the pound instead of one. The series may be increased indefinitely, additional points of difference being put first on the grain side of the series then on the corresponding half of the other side. It is evident that, however much the series may be enlarged, the primary points of difference will remain unaltered, because they always must be points of greater difference than any that can be perceived subsequently. Thus, however numerous the units in a psychophysical weight series are, the two points of greatest difference must be the grain and the pound, the three points of greatest difference the grain, pound, and halfpound, and so on.

7. Effects of Defective Length of Psycho-physical Series. -The above is written to show the variations which we may expect in the perception of individuals when the length of the psycho-physical series is the same in each. But the series is not necessarily of the same length in each, and then other defects of perception will be produced. It is a well-known fact that persons differ very considerably in the height of the notes which they are able to hear. One person may hear a note which is more than an octave higher than that heard by another. Similar conditions are found with regard to low notes. It must be remarked that the note produces no effect whatever upon the person who is unable to hear it. As far as he is concerned it is non-existent. The following, given in the Medical Press, April 2, 1890, is an extreme example of this condition. The writer, referring to the late Mr. Cowles, an American journalist, says

"It is stated that it was not until Mr. Cowles was twenty-five years of age that he became perfectly cognizant of his defect. Up to this time he treated all he read about the songs of birds as nothing more or less than poetical fiction. To him birds were perfectly mute; and

he was perfectly deaf to the shrillest and highest notes of the piano, fife, or other musical instruments. At length, after considerable pains, he was convinced that he laboured under some physical defect of hearing. When put to the test in a room where a large number of canary birds were singing very loudly, he declared he could not hear the slightest sound even when placed close to their cages. Moreover, it was found that all the sibilant sounds of the human voice were equally inaudible. The consequence was, he, like the deaf-mute, never used them in his conversation. Curiously enough, in all other respects his hearing was not only perfect, but somewhat acute."

It is therefore obvious that when a psycho-physical series is shortened relatively to that of other persons, the physical units included in the shortened portion are not perceived at all, and are practically non-existent. It is therefore impossible for a person to form any opinion with regard to their qualities, and in any mixture in which these physical units form part of the exciting stimuli they will have to be subtracted before the result can be obtained.

When the length of a psycho-physical series is different from that of the majority of persons, either shorter or longer, the centres of the different units will not correspond for both classes of persons. For instance, if one end of a series be shortened for any person, the third point of difference will be situated at a point rather nearer the other end of the series than it will be for those whose series is not shortened.

8. A Psycho-physical Impression as a Whole. In the foregoing pages I have described the psycho-physical perception of a series. The result of this is that we have obtained the units of perception. It now only remains to show how these units are combined so as to make up an

impression as ordinarily perceived. In this book it is not my intention to show how many phenomena psychophysical perception will explain, but only that it will explain the phenomena of colour-perception. I shall therefore confine myself to impressions of sight. Impressions of sight may be divided into four sets-those of colour, form, size, and shade. A psycho-physical impression as a whole is made up of the contiguous association of psychophysical units; thus there will be the units of colour, form, size and shade. It will be seen that one set of impressions cannot be absolutely taken away from the others.

An impression of sight may be represented by a coloured photograph. We know that most persons see six definite colours. Let us suppose that most persons also see six definite varieties of form, size, and shade. As I have shown in the preceding pages, each psycho-physical unit might be represented by the physical unit occupying a position in the series corresponding to the centre of the psycho-physical unit. Then, from the photograph, we might construct a series of pictures which would approximately represent different varieties of psycho-physical perception. In the case of the normal-sighted we should construct a picture in which six different colours, six different form-units, six different size-units, and six different shade-units were used. In the case of diminished colour-perception only five, four, three, two, or one colour would be used instead of six. In the case of diminished form-perception, only five, four, three, two, or one form-unit would be used instead of six. In the above examples the results would only be approximately correct, because approximate psycho-physical units would be used; thus all greens would be represented by one colour. To obtain perfectly correct results, we should have to use absolute psycho-physical units.

What under ordinary circumstances is the result of diminished form-perception? It is that persons with this defect do not perceive differences of form which are evident to other persons. It is a very common occurrence for two persons to be looking over a photograph album and one to say, "These men are brothers, are they not?" and for the other to reply, "Yes; but how could you tell? There's not the slightest resemblance between them." But the original speaker declares that he sees a striking likeness. The reason of this is, that the man who fails to perceive the likeness has a psychophysical form series the units of which are far less numerous than those of his friend, and so he is not able to perceive a difference less than that of the difference between two of the units. This may be made plainer with a simple illustration. Let six figures be drawn on paper, four being perfect circles, but the other two differing from circles in having one diameter slightly shorter than the other. Now, the above person would say that these were six exactly similar figures, the difference between the units of form making up the figures being less than that between the units of his psycho-physical form series. His friend would recognize the "likeness between two of the circles. The countenance varies very considerably in different persons; but the above shows how a person with a deficient perception of form is often at a loss for a means of identification. Therefore, as the distance between the adjacent psycho-physical units increases so does the means of recognition diminish. A picture may be inaccurate in colour, form, size, or shade, and a person with ability for perceiving differences of form, but not those of size, will detect minute errors of form, but overlook very great errors in perspective and other points depending upon size. I have a friend who is par

ticularly quick at noticing differences of size; and his remarks when observing pictures are nearly always connected with size-thus the length of the arm of one man is out of proportion to the body, the height of a church in the distance is too great, etc.

In the perception of shade we may have a physical series in which the units vary from white to black. A person with defective perception of shade will put two shades of gray together as exactly alike when the match is markedly incorrect to a normal-sighted person. This defect is not necessarily associated with diminished colourperception. Thus we may meet with a person who has excellent shade-perception, but very defective colourperception, and vice versa. Defective shade-perception is of very little practical interest.

Observers do not take sufficient account of mental deficiencies of perception when reasoning upon the functions of the senses. Thus we cannot say for certain that a photograph represents the image on the retina; in reality it may be far more complicated. It must be remembered that the impression of the photograph has to pass through the same channel (the eye, optic tract, and brain) before it reaches the mind; thus, if there were no colour-perceiving centre, we should have no knowledge of colour however plainly it was represented in the retina. An illustration will make this clear. If total colour-blindness were universal in man no correct idea could possibly be formed of the coloured image on a rabbit's retina, because that colour would be as much lost as any other. It seems to me very probable that animals possess perceptions which are not found in man, and we have no means of finding out what these are.