themselves as early as societies take form, and speculation is awakened-and they bring forth quickly the flowers and fruits of music, poetry, the fine arts, logic, mathematics, and those generalities of speculative truth which are the products of imagination and reflection. The correspondence between the figure chosen and the facts to be illustrated would seem to be complete.

In time, the branches nearer to the earth, more material in their substance and more dependent upon observation, obtain development in their larger diversity of use. The sciences of substance, of natural objects, grow and ramify themselves almost indefinitelyphysical philosophy and organology, in their dependencies, shooting out in every direction of observation and experiment, at first overshadowed by the speculative branches above them, but always vivified by them; while in their turn repaying this service by affording substantive strength and corrective modification as they grow into maturity.

Such is the history of science, and such the illustration of its orderly divisions, succession, and co-ordination; it represents the compound nature of man, the sources of his powers, and the order of their development.

§ 4. Man seeks to obtain power over matter, and therefore is it that he desires to obtain a knowledge of the laws that have been instituted for its government. To become the subject of law it is required that there should be a regular and uniform succession of causes and effects, the nature of which may be expressed in several propositions—so that when we observe the former we may be enabled to predict the latter, or when the latter are observed we may safely assume the former to have pre-existed.

In the early ages of society theories abound, and they do so because, in default of knowledge, almost every occurrence is “ regarded as accidental, or is attributed to the direct interposition of mythological powers, whose qualities are so vaguely conceived as to make the idea of the events depending upon their action scarcely one remove from that of its being absolutely fortuitous and irreducible to order and rule”—and thus it was that the Greeks of the days of Homer were seen soliciting the aid of imaginary deities, who were moved to action by the same feelings and passions that influenced their worshippers; precisely as does now the poor Afri

can who makes his oblations of palm-wine or rum, corn or oil, to the stock or stone, the alligator, or the bundle of rags, he has chosen for his idol. With time, however, the regular succession of effects and causes comes to be understood, and with every stage of the progress, theory tends to pass away, yielding place to knowledge-and with the latter comes the power of man to direct the forces of nature to his service. With each such stage he obtains new evidence of the universality of natural lawsnew proof that where exceptions appear to exist they are but appearances and will, when carefully analyzed and fully understood, but prove the rule; as does the smoke when rising in apparent opposition to the great law in virtue of which all the matter of which the earth is composed tends towards its centre.*

To prove the universality of law, and thereby to establish the unity of science, seemed at first to be the intention of M. Comte, from whose work preliminary to, and intended as the basis of, the one that was to be specially devoted to social science, the above extracts have been made. The promised work has since appeared, but in it, as well as in all the parts of his previous one treating of man and his operations, he has intentionally ignored the mathematical method to which the earlier and more developed departments of science had so largely been indebted. That he should so have done would seem to have been a consequence of regarding mathematics as a science, and not as a mere instrument for the acquisition of scientific knowledge. Thus, in treating of chemistry, he tells us that "every attempt to refer chemical questions to mathematical doctrines must be considered, now and always, profoundly irrational, as being contrary to the nature of the phenomena."+ What, however, are those doctrines? Are they anything beyond simple formulæ adapted to the peculiar circumstances of the case under consideration? Certainly not. The geometer tells us that every whole is equal to all its parts, and that things which are

* "We ought to conceive the study of nature as destined to furnish the true rational basis of the action of man upon nature; because the knowledge of the laws of phenomena, of which the invariable result is foresight, and that alone, can conduct us in active life to modify the one by the other to our advantage. In short, SCIENCE WHENCE FORESIGHT, FORESIGHT WHENCE ACTION, Such is the simple formula which expresses the general relation of Science and Art.”— Comte.

† Ibid., vol. i. p. 299.

halves of the same thing are equal, axioms of universal application, and equally true in relation to all bodies, whether those treated by the chemist, the sociologist, or the measurer of land, but involving no question of doctrine whatsoever.

Occasionally, M. Comte speaks of mathematics as what it clearly is, an "instrument of admirable efficacy," but being an instrument it can no more be a science than can a key become a lock. That instrument, the mathematical method, is always applicable, whatever may be the subject of investigation. That method is analysis -the study of each separate cause tending to produce a given effect. To that method we owe all the discoveries of Copernicus, Kepler, Newton, and their successors-but such too is the method of the chemist, who commences by ascertaining the separate force of each of his various ingredients, and ends by deducing the law of the effect. The physiologist analyzes what is known, in hopes to be able to deduce that which remains as yet unknown, and uses always the formulæ belonging to the particular class of subjects of which he treats. When engaged in the study of the skeleton, he uses those of the physicist; but when studying the composition of the blood, he resorts necessarily to those of the chemist, in which is embodied all the knowledge derived from the observation of the philosophers by whom he has been preceded. This method, however, is discarded by M. Comte in treating of social science, as will be seen by the following passage :—

“There can be no scientific study of society, either in its conditions or its movements, if it is separated into portions, and its divisions are studied apart. I have already remarked upon this, in regard to what is called political economy. Materials may be furnished by the observation of different departments; and such observation may be necessary for that object: but it cannot be called science. The methodical division of studies which takes place in the simple inorganic sciences is thoroughly irrational in the recent and complex science of society, and can produce no results. The day may come when some sort of subdivision may be practicable and desirable; but it is impossible for us now to anticipate what the principle of distribution may be; for the principle itself must arise from the development of the science; and

3

that development can take place no otherwise than by our formation of the science as a whole."*

"In the organic sciences, the elements are much better known to us than the whole which they constitute: so that in that case we must proceed from the simple to the compound. But the reverse method is necessary in the study of man and of society; man and society as a whole being better known to us, and more accessible subjects of study, than the parts which constitute them. In exploring the universe, it is as a whole that it is inaccessible to us; whereas, in investigating man or society, our difficulty is in penetrating the details. We have seen, in our survey of biology, that the general idea of animal nature is more distinct to our minds than the simpler notion of vegetable nature; and that man is the biological unity; the idea of man being at once the most compound, and the starting-point of speculation in regard to vital existence. Thus, if we compare the two halves of natural philosophy, we shall find that in the one case it is the last degree of composition, and, in the other, the last degree of simplicity, that is beyond the scope of our research."+

This would seem to be going back to what M. Comte is accustomed to denominate the metaphysical stage of science. The philosopher of old would, in like manner, have said: "These masses of granite are better known to us than the parts of which they are composed, and therefore we will limit our inquiries to the question as to how they came to have their existing form and occupy their present position." Without the analysis of the chemist it would have been as impossible that we should be enabled to "penetrate into the details" of the piece of stone, and thus to acquire a knowledge of the composition of the distant mountain from which it had been taken, as it would now be for us to penetrate into those of the communities that have passed away, were we not in the midst of living ones, composed of men endowed with the same gifts and animated by the same feelings and passions observed to have existed among the men of ancient times; and were we not, too, possessors of the numerous facts accumulated during the many centuries that since have intervened. It is the details of

* Positive Philosophy, Martineau's Translation, vol. ii. p. 81.
† Ibid., vol. ii. p. 82.

life around us that we need to study, commencing by analysis and proceeding to synthesis, as does the chemist when he resolves the piece of granite into atoms, and thus acquires the secret of the composition of the mass. Having ascertained that it is composed of quartz, feldspar, and mica, and having fully satisfied himself of the circumstances under which it appears in the country around him, he feels entire confidence that wherever else it may be found, its composition, and its position in the order of formation, will be the same. He is constantly going from the near and the known, which he can analyze and examine, to the distant and the unknown, which he cannot; studying the latter by means of formulæ obtained by analysis of the former. Thus it was that by study of the deposits of Siberia and California, the geologist was enabled to predict that gold would be found among the mountains of Australia.

If we desire to understand the history of man in past ages, or in distant lands, we must commence by studying him in the present, and having mastered him in the past and present, we may then be enabled to predict the future. To do this, it is required that we should do with society as the chemist does with the piece of granite, resolve it into its several parts and study each part separately, ascertaining how it would act were it left to itself, and comparing what would be its independent action with that we see to be its action in society; and then by help of the same law of which the mathematician, the physicist, the chemist, and the physiologist. avail themselves-that of the composition of forces-we may arrive at the law of the effect. To do this would not, however, be to adopt the course of M. Comte, who gives us the distant and the unknown-the societies of past ages-as a means of understanding the movements of the men by whom we are surrounded, and of predicting what will be those of future men. With great respect for M. Comte, we must say that to pursue this course appears to us to be equivalent to furnishing his readers with a telescope by which to study the mountains of the moon for the purpose of understanding the movements of the laboratory.

The necessary consequence of this inverse and erroneous method is that he is led to arrive at conclusions directly the reverse of those to which men's natural instincts lead them; and directly opposed, too, to the tendencies of thought and action in all the