1. WE have given the appellation of _Ideas_ to certain comprehensive forms of thought,--as _space_, _number_, _cause_, _composition_, _resemblance_,--which we apply to the phenomena which we contemplate. But the special modifications of these ideas which are {31} exemplified in particular facts, we have termed _Conceptions_; as _a circle_, _a square number_, _an accelerating force_, _a neutral combination_ of elements, a _genus_. Such Conceptions involve in themselves certain necessary and universal relations derived from the Ideas just enumerated; and these relations are an indispensable portion of the texture of our knowledge. But to determine the contents and limits of this portion of our knowledge, requires an examination of the Ideas and Conceptions from which it proceeds. The Conceptions must be, as it were, carefully _unfolded_, so as to bring into clear view the elements of truth with which they are marked from their ideal origin. This is one of the processes by which our knowledge is extended and made more exact; and this I shall describe as the _Explication of Conceptions_. In the several Books of the History of Ideas we have discussed a great many of the Fundamental Ideas of the most important existing sciences. We have, in those Books, abundant exemplifications of the process now under our consideration. We shall here add a few general remarks, suggested by the survey which we have thus made. 2. Such discussions as those in which we have been engaged concerning our fundamental Ideas, have been the course by which, historically speaking, those Conceptions which the existing sciences involve have been rendered so clear as to be fit elements of exact knowledge. Thus, the disputes concerning the various kinds and measures of _Force_ were an important part of the progress of the science of Mechanics. The struggles by which philosophers attained a right general conception of _plane_, of _circular_, of _elliptical Polarization_, were some of the most difficult steps in the modern discoveries of Optics. A Conception of the _Atomic Constitution_ of bodies, such as shall include what we know, and assume nothing more, is even now a matter of conflict among Chemists. The debates by which, in recent times, the Conceptions of _Species_ and _Genera_ have been rendered more exact, have improved the science of Botany: the imperfection of the science of {32} Mineralogy arises in a great measure from the circumstance, that in that subject, the Conception of a _Species_ is not yet fixed. In Physiology, what a vast advance would that philosopher make, who should establish a precise, tenable, and consistent Conception of _Life_!