13. But in order that we may make any real advance in the discovery of truth, our Ideas must not only be clear, they must also be _appropriate_. Each science has for its basis a different class of Ideas; and the steps which constitute the progress of one science can never be made by employing the Ideas of another kind of science. No genuine advance could ever be obtained in Mechanics by applying to the subject the Ideas of Space and Time merely:--no advance in Chemistry, by the use of mere Mechanical Conceptions:--no discovery in Physiology, by referring facts to mere Chemical and Mechanical Principles. Mechanics must involve the Conception of _Force_;--Chemistry, the Conception of _Elementary Composition_;--Physiology, the Conception of _Vital Powers_. Each science must advance by means of its appropriate Conceptions. Each has its own field, which extends as far as its principles can be applied. I have already noted the separation of several of these fields by the divisions of the Books of the _History_ of Ideas. The Mechanical, the Secondary Mechanical, the Chemical, the Classificatory, the Biological Sciences form so many great Provinces in the Kingdom of knowledge, each in a great measure possessing its own peculiar fundamental principles. Every attempt to build up a {43} new science by the application of principles which belong to an old one, will lead to frivolous and barren speculations. This truth has been exemplified in all the instances in which subtle speculative men have failed in their attempts to frame new sciences, and especially in the essays of the ancient schools of philosophy in Greece, as has already been stated in the History of Science. Aristotle and his followers endeavoured in vain to account for the mechanical relation of forces in the lever by applying the _inappropriate_ geometrical conceptions of the properties of the circle:--they speculated to no purpose about the elementary composition of bodies, because they assumed the _inappropriate_ conception of _likeness_ between the elements and the compound, instead of the genuine notion of elements merely _determining_ the qualities of the compound. And in like manner, in modern times, we have seen, in the history of the fundamental ideas of the physiological sciences, how all the _inappropriate_ mechanical and chemical and other ideas which were applied in succession to the subject failed in bringing into view any genuine physiological truth. 14. That the real cause of the failure in the instances above mentioned lay in the _Conceptions_, is plain. It was not ignorance of the facts which in these cases prevented the discovery of the truth. Aristotle was as well acquainted with the fact of the proportion of the weights which balance on a Lever as Archimedes was, although Archimedes alone gave the true mechanical reason for the proportion.