complementary. It follows that colours cannot, like tones, be represented by a straight line or a continuum of one dimension. We must think of them as distributed over a space of two dimensions, viz., that of a circle of which the circumference represents the series of the spectrum and the connecting purple, and the centre, white.

There are three ways in which colours may be said to be mixed. One is that familiar to painters by a mixture of pigments. Here the result (e.g., green by mixing blue and yellow) depends on certain physical properties of the pigments themselves, and does not involve a compounding of colour-sensations. Coloursensations can be compounded either by combining different kinds of rays, or by compounding effects on the retina, as when a disc with different coloured sectors is made to rotate rapidly, so that the successive sensations, owing to the fact that each persists as an after-sensation beyond the moment of actual stimulation, overlap and combine.

It follows from what is known of the effects of compounding