.

physical series is therefore a physical series as it appears to the mind. The series will appear as if it were divided into a number of units, each containing a number of spheres of apparently the same size. It will then be found that the person who is able to distinguish most easily minute differences of size, will be able to see more of these units than other persons; that is to say, he will not put so many of the physical units together, as being exactly alike, as another person would. We then find that people differ very much in the number of units which they put together as exactly alike. So we are able to make definite classes, varying from those who are able to perceive very minute differences of size to those who can only distinguish (by the eye) large and small objects, and are therefore size-blind. It will be noticed that individuals will mark out points in the series where the difference between the units is so distinct that they would have noticed it if these units had been shown separately, and not in the form of a series; others in which they are able to notice a difference because the adjacent units are present for comparison; and others in which no difference can be detected, even with the most careful comparison. These latter will be included in an absolute psycho-physical unit. But the former class will form an approximate psycho-physical unit—that is, a psycho-physical unit containing physical units which are not easily distinguished from each other, and are so much alike as to be put in the same class and called by the same name. These approximate psycho-physical units are the most important, and they are the ones to which definite names are given. As the size of the absolute is proportional to that of the approximate psycho-physical units, the latter are the only ones which it is necessary to ascertain. Thus, if each of the absolute psycho-physical units of a series contain

more physical units than the normal number, it must follow that the approximate psycho-physical units will be fewer, as the length of the series remains the same.

This outline of the theory having been given, we can discuss it in detail under the following heads :

1. A Physical Series. Before we can have a psychophysical series, we must have a physical series. Physical series agree in their ill-defined character. For instance, let us consider a time series. It is impossible to conceive how there could be a commencement to time, or that time. can ever end, or that we can conceive a portion of time, however small, which cannot be subdivided; thus the portion of time which light takes to pass through the space of an inch can be divided into millionths.

Again, let us consider a position series. This may be illustrated with a compass. It is obvious that the circle representing definite positions may be subdivided to any extent. Innumerable degrees can be made between the points of the compass, as one passes by imperceptible gradations into another; thus the space between N. and N.W. could be subdivided any number of times, the circumference being, if necessary, enlarged.

With regard to a heat series, we do not know what is the lowest or highest possible temperature, and it is evident that there are innumerable gradations from one degree to another.

It is the same with a sound series, which appears at first sight to form an exception as far as the indefinite character of the units are concerned. It is evident that we do not know what is the lowest or highest possible number of vibrations which bodies may be put into, but it appears that there are definite units-that is to say, so many vibrations per second. But the second itself is quite an arbitrary standard of time, and it is quite possible, and

appears to me probable, that there are innumerable degrees between, say, 14 vibrations per second and 15 vibrations per second; for instance, 14, 147, 14, etc., vibrations per second. These may exist, but we are not able to perceive them. An illustration will make this clear. It is evident that a second is quite an arbitrary division of time; we might with equal propriety have divided the minute into one hundred, eighty, or fifty equal parts. We can range sounds in a series from those which are produced by 8 vibrations per second, to those which are produced by 36,500 vibrations per second. Let us then change the standard of time, and suppose that there are only 59 seconds in a minute instead of 60, and then estimate the vibrations per second according to this scale of time. It is evident that nearly every one of the units will have fractional vibrations per second. It is probable that in some hundreds of apparently similar sounds that there are not two alike, simply considering the vibrations per second. For instance, supposing we take one hundred sounds all apparently produced by bodies vibrating 75 times to the second, as ascertained by the most accurate apparatus obtainable. There is nothing to show that one. body is not vibrating 751365 times per second, another 75 times per second, and so on.

Then we may have a form series, the units ranging from a perfectly straight line to the greatest possible

curve.

In the same way we may have a weight series. It is impossible to conceive a weight which cannot be diminished, and it is impossible to conceive a weight which could not be increased. Also it is impossible to conceive a unit of weight which could not be subdivided.

It is the same with all other physical stimuli which are capable of giving rise to definite sensations. These

C

may be ranged in series, each of which has no definite commencement, no definite termination, and no definite

unit.

For the purposes of physics, it is necessary to assume a physical unit, though in reality we are not able to define or obtain one. As long as these approximate physical units each contain a similar number of the hypothetical physical units, they will be adequate for purposes of comparison. If we take one tenth of a second as representing an approximate physical time unit, it is evident that we could make a series of an hour which would then consist of 60 x 60 x 10 = 36,000 equal portions, each of which would contain an equal number of the hypothetical time units.

For the purposes of this book, I shall use the term physical unit as meaning the smallest conceivable portion of a physical series.

2. A Psycho-physical Series.-By a psycho-physical series, I mean a physical series as it appears to the mind. A psycho-physical series is a sensation which is referred to external objects. It is obvious that the product of the physical stimulus may be considerably altered before it reaches the mind.

The chief points in which a psycho-physical series differs from a physical series are, that it has a definite commencement, a definite termination, and consists of certain definite units. The limitation of the series is probably due to the external sensory apparatus, and any unit of a physical series not coming within the defined range is not perceived. A high note which is heard distinctly by one person, may be quite inaudible to another, and therefore he can form no opinion respecting its qualities. It is the same with the sense of smell. Professor Ramsay informs me that he has met with many persons who are unable to distinguish

that hydrocyanic acid has any odour whatever, whilst they are able to recognize other odoriferous bodies. It is obvious that if this condition were general, prussic acid would be said to be odourless. Therefore, the definite standard length of a psycho-physical series having been found for the majority of persons, any increase in this length for any individual will be a gain, and any decrease a loss for the person examined. When the psycho-physical series is shortened, the physical stimuli occupying the shortened portion will not be perceived, and the same result will be produced as if the physical stimuli did. not exist.

The psycho-physical perception of colour will be con-sidered in the next chapter. Unfortunately we cannot form series of other physical stimuli in the same way that we can with the rays of light, and therefore the study of the psycho-physical perception of these stimuli is attended with as much difficulty as the study of colour without the aid of the spectrum. Taking, for instance,. odours, we are unable to range these in a series, though. a good deal of light has been thrown upon the subject by Professor Ramsay, who suggests that a series might be formed in accordance with the molecular weight of the odoriferous body.

3. An Absolute Psycho-physical Unit.-The absolute psycho-physical units are the basis of every psycho-physical series. When a person has succeeded in obtaining a match, which to him appears perfect, it is evident that he has brought both stimuli within one of his absolute psychophysical units, because all physical stimuli included in one of these units are regarded as identical. When a violin is tuned to the piano the following takes place. The A string of the violin is tuned until it is vibrating in harmony with a certain A of the piano. When a person