particular truth can be recognized as a case of the operation of wider laws. This point of progress, at which the study passes from the preliminary state of mere preparation, into a science, cannot be reached by the more complex studies until it has been attained by the simpler ones. A certain regularity of recurrence in the celestial appearances was ascertained empirically before much progress had been made in geometry; but astronomy could no more be a science until geometry was a highly advanced one, than the rule of three could have been practised before addition and subtraction. The truths of the simpler sciences are a part of the laws to which the phaenomena of the more complex sciences conform: and are not only a necessary element in their explanation, but must be so well understood as to be traceable through complex combinations, before the special laws which co-exist and co-operate with them can be brought to light. This is all that M. Comte affirms, and enough for his purpose.[5] He no doubt occasionally indulges in more unqualified expressions than can be completely justified, regarding the logical perfection of the construction of his series, and its exact correspondence with the historical evolution of the sciences; exaggerations confined to language, and which the details of his exposition often correct. But he is sufficiently near the truth, in both respects, for every practical purpose.[6] Minor inaccuracies must often be forgiven even to great thinkers. Mr Spencer, in the very-writings in which he criticises M. Comte, affords signal instances of them.[7]

Combining the doctrines, that every science is in a less advanced state as it occupies a higher place in the ascending scale, and that all the sciences pass through the three stages, theological, metaphysical, and positive, it follows that the more special a science is, the tardier is it in effecting each transition, so that a completely positive state of an earlier science has often coincided with the metaphysical state of the one next to it, and a purely theological state of those further on. This statement correctly represents the general course of the facts, though requiring allowances in the detail. Mathematics, for example, from the very beginning of its cultivation, can hardly at any time have been in the theological state, though exhibiting many traces of the metaphysical. No one, probably, ever believed that the will of a god kept parallel lines from meeting, or made two and two equal to four; or ever prayed to the gods to make the square of the hypothenuse equal to more or less than the sum of the squares of the sides. The most devout believers have recognized in propositions of this description a class of truths independent of the devine omnipotence. Even among the truths which popular philosophy calls by the misleading name of Contingent the few which are at once exact and obvious were probably, from the very first, excepted from the theological explanation. M. Comte observes, after Adam Smith, that we are not told in any age or country of a god of Weight. It was otherwise with Astronomy: the heavenly bodies were believed not merely to be moved by gods, but to be gods themselves: and when this theory was exploded, there movements were explained by metaphysical conceptions; such as a tendency of Nature to perfection, in virtue of which these sublime bodies, being left to themselves, move in the most perfect orbit, the circle. Even Kepler was full of fancies of this description, which only terminated when Newton, by unveiling the real physical laws of the celestial motions, closed the metaphysical period of astronomical science. As M. Comte remarks, our power of foreseeing phaenomena, and our power of controlling them, are the two things which destroy the belief of their being governed by changeable wills. In the case of phaenomena which science has not yet taught us either to foresee or to control, the theological mode of thought has not ceased to operate: men still pray for rain, or for success in war, or to avert a shipwreck or a pestilence, but not to put back the stars in their courses, to abridge the time necessary for a journey, or to arrest the tides. Such vestiges of the primitive mode of thought linger in the more intricate departments of sciences which have attained a high degree of positive development. The metaphysical mode of explanation, being less antagonistic than the theological to the idea of invariable laws, is still slower in being entirely discarded. M. Comte finds remains of it in the sciences which are the most completely positive, with the single exception of astronomy, mathematics itself not being, he thinks, altogether free from them: which is not wonderful, when we see at how very recent a date mathematicians have been able to give the really positive interpretation of their own symbols.[8] We have already however had occasion to notice M. Comte's propensity to use the term metaphysical in cases containing nothing that truly answers to his definition of the word. For instance, he considers chemistry as tainted with the metaphysical mode of thought by the notion of chemical affinity. He thinks that the chemists who said that bodies combine because they have an affinity for each other, believed in a mysterious entity residing in bodies and inducing them to combine. On any other supposition, he thinks the statement could only mean that bodies combine because they combine. But it really meant more. It was the abstract expression of the doctrine, that bodies have an invariable tendency to combine with one thing in preference to another: that the tendencies of different substances to combine are fixed quantities, of which the greater always prevails over the less, so that if A detaches B from C in one case it will do so in every other; which was called having a greater attraction, or, more technically, a greater affinity for it. This was not a metaphysical theory, but a positive generalization, which accounted for a great number of facts, and would have kept its place as a law of nature, had it not been disproved by the discovery of cases in which though A detached B from C in some circumstances, C detached it from A in others, showing the law of elective chemical combination to be a less simple one than had at first been supposed. In this case, therefore, M. Comte made a mistake: and he will be found to have made many similar ones. But in the science next after chemistry, biology, the empty mode of explanation by scholastic entities, such as a plastic force, a vital principle, and the like, has been kept up even to the present day. The German physiology of the school of Oken, notwithstanding his acknowledged genius, is almost as metaphysical as Hegel, and there is in France a quite recent revival of the Animism of Stahl. These metaphysical explanations, besides their inanity, did serious harm, by directing the course of positive scientific inquiry into wrong channels. There was indeed nothing to prevent investigating the mode of action of the supposed plastic or vital force by observation and experiment; but the phrases gave currency and coherence to a false abstraction and generalization, setting inquirers to look out for one cause of complex phaenomena which undoubtedly depended on many.

According to M. Comte, chemistry entered into the positive stage with Lavoisier, in the latter half of the last