The nature of a ray of homogeneous light is strictly defined, either by its place in the spectrum or by the corresponding wave-length, but a ray of mixed light admits of no simple classification; any of the infinitely numerous rays of the continuous spectrum may be present or absent, or present in various intensities, so that we can only class and define a mixed colour by defining the intensity and wave-length of each ray of homogeneous light which is present in it. Complete spectroscopic analysis and the determination of the intensity of every part of the spectrum yielded by a mixed ray is requisite for its accurate classification. Nearly the same may be said of complex sounds. A simple sound undulation, if we could meet with such a sound, would admit of precise and exhaustive classification as regards pitch, the length of wave, or the number of waves reaching the ear per second being a sufficient criterion. But almost all ordinary sounds, even those of musical instruments, consist of complex aggregates of undulations of several different pitches, and in order to classify the sound we should have to measure the intensities of each of the constituent sounds, a work which has been partially accomplished by Professor Helmholtz, as regards the vowel sounds. The different tones of voice distinctive of different individuals must also be due to the intermixture of minute waves of various pitch, which are at present quite beyond the range of experimental investigation. We cannot, then, at present, attempt to classify the different kinds or timbres of sound.

The difficulties of classification are even greater when a varying phenomenon cannot be shown to be a mixture of simpler phenomena. If we attempt, for instance, to classify the tastes of natural and artificial substances, we may rudely group them according as they are sweet, bitter, saline, alkaline, acid, astringent, or fiery; but it is evident that these groups are bounded by no sharp lines

of definition. Tastes of mixed or intermediate character may exist almost ad infinitum, and, what is still more troublesome, the tastes clearly united within one class may differ more or less from each other, without our being able to arrange them in subordinate genera and species. The same remarks may be made concerning the classification of odours, which may be roughly grouped according to the arrangement of Linnæus as, Aromatic, Fragrant, Ambrosiac, Alliaceous, Fetid, Virulent, Nauseous. Within each of these vague classes, however, there would be infinite shades of variety, and each class would graduate probably into each other class. The varieties of odour which can be discriminated by an acute olfactory organ are almost infinite; every rock, stone, plant, or animal has some slight odour, and it is well known that dogs, or even blind human beings, can discriminate persons by a slight distinctive odour which usually passes unnoticed.

Nearly similar remarks may be made concerning the higher feelings of the human mind, usually called emotions. We know what is anger, grief, fear, hatred, love; and many systems for classifying these feelings have been proposed at one time or another. They may be roughly distinguished according as they are pleasurable or painful, prospective or retrospective, selfish or sympathetic, active or passive, and possibly in many other ways, but each mode of arrangement will be indefinite and unsatisfactory when followed into details. As a general rule, the emotional state of the mind at any moment will be neither pure anger nor pure fear, nor any one pure feeling, but an indefinite and complex aggregate of feelings. It may be that the state of mind is really a sum of several distinct modes of agitation, just as a mixed colour is the sum of the several distinct rays of the spectrum. In this case there may be more hope of some method of analysis being successfully applied at some future time. But it may

be found that states of mind really graduate into each other, so that rigorous classification would prove to be hopeless.

A little reflection will show that there are whole worlds of existences which in like manner are incapable of logical analysis and classification. One friend may be able to single out and identify another friend by his countenance among a million other countenances. Faces are capable of infinite discrimination, but who shall classify and define them, or say by what particular shades of feature he does judge. There are of course certain distinct types of face, but each type is connected with each other type by infinite intermediate specimens. We may classify melodies according to the major or minor key, the character of the time, and some other distinct points; but every melody has independently of such circumstances its own distinctive character and effect upon the mind. Similar remarks might be made concerning a multitude of other circumstances. We can detect differences between the styles of literary, musical, or artistic compositions. We can even in some cases assign a picture to its painter, or a symphony to its composer, by a subtle feeling of resemblances or differences of character and expression, which may be felt, but cannot be described.

Finally, it is apparent that in human character there is unfathomable and inexhaustible diversity. Every mind is more or less like every other mind; there is always a basis of similarity, but there is a superstructure of feelings, impulses, or motives which is distinctive for each person. We can often, indeed, predict the general character of the feelings or actions which will be produced in a given individual well known to us, by a given external event, but we also know that we are often inexplicably at fault in all our inferences. No one can safely generalize upon. the subtle variations of temper and emotion which may

arise even in a person of ordinary character. As human knowledge and civilization progress, these characteristic differences tend to develop and multiply themselves rather than decrease. Character grows more evidently manysided. Two well educated Englishmen are far better distinguished from each other than two common labourers, and these are better distinguished, again, than two Australian aborigines. Thus the complexities of existing phenomena develop themselves more rapidly than scientific method can overtake them. In spite of all the boasted powers of science, we cannot really apply method to those existences, namely, our own minds and characters, which are more important to us than all the stars and nebulæ.

BOOK VI.

CHAPTER XXXI.

REFLECTIONS ON THE RESULTS AND LIMITS OF

SCIENTIFIC METHOD.

BEFORE Concluding a work on the Principles of Science, it will not be inappropriate to add some remarks upon the limits and ultimate bearings of the knowledge which we may acquire by the constant employment of scientific method. All science consists, it has several times been stated, in the detection of identities and uniformities in the action of natural agents. The purpose of inductive inquiry is to ascertain the apparent existence of necessary connexion between causes and effects, the establishment of natural laws. Now so far as we thus learn the invariable course of nature, the future becomes the necessary sequel of the present, and we are brought beneath the sway of powers with which nothing can interfere.

By degrees it is found, too, that the chemistry of organized substances is not widely separated from, but is rather continuous with, that of earth and stones. Life itself seems to be nothing but a special form of that energy which is manifested in heat and electricity and mechanical force. The time may come, it almost seems,